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Electrically programmable magnetoresistance in AlOx-based magnetic tunnel junctions
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120790
title: Electrically programmable magnetoresistance in AlOx-based magnetic tunnel junctions abstract: We report spin-dependent transport properties and I–V hysteresis characteristics in an AlOx-based magnetic tunnel junction (MTJ). The bipolar resistive switching and the magnetoresistances measured at high resistance state (HRS) and low resistance state (LRS) yield four distinctive resistive states in a single device. The temperature dependence of resistance at LRS suggests that the resistive switching is not triggered by the metal filaments within the AlOx layer. The role played by oxygen vacancies in AlOx is the key to determine the resistive state. Our study reveals the possibility of controlling the multiple resistive states in a single AlOx-based MTJ by the interplay of both electric and magnetic fields, thus providing potential applications for future multi-bit memory devices.
<br>The structures and thermoelectric properties of Zn-Sb alloy films fabricated by electron beam evaporation through an ion beam assisted deposition
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120789
title: The structures and thermoelectric properties of Zn-Sb alloy films fabricated by electron beam evaporation through an ion beam assisted deposition abstract: Zn-Sb alloys are potential low-cost and non-toxic p-type thermoelectric materials for applications in the temperature range between 300 and 700 K. In this experiment, Zn-Sb alloy films were prepared by electron beam evaporation through an ion beam assisted deposition (IBAD). Our studies have confirmed that the structural phase, chemical composition, chemical binding, carrier concentration and microstructures of the film can indeed be effectively controlled by the voltage and current of the ion beam. Particularly, the carrier concentration of the film will rise along with the increase of the argon ion beam current. When the ion beam currents are set at 0.2–0.6 A, the carrier concentrations of the films can be controlled at around 1019–1020 cm−3, which fall within the optimal carrier concentration range for Zn-Sb based thermoelectric materials. The temperature dependence of Seebeck coefficient and the electrical conductivity of the films were measured to evaluate their thermoelectric performance. The results indicate that the film with Zn4Sb3 + ZnSb mixed phase will have better thermoelectric properties. A high power factor value of ~1280 μW/m-K2 is obtained in the films assisted by the ion beam current of 0.6 A. Our results demonstrate that the IBAD technique is extraordinary promising to fabricate Zn-Sb films with excellent thermoelectric performance and can be used to produce other potential thermoelectric materials.
<br>Photoelectric properties of Sr2MgSi2O7: Eu2+ phosphors produced by co-precipitation method
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120779
title: Photoelectric properties of Sr2MgSi2O7: Eu2+ phosphors produced by co-precipitation method abstract: Eu2+-doped phosphors Sr2MgSi2O7: xEu2+ (x = 1–5 mol%) with blue color are synthesized by the co-precipitation method. The X-ray diffraction patterns of these phosphors indicate a tetragonal crystal structure. The emission peak centered at 486 nm is attributed to the 4 F7→ 4F65D1 transitions of Eu2+ ions with CIE coordinates of (x = 0.176, y = 0.637). We use Sr2MgSi2O7: 4 mol% Eu2+ phosphors to find latent fingerprints (LFPs) with visible patterns on different surfaces under 337 nm UV light. The results indicate that this phosphor may possess the potential to be used for LFP recognition. Three calculated models mimicking the crystal host, Eu2+ ion-doped phosphor, and Eu2+ ion-doped phosphor with oxygen vacancy are built using CASTEP software to perform density functional theory (DFT) calculations. The geometry optimization results of the Eu2+ doping ion reveal that a coordinate covalent bond is formed by the Eu2+ doping ion with its neighboring oxygen atoms. The oxygen vacancy VO causes obvious changes in the electron orbitals of Si and O atoms as well as the 5d empty orbital of Eu2+ ions.
<br>Synthesis of G-La2Si2O7:Eu2+ phosphors by addition of AlF3: Experimental and theoretical analysis
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120778
title: Synthesis of G-La2Si2O7:Eu2+ phosphors by addition of AlF3: Experimental and theoretical analysis abstract: The Eu2+-doped G-La2Si2O7 phosphor was successfully prepared through the high-temperature solid-state reaction method with the aid of AlF3 flux. The results of Eu L3-edge XANES characterization showed that only Eu3+ can be detected in as-received G-La2Si2O7 phosphor and that Al2O3 addition leads to a partial reduction of Eu3+ to Eu2+, while complete reduction occurs with AlF3 addition. The obtained Eu2+-doped G-La2Si2O7 phosphor exhibited typical Eu2+ blue-green emission under the near-UV light excitation. The analysis of Fourier transform infrared spectroscopy (FT-IR) and 27Al nuclear magnetic resonance (NMR) results suggests that Al occupies the Si sites and F occupies the O sites. The positive influence of Al–F doping is related to the structure of the produced phosphors, which was analyzed with the aid of first-principles density functional calculations. The results of the theoretical calculations are a good match to the experimental findings.
<br>A3BBi(P2O7)2 (A = Rb, Cs; B = Pb, Ba): Isovalent Cation Substitution to Sustain Large Second-Harmonic Generation Responses
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120777
title: A3BBi(P2O7)2 (A = Rb, Cs; B = Pb, Ba): Isovalent Cation Substitution to Sustain Large Second-Harmonic Generation Responses abstract: Exploring novel photoelectric functional materials via chemical substitution-oriented design is an effective strategy, which can be expanded to the discovery of high-performance UV nonlinear optical (NLO) materials. Two new NLO pyrophosphates, Rb3BaBi(P2O7)2 (I) and Cs3BaBi(P2O7)2 (II), are rationally developed by a cation substitution technique based on A3PbBi(P2O7)2 (A = Rb and Cs), of which I inherits the large second-harmonic generation (SHG) response (exptl 2.5 × KDP; calcd 2.9 × KDP) and moderate birefringence (0.025@1064 nm) accompanied by a broadened UV transparent region. Compounds I and II are isomeric and exhibit different Ba–P–O frameworks. Especially, I possesses a large SHG effect benefiting from the favorable pentagonal-net topological structure. Detailed theory calculations elucidate the origin of the linear and nonlinear optical properties of the compounds. The insights obtained from the atomic-level module adjustment involving lone-pair-active optical anisotropy are useful for designing more efficient UV NLO materials.
<br>Finding Optimal Mid-Infrared Nonlinear Optical Materials in Germanates by First-Principles High-Throughput Screening and Experimental Verification
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120776
title: Finding Optimal Mid-Infrared Nonlinear Optical Materials in Germanates by First-Principles High-Throughput Screening and Experimental Verification abstract: Owing to wide infrared (IR) transparency ranges, high laser damage thresholds, and being easy to grow in open air, germanates are emerging as promising mid-infrared (mid-IR) nonlinear optical (NLO) materials. However, the germanates as NLO materials have not been investigated comprehensively and the crystals with large second harmonic generation (SHG) response have not been identified. Herein, we used the first-principles high-throughput screening pipeline for NLO materials to search for excellent NLO crystals from germanates collected in the inorganic crystal structure database. After two steps of screening, three crystals are picked out from 128 structures based on their predicted energy gaps, birefringences, and SHG coefficients. Subsequently, the three germanates are synthesized and measured. The results show that Pb3Ga2Ge4O14 and Ba2TiGe2O8 exhibit a wide energy gap (>3.1 eV) and a strong phase-matchable SHG intensity that are comparable to the benchmark AgGaS2 (0.8 and 1.2 × AgGaS2, respectively). In addition, the statistical analyses of different categories classified according to their cations show that the d0-transition metal and lone pair cations are more conducive to achieving a larger SHG response and birefringence compared to other cations in germanates. It gives a guideline for exploring new mid-IR NLO materials.
<br>A2BBi2(PO4)2(P2O7) (A = K, Rb, B = Pb, Cd): the Effect of Cation Sizes on Structural Evolution
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120775
title: A2BBi2(PO4)2(P2O7) (A = K, Rb, B = Pb, Cd): the Effect of Cation Sizes on Structural Evolution abstract: Two homologous new mixed‐metal phosphates K2PbBi2(PO4)2(P2O7) (I) and Rb2CdBi2(PO4)2(P2O7) (II) were successfully synthesized in A2BBi2(PO4)2(P2O7) (A = K, Rb, B = Pb, Cd) system through the traditional high‐temperature solid‐phase method. The single crystal structures of the two compounds are shown to be the unique three‐dimensional (3D) framework composed of different types of layers, but not isomorphic. We compared series compounds A2PbBi2(PO4)2(P2O7) (A = K, Rb, Cs), which are isomorphic and crystallize in the same space group Pnma. It is noteworthy that they are distinct different in degree of structural disorder, which is tuned by A‐site cations. The effect of A‐site cations is recognized by analyzing the disorder degree in three related structures and other available 182 mixed‐metal phosphates. To the best of our knowledge, such structural analysis is rarely reported in inorganic phosphates and the cation modulation strategy can be used to guide structural disorder according to the difference‐value (D‐value) of cation radii. Furthermore, the syntheses, thermal analysis, relevant spectroscopic measurements and theoretical calculations for I and II compounds were also discussed.
<br>Two Pyrophosphates with Large Birefringences and Second-Harmonic Responses as Ultraviolet Nonlinear Optical Materials
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120774
title: Two Pyrophosphates with Large Birefringences and Second-Harmonic Responses as Ultraviolet Nonlinear Optical Materials abstract: Two new pyrophosphates nonlinear optical (NLO) materials, Rb3PbBi(P2O7)2 (I) and Cs3PbBi(P2O7)2 (II), were successfully designed and synthesized. Both compounds exhibit large NLO effects and birefringences. Material I presents the scarce case of possessing the coexistence of large birefringence (0.031 at 1064 nm and 0.037 at 532 nm) and second harmonic generation (SHG) response (2.8× potassium dihydrogen phosphate (KDP)) in ultraviolet NLO phosphates and its SHG is the largest in the phase‐matching (PM) pyrophosphates. Both I and II have three‐dimensional (3D) crystal structures composed of corner‐shared RbO12 (CsO11), RbO10 (CsO10), BiO6, PbO7 (PbO6) and P2O7 groups, in which P2O7 and PbO7 (PbO6) units form an alveolate [PbPO]∞ skeleton frame. Theoretical calculations reveal that the P−O, Bi−O and Pb−O units are mainly responsible for the moderate birefringence and large SHG efficiency of I.
<br>Different mechanism of response of asymmetric lone pair electrons around ns2 cations to birefringence and second harmonic generation
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120773
title: Different mechanism of response of asymmetric lone pair electrons around ns2 cations to birefringence and second harmonic generation abstract: The 6s2 lone-pair electrons (Pb2+, Bi3+) and 5s2 lone-pair electrons (Sn2+, Sb3+) show different responses to birefringence than they do to second harmonic generation (SHG). In the current work, different mechanisms of birefringence and SHG responses induced by Pb2+/Sn2+ cations were investigated using the first-principles method on AB2O3F2 (A = Ba, Sn, Pb). The obtained birefringence and SHG coefficients were in good agreement with the experimental values. The anisotropic lone-pair electron distribution was found at the states near the Fermi level containing cation sp-oxygen p states. Our analyses showed the birefringences of the AB2O3F2 (A = Ba, Sn, Pb) compounds to be directly affected by the anisotropic lone-pair electron distribution, however, the SHG responses of these three compounds have a more complicated relationship with the hybrid cation-oxygen states. The expanded hybrid cation-oxygen states including the lone-pair states were concluded to endow the PbB2O3F2 compound with a stronger SHG response than those displayed by the other compounds.
<br>First-Principles High-Throughput Screening Pipeline for Nonlinear Optical Materials: Application to Borates
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120772
title: First-Principles High-Throughput Screening Pipeline for Nonlinear Optical Materials: Application to Borates abstract: Discovering new nonlinear optical (NLO) materials that require an optimization between multiple properties is a time-consuming and high-cost process. To speed up material development, a first-principles high-throughput screening pipeline for nonlinear optical materials (FHSP-NLO) that combines density functional theory (DFT) codes, linear and nonlinear optical property calculation codes, and data transformation and extraction codes has been developed for searching promising NLO materials from crystals collected in the Inorganic Crystal Scientific Structure Database (ICSD). The tests for a dozen of well-known NLO crystals covering deep-ultraviolet (DUV), UV, vis–NIR, and middle/far-infrared (M-F-IR) wavelength ranges verify the high-accuracy of FHSP-NLO. Subsequently, nearly 300 noncentrosymmetric borates are tested with FHSP-NLO. The screened deep-ultraviolet (DUV) NLO crystals are fully consistent with previously reported results. Besides, five crystals, whose NLO properties have not been reported, i.e., B2S2O9, Al4B6O15, HP-Na2B4O7, KB(SO3CI)4, and H3BO3-3T, are identified as new promising NLO materials. Two hydrated borates [Ca2B5O9]·[H(OH)2] and Ca(B8O11(OH)4), whose second-harmonic generation (SHG) responses are primarily measured, are screened out and suggested to grow large-size crystals for further evaluation. FHSP-NLO provides a powerful and efficient tool to screen and reduce the total number of experiments necessary for searching NLO materials from reported crystals.
<br>An arm length stabilization system for KAGRA and future gravitational-wave detectors
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120683
title: An arm length stabilization system for KAGRA and future gravitational-wave detectors abstract: Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities. We designed a new type of the ALS, which is compatible with the interferometers having long arms like the next generation GW detectors. The features of the new ALS are that the control configuration is simpler than those of previous ones and that it is not necessary to lay optical fibers for the ALS along the kilometer-long arms of the detector. Along with simulations of its noise performance, an experimental test of the new ALS was performed utilizing a single arm cavity of KAGRA. This paper presents the first results of the test where we demonstrated that lock acquisition of the arm cavity was achieved using the new ALS. We also demonstrated that the root mean square of residual noise was measured to be 8.2 Hz in units of frequency, which is smaller than the linewidth of the arm cavity and thus low enough to lock the full interferometer of KAGRA in a repeatable and reliable manner.
<br>Application of independent component analysis to the iKAGRA data
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120682
title: Application of independent component analysis to the iKAGRA data abstract: We apply independent component analysis (ICA) to real data from a gravitational wave detector for the first time. Specifically, we use the iKAGRA data taken in April 2016, and calculate the correlations between the gravitational wave strain channel and 35 physical environmental channels. Using a couple of seismic channels which are found to be strongly correlated with the strain, we perform ICA. Injecting a sinusoidal continuous signal in the strain channel, we find that ICA recovers correct parameters with enhanced signal-to-noise ratio, which demonstrates the usefulness of this method. Among the two implementations of ICA used here, we find the correlation method yields the optimal results for the case of environmental noise acting on the strain channel linearly.
<br>Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120681
title: Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA abstract: We present our current best estimate of the plausible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next several years, with the intention of providing information to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals for the third (O3), fourth (O4) and fifth observing (O5) runs, including the planned upgrades of the Advanced LIGO and Advanced Virgo detectors. We study the capability of the network to determine the sky location of the source for gravitational-wave signals from the inspiral of binary systems of compact objects, that is binary neutron star, neutron star–black hole, and binary black hole systems. The ability to localize the sources is given as a sky-area probability, luminosity distance, and comoving volume. The median sky localization area (90% credible region) is expected to be a few hundreds of square degrees for all types of binary systems during O3 with the Advanced LIGO and Virgo (HLV) network. The median sky localization area will improve to a few tens of square degrees during O4 with the Advanced LIGO, Virgo, and KAGRA (HLVK) network. During O3, the median localization volume (90% credible region) is expected to be on the order of 105,106,107 Mpc3 for binary neutron star, neutron star–black hole, and binary black hole systems, respectively. The localization volume in O4 is expected to be about a factor two smaller than in O3. We predict a detection count of 1+12−1(10+52−10) for binary neutron star mergers, of 0+19−0(1+91−1) for neutron star–black hole mergers, and 17+22−11(79+89−44) for binary black hole mergers in a one-calendar-year observing run of the HLV network during O3 (HLVK network during O4). We evaluate sensitivity and localization expectations for unmodeled signal searches, including the search for intermediate mass black hole binary mergers.
<br>Electrically programmable magnetoresistance in AlOx‑based magnetic tunnel junctions
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120680
title: Electrically programmable magnetoresistance in AlOx‑based magnetic tunnel junctions abstract: We report spin-dependent transport properties and I–V hysteresis characteristics in an AlOx-based magnetic tunnel junction (MTJ). The bipolar resistive switching and the magnetoresistances measured at high resistance state (HRS) and low resistance state (LRS) yield four distinctive resistive states in a single device. The temperature dependence of resistance at LRS suggests that the resistive switching is not triggered by the metal filaments within the AlOx layer. The role played by oxygen vacancies in AlOx is the key to determine the resistive state. Our study reveals the possibility of controlling the multiple resistive states in a single AlOx-based MTJ by the interplay of both electric and magnetic fields, thus providing potential applications for future multi-bit memory devices.
<br>Electromagnetic coupling effects in natural inflation
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120661
title: Electromagnetic coupling effects in natural inflation abstract: In this work we study the effects of the electromagnetic coupling in natural inflation in a systematic manner using the Schwinger–Keldysh formalism. The corresponding influence functional is evaluated in the one-loop level. It can be interpreted as due to a single stochastic force. The equation of motion of the inflaton field is therefore given in the form of a Langevin equation. Lastly, the two-point and the three-point correlation functions of the inflaton field are worked out. They are related to the power spectrum and the nongaussianity of the inflaton field, respectively.
<br>A new (original) set of quasinormal modes in spherically symmetric AdS black hole spacetimes
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120660
title: A new (original) set of quasinormal modes in spherically symmetric AdS black hole spacetimes abstract: From black hole perturbation theory, quasi-normal modes (QNMs) in spherically symmetric AdS black hole spacetimes are usually studied with the Horowitz and Hubeny methods [1] by imposing the Dirichlet or vanishing energy flux boundary conditions. This method was constructed using the scalar perturbation case and box-like effective potentials, where the radial equation tends to go to infinity when the radial coordinate approaches infinity. These QNMs can be realized as a different set of solutions from those obtained by the barrier-like effective potentials. However, in some cases the existence of barrier-like effective potentials in AdS black hole spacetimes can be found. In these cases this means that we would obtain a new (original) set of QNMs by the purely ingoing and purely outgoing boundary conditions when the radial coordinate goes to the event horizon and infinity, respectively. Obtaining this set of QNMs in AdS black hole cases is the main focus of this paper.
<br>Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120601
title: Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement abstract: An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.
<br>Quantum enhancement of sensitivity achieved by photon-number-resolving detection in the dark port of a two-path interferometer operating at high intensities
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120600
title: Quantum enhancement of sensitivity achieved by photon-number-resolving detection in the dark port of a two-path interferometer operating at high intensities abstract: It is shown that the maximal phase sensitivity of a two-path interferometer with high-intensity coherent light and squeezed vacuum in the input ports can be achieved by photon-number-resolving detection of only a small number of photons in a dark output port. It is then possible to achieve the quantum Cramér-Rao bound of the two-path interferometer using only the field displacement dependence of the photon number statistics in the single mode output of the dark port represented by a field-displaced squeezed vacuum state. We find that, at small field displacements, it is not sufficient to use the average photon number as the estimator, indicating that an optimal phase estimation depends critically on measurements of the precise photon number. We therefore analyze the effect of detection efficiency on the Fisher information and show that there is a transition from low robustness against photon losses associated with quantum interference effects at low field displacements to high robustness against photon losses at high field displacements. The transition between the two regimes occurs at field shifts proportional to the third power of the squeezing factor, indicating that squeezing greatly enhances the phase interval in which quantum effects are relevant in optimal phase estimations using photon resolving detectors. The case under study could thus be understood as a “missing link” between genuine multiphoton interference and the straightforward suppression of noise usually associated with squeezed light.
<br>Derivation of the statistics of quantum measurements from the action of unitary dynamics
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120599
title: Derivation of the statistics of quantum measurements from the action of unitary dynamics abstract: Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states is an eigenstate of energy E and the other represents an observable B . In this paper, we investigate this relation between the observable time evolution of quantum systems and the coherence of Hilbert space products in detail. It is shown that the times of arrival for a specific value of B observed with states that have finite energy uncertainties can be used to derive the Hilbert space product between eigenstates of energy E and eigenstates of the dynamical variable B . Quantum phases and interference effects appear in the form of an action that relates energy to time in the experimentally observable dynamics of localized states. We illustrate the relation between quantum coherence and dynamics by applying our analysis to several examples from quantum optics, demonstrating the possibility of explaining non-classical statistics in terms of the energy-time relations that characterize the corresponding transformation dynamics of quantum systems.
<br>Evaluation of bipartite entanglement between two optical multi-mode systems using mode translation symmetry
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120598
title: Evaluation of bipartite entanglement between two optical multi-mode systems using mode translation symmetry abstract: Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M-mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.
<br>Quantum effects in the interference of photon number states
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120597
title: Quantum effects in the interference of photon number states abstract: Multiphoton interference results in modulations of output probabilities with phase shift periods that are much shorter than 2π. Here, we investigate the physics behind these statistical patterns in the case of well-defined photon numbers in the input and output modes of a two-path interferometer. We show that the periodicity of the multiphoton interference is related to the weak value of the unobserved intensity difference between the two arms of the interferometer. This means that the operator relations between the photon number differences in input, path, and output can be used to determine the periodicity of the experimentally observed quantum interference, establishing an important link between the classical causality of random phase interference and quantum effects that depend on the superposition of classically distinct possibilities.
<br>Determining X-chains in graph states
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120596
title: Determining X-chains in graph states abstract: The representation of graph states in the X-basis as well as the calculation of graph state overlaps can efficiently be performed by using the concept of X-chains (Wu et al 2015 Phys. Rev. A 92 012322). We present a necessary and sufficient criterion for X-chains and show that they can efficiently be determined by the Bareiss algorithm. An analytical approach for searching X-chain groups of a graph state is proposed. Furthermore we generalize the concept of X-chains to so-called Euler chains, whose induced subgraphs are Eulerian. This approach helps to determine if a given vertex set is an X-chain and we show how Euler chains can be used in the construction of multipartite Bell inequalities for graph states.
<br>Group structures and representations of graph states
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120595
title: Group structures and representations of graph states abstract: A special configuration of graph state stabilizers, which contains only Pauli σX operators, is studied. The vertex sets ξ associated with such configurations are defined as what we call X chains of graph states. The X chains of a general graph state can be determined efficiently. They form a group structure such that one can obtain the explicit representation of graph states in the X basis via the so-called X-chain factorization diagram. We show that graph states with different X-chain groups can have different probability distributions of X-measurement outcomes, which allows one to distinguish certain graph states with X measurements. We provide an approach to find the Schmidt decomposition of graph states in the X basis. The existence of X chains in a subsystem facilitates error correction in the entanglement localization of graph states. In all of these applications, the difficulty of the task decreases with increasing number of X chains. Furthermore, we show that the overlap of two graph states can be efficiently determined via X chains, while its computational complexity with other known methods increases exponentially.
<br>Randomized graph states and their entanglement properties
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120594
title: Randomized graph states and their entanglement properties abstract: We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of these states by investigating both bipartite and genuine multipartite entanglement. Bipartite entanglement is studied via the concepts of connectedness and persistency, which are related to measurement based quantum computation. The presence of multipartite entanglement is instead revealed by the use of witness operators which are subsequently adapted to study nonlocal properties through the violation of suitable Bell inequalities. We also present results on the entanglement detection of particular randomized graph states, by deriving explicit thresholds for entanglement and nonlocality in terms of the noise parameter that characterizes the controlled-Z gates exploited for their generation. Finally, we propose a method to further improve the detection of genuine multipartite entanglement in this class of states.
<br>Direct and efficient verification of entanglement between two multimode–multiphoton systems
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120593
title: Direct and efficient verification of entanglement between two multimode–multiphoton systems abstract: Linear-optic photonic networks with multiple single-photon inputs are attracting attention due to their great potential for quantum computation, quantum communication, and quantum sensing. They are also essential for verifying quantum advantages via boson sampling schemes. The quantum coherence of generated multimode–multiphoton states is crucial for various applications. However, the coherence is invisible in the normally obtained photon number distributions, which strictly limits the efficiency of entanglement verification between multimode–multiphoton systems since the required resources for quantum state tomography increase exponentially as the number of photons/modes increases. In this paper, we report the experimental demonstration of direct and efficient verification of entanglement between two multimode–multiphoton systems (one photon in three modes and two photons in three modes) using just two sets of classical correlation tables with and without a discrete Fourier transformation of the optical modes, clearly demonstrating a dramatic reduction in the resources required for entanglement verification. Our experimental demonstration paves the way to understanding the coherence and entanglement of multi-partite systems, not only for photons but for other quantum resources with high-dimensional degrees of freedom.
<br>Complementary properties of multiphoton quantum states in linear optics networks
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120592
title: Complementary properties of multiphoton quantum states in linear optics networks abstract: We have developed a theory for accessing quantum coherences in mutually unbiased bases associated with generalized Pauli operators in multiphoton multimode linear optics networks (LONs). We show a way to construct complementary Pauli measurements in multiphoton LONs and establish a theory for evaluation of their photonic measurement statistics without dealing with the computational complexity of Boson samplings. This theory extends characterization of complementary properties in single-photon LONs to multiphoton LONs employing convex-roof extension. It allows us to detect quantum properties such as entanglement using complementary Pauli measurements, which reveals the physical significance of entanglement between modes in bipartite multiphoton LONs.
<br>Determining lower bounds on a measure of multipartite entanglement from few local observables
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120591
title: Determining lower bounds on a measure of multipartite entanglement from few local observables abstract: We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore, we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases, we show that only a few local measurements are necessary to determine these lower bounds.
<br>Surface Electronic Structure Reconfiguration of Hematite Nanorods for Efficient Photoanodic Water Oxidation
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120503
title: Surface Electronic Structure Reconfiguration of Hematite Nanorods for Efficient Photoanodic Water Oxidation abstract: Hematite (α‐Fe2O3) is a promising candidate as a semiconducting photoanode for photoelectrochemical (PEC) water splitting. However, its PEC performance is much limited by the sluggish charge transfer kinetics at the α‐Fe2O3/electrolyte interface. Herein, an insulative metal oxide, hafnium dioxide (HfO2), is deposited on the surface of α‐Fe2O3 to engineer the photoelectrode/electrolyte interfacial electronic structure. With the conformal HfO2 overlayer coating, the surface defects of α‐Fe2O3 are effectively passivated, whereas the charge migration from α‐Fe2O3 to the electrolyte is blocked by the continuous HfO2 overlayer, leading to a moderate PEC enhancement. In contrast, with HfO2 nanoparticles deposited, the photogenerated holes are not only effectively extracted from the bulk of α‐Fe2O3 but are also promptly injected into the electrolyte for water oxidation, due to the reconfigurated surface electronic structure. Consequently, the HfO2 nanoparticles‐decorated α‐Fe2O3 photoanode achieves an onset potential cathodic shift by 180 mV and a 460% photocurrent density enhancement, reaching up to 1.20 mA cm−2 at 1.23 V versus reversible hydrogen electrode as compared with pristine α‐Fe2O3. An alternative approach to engineer the photoelectrode/electrolyte interfacial electronic structure to improve the PEC performance for water splitting is demonstrated herein.
<br>Polyacrylate grafted graphene oxide nanocomposites for biomedical applications
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120502
title: Polyacrylate grafted graphene oxide nanocomposites for biomedical applications abstract: Utilizing a reverse micelle process, we have grafted polyacrylate (P) on graphene oxide (GO) to realize polyacrylate grafted graphene oxide (P-GO) nanocomposites, upon whose subsequent reduction, polyacrylate grafted reduced graphene oxide (P-rGO) nanocomposites are achieved. Using techniques such as ultraviolet photoelectron spectroscopy (UPS), x-ray photoelectron spectroscopy, and x-ray absorption near edge structure (XANES) spectroscopy, in conjunction with high-resolution microscopy, Raman spectroscopy, and superconducting quantum interference device analysis, we have studied in depth the electronic, microstructural, electrical, and magnetic properties of these P-GO and P-rGO nanocomposites. While polyacrylate grafting ensures a high solubility of P-GO and P-rGO, the P-rGO nanocomposites additionally show a near doubling of the paramagnetic response (9.6 × 10−3 emu/g) as compared to the r-GO (5.6 × 10−3 emu/g) and P-GO (5.5 × 10−3 emu/g), respectively, at 2 K. The grafting of diamagnetic polyacrylate enhances the magnetic response for the P-GO and P-rGO owing to the increase in the defect states, sp3-type bonding, and enhanced magnetic coupling between the magnetic moments arising due to the presence of nitrogen functionalities. This behavior is further corroborated via the measurements of the electronic structure by XANES and UPS measurements. Thus, the possibility of manipulation of the magnetic behavior along with the abundance of surface functional groups makes both P-GO and P-rGO nanocomposites highly conducive for deriving water-soluble functionalized graphene by linking affinity molecules with polyacrylate backbone for biological and biomedical applications.
<br>Effect of Fe2O3 coating on ZnO nanowires in photoelectrochemical water splitting: A synchrotron x-ray spectroscopic and spectromicroscopic investigation
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120501
title: Effect of Fe2O3 coating on ZnO nanowires in photoelectrochemical water splitting: A synchrotron x-ray spectroscopic and spectromicroscopic investigation abstract: An array of ZnO/Fe2O3 core-shell nanowires (NW) for the highly efficient absorption of light and carrier collection is developed for use in photoelectrochemical (PEC) water-splitting. The oriented NW architecture favors physical matching, providing a direct electron conduction pathway and reducing the diffusion length of photogenerated holes. This work involves a combination of spectral imaging, spectromicroscopy and in situ x-ray absorption spectroscopy; spectra are obtained under operando conditions. Direct investigation of oriented nanowires using polarization-dependent x-ray spectromicroscopy enables the determination of the relationship between anisotropic electronic orbitals and charge carrier water-splitting efficiency. The results of O K-edge STXM demonstrated that the ZnO/Fe2O3 core-shell NW exhibits strong anisotropy and thus provides higher electron-hole transport efficiency than bare ZnO. In situ XAS revealed that interfacial charge transfer between Fe 3d and Zn 4p states enhances the photoelectrochemical reaction in the ZnO/Fe2O3 core-shell NW. The photogenerated electrons of Fe2O3 are transferred from Fe 3d states to the Zn 4p state under photoelectrochemical conditions.
<br>Microstructure and electronic properties of ultra-nano-crystalline-diamond thin films
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120500
title: Microstructure and electronic properties of ultra-nano-crystalline-diamond thin films abstract: Ultra-nano-crystalline diamond (UNCD) thin films with average thickness ∼200 nm, were grown on n-type mirror polished silicon (100) substrates using microwave plasma enhanced chemical vapour deposition system in different gas (H2 - N2 - Ar - CH4) composition plasma atmospheres at 1200 W (2.45 GHz) and in a pressure of 120 Torr with plasma-temperature ∼475 °C. Raman spectroscopy was used for microstructural study and nano-indentation was used for Hardness/Young’s modulus study; whereas X-ray absorption near edge structure, X-ray photoelectron and ultraviolet photoemission spectroscopies were used for electronic structure of UNCD thin films. The hardness of the films is found to be ∼30 GPa, Young’s modulus ∼300 GPa and induced electron field emission, the turn on electric field, ETOE = 11 V/μm. All results show that the UNCD could be useful for different industrial semiconductor/optoelectronic devices and as flexible materials for thin film coating technology.
<br>Tuning the electronic and magnetic properties of PEDOT-PSS-coated graphene oxide nanocomposites for biomedical applications
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120499
title: Tuning the electronic and magnetic properties of PEDOT-PSS-coated graphene oxide nanocomposites for biomedical applications abstract: We have synthesized graphene oxide (GO) using Hummer's method which was subsequently reduced (rGO) by hydrazine hydrate. The synthesized GO was coated with poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT-PSS) conducting polymer (CP) to obtain CP-GO which was also further reduced using hydrazine hydrate to form CP-rGO. Scanning electron microscopy, Raman spectroscopy, X-ray diffraction, ultraviolet photoelectron spectroscopy, and X-ray photoelectron spectroscopy, X-ray absorption near-edge structure (XANES) techniques were used to study the electronic and structural properties of GO, rGO, CP-GO, and CP-rGO nanocomposites for biomedical applications. The superconducting quantum interference device method was used to investigate the magnetic properties of the nanocomposites. The electrical conductivity of the CP-GO nanocomposites was found to be ~104 times higher than that of GO due to an increase in sp2 content and subsequent decrease in oxygen functional groups. In rGO, we observed an improved paramagnetic saturation magnetization of approximately 5.6 × 0−3 emu/g at 2 K. The electronic and magnetic behavior of PEDOT-PSS-coated nanocomposites, as a result, were successfully tuned for potential biological and biomedical applications.
<br>FeMo sub-nanoclusters/single atoms for neutral ammonia electrosynthesis
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120498
title: FeMo sub-nanoclusters/single atoms for neutral ammonia electrosynthesis abstract: Electrochemical N2 reduction reaction (NRR) has long been regarded as a promising process to generate NH3 under ambient conditions. Therefore, developing cost-effective and high-performance non-noble-metal catalysts for NRR is highly desirable. Inspired by the biological nitrogenase structure, we here designed and synthesized a catalyst with iron-molybdenum sub-nanoclusters and single atoms on porous nitrogen-doped carbon (FeMo/NC). The catalyst features porous structure beneficial to active site exposure and accessibility to electrolyte as well as FeMo sub-nanoclusters and single atoms enabling to activate N2 molecular. In situ near-ambient pressure X-ray photoelectron spectroscopy tests reveal that during the process from vacuum to nitrogen saturation, N2 was close to, adsorbed on and interacted with Fe and Mo in FeMo/NC. The Fe and Mo through electron transfer play a key role in activating the N2 molecules. Therefore, when tested for NRR, FeMo/NC achieves the maximum Faradaic efficiency (FE) of 11.8 ± 0.8% at −0.25 V and NH3 yield rate of 26.5 ± 0.8 μg h−1 mgcat.−1 at −0.3 V in neutral electrolyte. Moreover, the catalyst exhibits ignorable variations in the FE and a slight decrease in current density for 100,000 s. This work develops a non-precious bimetallic electrocatalyst with synergetic effect capability for efficient NH3 production and provides a guideline for the design of efficient and robust catalysts with coexistence of sub-nanoclusters and single atoms.
<br>Correlation among photoluminescence and the electronic and atomic structures of Sr2SiO4:xEu3+ phosphors: X-ray absorption and emission studies
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120497
title: Correlation among photoluminescence and the electronic and atomic structures of Sr2SiO4:xEu3+ phosphors: X-ray absorption and emission studies abstract: A series of Eu3+-activated strontium silicate phosphors, Sr2SiO4:xEu3+ (SSO:xEu3+, x = 1.0, 2.0 and 5.0%), were synthesized by a sol–gel method, and their crystalline structures, photoluminescence (PL) behaviors, electronic/atomic structures and bandgap properties were studied. The correlation among these characteristics was further established. X-ray powder diffraction analysis revealed the formation of mixed orthorhombic α'-SSO and monoclinic β-SSO phases of the SSO:xEu3+ phosphors. When SSO:xEu3+ phosphors are excited under ultraviolet (UV) light (λ = 250 nm, ~ 4.96 eV), they emit yellow (~ 590 nm), orange (~ 613 nm) and red (~ 652 and 703 nm) PL bands. These PL emissions typically correspond to 4f–4f electronic transitions that involve the multiple excited 5D0 → 7FJ levels (J = 1, 2, 3 and 4) of Eu3+ activators in the host matrix. This mechanism of PL in the SSO:xEu3+ phosphors is strongly related to the local electronic/atomic structures of the Eu3+–O2− associations and the bandgap of the host lattice, as verified by Sr K-edge and Eu L3-edge X-ray absorption near-edge structure (XANES)/extended X-ray absorption fine structure, O K-edge XANES and Kα X-ray emission spectroscopy. In the synthesis of SSO:xEu3+ phosphors, interstitial Eu2O3-like structures are observed in the host matrix that act as donors, providing electrons that are nonradiatively transferred from the Eu 5d and/or O 2p–Eu 4f/5d states (mostly the O 2p–Eu 5d states) to the 5D0 levels, facilitating the recombination of electrons that have transitioned from the 5D0 level to the 7FJ level in the bandgap. This mechanism is primarily responsible for the enhancement of PL emissions in the SSO:xEu3+ phosphors. This PL-related behavior indicates that SSO:xEu3+ phosphors are good light-conversion phosphor candidates for use in near-UV chips and can be very effective in UV-based light-emitting diodes.
<br>Structural, electronic, and electrical behaviour of MWCNTs: TiO2 (:SiO2) nanocomposites
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120496
title: Structural, electronic, and electrical behaviour of MWCNTs: TiO2 (:SiO2) nanocomposites abstract: We have functionalized multiwall carbon nanotubes (MWCNTs) with the composition of SiO2 and TiO2 (MWCNTs:TiO2:SiO2) at different Ti:Si stoichiometric ratios (Ti:Si ≈ 6:6 at% and ≈10:10 at%) using the hydrothermal process. The micro-structural, electronic and electrical properties of the unfunctionalized and functionalized MWCNTs were studied. Changes in surface morphology, degree of hybridization, crystallite structure and bonding structure due to functionalization were studied using field-emission scanning electron microscopy, Raman spectroscopy, x-ray diffraction, x-ray photoemission spectroscopy (XPS) and x-ray absorption near edge structure (XANES) spectroscopy techniques. Memristive and charge storage properties for MWCNTs:TiO2:SiO2 nanocomposites (NCs) are more pronounced on NCs functionalised with high stoichiometric ratio (Ti:Si ≈ 10:10) due to the contribution of Ti3+ and Si 2p core states as indicated by XPS and XANES results. The tunability of electrical conductivity is shown by an increase in the measured current and semiconducting I–V behaviour of the material as a result of high content of Ti-charge transfer. These observed changes in the electrical behaviour and electronic/bonding structure of the NCs indicate that the material could be useful for electrical/electronic applications and photocatalytic activity.
<br>Mechanical property of a three-dimensional freely rotating chain -- A Monte Carlo approach
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120128
title: Mechanical property of a three-dimensional freely rotating chain -- A Monte Carlo approach abstract: Free rotating chain (FRC) is a well-known model of polymer but the knowledge to its mechanical property is yet incomplete. This work uses Monte Carlo simulation to evaluate the relation between force and extension, the specific heat, the stretching strength and the fourth-order cumulants of the order parameter of a three-dimensional (3D) FRC. We simplify some expressions to calculate the thermodynamical quantities. Our results reveal that at low force, the behavior of the mechanical property of the model is the same as that of a free jointed chain (FJC) in both two-dimensional (2D) and 3D cases. But beginning from a moderate force, the two models have different mechanical properties. Moreover, we find that a 3D FRC has essential different mechanical property from its 2D counterpart, because the extension of a stretched 2D FRC can subject to a first order transition when the bond angle is large enough, but there is no such a transition for a 3D chain despite its stretching strength exhibits a peaks at large bond angle. Our findings reveal that the space constraint on a stretched polymer favors a sharp change in its size.
<br>Bistability induced by a spontaneous twisting rate for a two-dimensional intrinsically curved filament
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/120127
title: Bistability induced by a spontaneous twisting rate for a two-dimensional intrinsically curved filament abstract: We find that a moderate intrinsic twisting rate (ITR) can induce a bistable state for a force-free two-dimensional intrinsically curved filament. There are two different configurations of equal energy in a bistable state so that the filament is clearly different from its three-dimensional counterpart. The smaller the ITR or the larger the intrinsic curvature (IC), the clearer the distinction between two isoenergetic configurations and the longer the filament. In bistable states, the relationship between length and ITR is approximately a hyperbola and relationship between IC and critical ITR is approximately linear. Thermal fluctuation can result in a shift between two isoenergetic configurations, but large bending and twisting rigidities can prevent the shift and maintain the filament in one of these two configurations. Moreover, a filament can have a metastable state and at a finite temperature such a filament has the similar property as that of a filament with bistable state.
<br>Partitioning interatomic force constants for first-principles phonon calculations: applications to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/119943
title: Partitioning interatomic force constants for first-principles phonon calculations: applications to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene abstract: First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell can be introduced in both methods. Unless the supercell is large enough, the interpolated phonon property highly depends on the shape and size of the supercell and the imposed periodicity could give unphysical results that can be easily overlooked. Along this line, we discuss how a traditional method can be used to partition the force constants at the supercell boundary and then propose a more flexible method based on the translational symmetry and interatomic distances. The partition method is also compatible with the mixed-space approach for describing LO–TO splitting. We have applied the proposed partition method to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene, where we show how the method can deliver reasonable results. The proper partition is especially important for studying moderate-size systems with low symmetry, such as two-dimensional materials on substrates, and useful for the implementation of phonon calculations in first-principles packages using atomic basis functions, where symmetry operations are usually not applied owing to the suitability for large-scale calculations.
<br>Atomistic Full-quantum and Full-band Transport Model for Zigzag Group-IVA Nanoribbon-based Structures with Noniterative Calculation Framework
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/119632
title: Atomistic Full-quantum and Full-band Transport Model for Zigzag Group-IVA Nanoribbon-based Structures with Noniterative Calculation Framework abstract: In this paper, we expand our previous paper [Mod. Phys. Lett. B 32 (2018) 1750355] from the calculation of planar graphene with one band (pz) to the calculation of two-dimensional buckled group-IVA materials with multiple bands (S, px, py, and pz); thus, the proposed method is a fullband model. Furthermore, the proposed method is established using a nonequilibrium Green's function (NEGF) method in association with the complex energy-band technique, so it is in the full-quantum framework. Unlike other methods, the proposed method is noniterative and thus computationally cost-efficient.
<br>Partitioning interatomic force constants for first-principles phonon calculations: applications to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene
http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/119524
title: Partitioning interatomic force constants for first-principles phonon calculations: applications to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene abstract: First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell can be introduced in both methods. Unless the supercell is large enough, the interpolated phonon property highly depends on the shape and size of the supercell and the imposed periodicity could give unphysical results that can be easily overlooked. Along this line, we discuss how a traditional method can be used to partition the force constants at the supercell boundary and then propose a more flexible method based on the translational symmetry and interatomic distances. The partition method is also compatible with the mixed-space approach for describing LO–TO splitting. We have applied the proposed partition method to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene, where we show how the method can deliver reasonable results. The proper partition is especially important for studying moderate-size systems with low symmetry, such as two-dimensional materials on substrates, and useful for the implementation of phonon calculations in first-principles packages using atomic basis functions, where symmetry operations are usually not applied owing to the suitability for large-scale calculations.
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