Phonon Velocity Research Articles

AICON: A program for calculating thermal conductivity quickly and accurately

AICON (Ab Initio Conductivities) is a program written in Python for computing lattice thermal conductivity of crystalline bulk materials using the modified Debye–Callaway model. Building upon the traditional Debye–Callaway theory, the modified model obtains the lattice thermal conductivity by averaging the contributions from acoustic and optical branches based on their specific heat. The only inputs of this program are the phonon spectrum, phonon velocity and Grüneisen parameter, all of which can be calculated using third-party ab initio packages, making the method fully parameter-free. This leads to a fast and accurate evaluation and enables high-throughput calculations of lattice thermal conductivity even in large and complex systems. In addition, this program calculates the specific heat and phonon relaxation times for different scattering processes, which will be beneficial for understanding the phonon transfer behavior. Program summaryProgram Title: AICONProgram Files doi:http://dx.doi.org/10.17632/s9b8y8t92c.1Licensing provisions: GNU General public license 3Programming language: Python3External routines/libraries: Numpy, Scipy, spglib, pymatgenNature of problem: The calculation of lattice thermal conductivity from first principles with an anharmonic approximation requires a large number of calculations to construct the third-order force constants matrix, which could be prohibitively long time.Solution method: Modified Debye–Callaway model, where only the phonon spectrum, phonon velocity and Grüneisen parameter are needed. The acoustic branch and optic branch are both considered to obtain the final lattice thermal conductivity.

Large Thermal Conductivity Drops in the Diamondoid Lattice of CuFeS2 by Discordant Atom Doping.

Doping in a lattice refers to the introduction of very small quantities of foreign atoms and has a generally small effect on decreasing the lattice thermal conductivity, unlike alloying which involves large fractions of other elements and strongly enhances point defect phonon scattering. Here, we report that, by alloying only 3% of In on the Cu sites of the diamond-like lattice of CuFeS2 chalcopyrite compound (Cu1-xInxFeS2, x = 0.03) has a disproportionally large effect in reducing the lattice thermal conductivity of the compound from 2.32 to 1.36 Wm-1K-1 at 630 K. We find that In is not fully ionized to +3 when on the Cu sublattice and exists mainly in the +1 oxidation state. The 5s2 lone pair of electrons of In+ makes this atom incompatible (referred to as discordant) with the tetrahedral geometry of the crystallographic site. This causes strong local bond distortions thereby softening the In-S and Cu-S chemical bonds and introducing localized low frequency vibrations. The latter couple with the base phonon frequencies of the CuFeS2 matrix enhancing the anharmonicity and decreasing the phonon velocity, and consequently the lattice thermal conductivity. The control material in which the In doping is on the Fe3+ site of the structure at the same doping level (and found in the site-compatible In3+ state), has a far smaller effect on the phonon scattering.

Temperature behavior of long-wave acoustic phonons in relaxor ferroelectric Na1/2Bi1/2TiO3

This work presents the results of study of the behavior of longitudinal (LA), quasilongitudinal (QLA), and transverse (TA) acoustic phonons in single crystals of Na1/2Bi1/2TiO3 (NBT) within a temperature range from 110 K to 850 K. Measurements were carried out by means of Brillouin light scattering on phonons with a wave vector qph || [100], qph || [010], and qph || [110], regarding the cubic phase of NBT. Temperature dependences of sound velocity, attenuation, and intensity of LA, QLA, and TA phonons have been plotted. Anomalies in the behavior of sound velocity and attenuation of LA phonons in the vicinity of antiferrodistortive structural phase transition from the cubic to the tetragonal phases have been found. It is shown that broad anomalies in the sound velocity and attenuation of acoustic phonons typical to diffuse phase transition are not connected directly with the anomaly in the dielectric permittivity of the crystal. Elastic C11 and C44 modules in the cubic phase of NBT have been defined.

N-Type TaCoSn-Based Half-Heuslers as Promising Thermoelectric Materials.

Half-Heusler compounds are recognized as promising thermoelectric materials for high-temperature power generation, but their relatively high lattice thermal conductivity impedes further improvement of ZT. Here, we report the synthesis of a new half-Heusler compound TaCoSn with a low thermal conductivity. Experimentally, the pristine TaCoSn exhibits a low lattice thermal conductivity of ∼5.7 W m-1 K-1 at 300 K, which is lower than that of most of the other half-Heusler compounds. Phonon calculations by density functional theory indicate that the low phonon velocity, small Debye temperature, and large Grüneisen parameter are the contributors to the low thermal conductivity of TaCoSn. Importantly, intense point-defect scattering can be induced by alloying Nb at the Ta site, which further suppresses the thermal conductivity of TaCoSn. Additionally, Sb has been identified as an efficient dopant for supplying high electron concentration. Finally, the optimized n-type Ta0.6Nb0.4CoSn0.94Sb0.06 demonstrates a peak ZT above 0.7 at 973 K. Our work demonstrates that the TaCoSn-based half-Heuslers are promising thermoelectric materials.

Mechanical properties of amorphous PEI, PES, and PVC up to 11 GPa studied by Brillouin light scattering

We applied high-pressure Brillouin light spectroscopy to study the mechanical properties of representative amorphous polymers: polyetherimide (PEI), polyethersulfone (PES), and unplasticized polyvinylchloride (PVC). The pressure dependence of optical and elastic properties such as refractive indices and acoustic phonon velocities was obtained by employing both a forward, symmetric scattering and a backscattering geometry up to ~11 GPa. While PEI and PES showed longitudinal and transverse acoustic phonon modes simultaneously at above a certain pressure, PVC showed only one longitudinal acoustic phonon mode, which limited the access to further information. For PEI, PES, and PVC films, we successfully calculated pressure-dependent Poisson's ratios, bulk moduli, shear moduli, Young's moduli, and density-pressure isotherms. Furthermore, by using the Lorentz-Lorenz equation, we corroborated the conventional assumption that the mean polarizability of polymeric materials is nearly constant even when pressure is applied.

Thermalization and possible signatures of quantum chaos in complex crystalline materials

Analyses of thermal diffusivity data on complex insulators and on strongly correlated electron systems hosted in similar complex crystal structures suggest that quantum chaos is a good description for thermalization processes in these systems, particularly in the high-temperature regime where the many phonon bands and their interactions dominate the thermal transport. Here we observe that for these systems diffusive thermal transport is controlled by a universal Planckian timescale [Formula: see text] and a unique velocity [Formula: see text] Specifically, [Formula: see text] for complex insulators, and [Formula: see text] in the presence of strongly correlated itinerant electrons ([Formula: see text] and [Formula: see text] are the phonon and electron velocities, respectively). For the complex correlated electron systems we further show that charge diffusivity, while also reaching the Planckian relaxation bound, is largely dominated by the Fermi velocity of the electrons, hence suggesting that it is only the thermal (energy) diffusivity that describes chaos diffusivity.

Layer-Dependent Coherent Acoustic Phonons in Two-Dimensional Ruddlesden-Popper Perovskite Crystals.

By combining femtosecond transient reflectance (TR) spectroscopy and density functional theory (DFT) calculations, we reveal the impact of the length of the organic linkers (HOC2H4NH3+ and C6H5C2H4NH3+) and the number of inorganic layers (n = 1-3) on the hot carrier relaxation dynamics and coherent acoustic phonons in 2D Ruddlesden-Popper (RP) perovskites. We find that the interplay between the hot carriers and the coherent longitudinal acoustic phonons (CLAPs) can extend the oscillation of the TR kinetics to nanoseconds, which could lead to the higher thermal conductivities of 2D RP perovskites. Moreover, we find that the frequency of the acoustic phonon oscillation and phonon velocity decreases with the increasing number of layers due to the increased mass of the inorganic layers and reduced electron-phonon coupling. This finding provides new physical insights into how the organic spacers and number of inorganic layers control the overall carrier dynamics of 2D perovskite materials.

Ultralow Thermal Conductivity and High-Temperature Thermoelectric Performance in n-Type K2.5Bi8.5Se14

We studied the narrow band-gap (0.55 eV) semiconductor K2.5Bi8.5Se14 as a potential thermoelectric material for power generation. Samples of polycrystalline K2.5Bi8.5Se14 prepared by spark plasma sintering exhibit exceptionally low lattice thermal conductivities (κlat) of 0.57–0.33 W m–1 K–1 in the temperature range of 300–873 K. The physical origin of such low κlat in K2.5Bi8.5Se14 is related to the strong anharmonicity and low phonon velocity caused by its complex low symmetry, large unit cell crystal structure, and mixed occupancy of Bi and K atoms in the lattice. High-resolution scanning transmission electron microscopy studies and microanalysis indicate that the K2.5Bi8.5Se14 sample is a single phase without intergrowth of the structurally related K2Bi8Se13 phase. The undoped material exhibits an n-type character and a figure-of-merit (ZT) value of 0.67 at 873 K. Electronic band structure calculations indicate that K2.5Bi8.5Se14 is an indirect band-gap semiconductor with multiple conduction bands clo...

Phonon Engineering to Modify Acoustic Phonon Velocity in Hexagonal Layered Superlattices

This letter presents the possibility of using the effective medium model coupled with the piezoelectric stiffening to quantitatively explain and engineer acoustic phonons as a heat dissipation channel in GaN-based devices. These effects will be described for a GaN/AlN superlattice that exhibits enhanced acoustic phonon velocities as compared with bulk GaN. We numerically calculate the stiffened elastic constant values and apply them within the effective medium model for elastic constants. With the recent advances in epitaxial GaN growth technology, it may be possible to consider this phonon engineering option to investigate the effect on the longitudinal sound velocity to increase the rate of heat transport in GaN/AlN superlattice.

Slow sound in matter-wave dark soliton gases

We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton "gas" that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter wave phononics, in analogy with the electric induced transparency (EIT) effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to $\sim 5$ $\mu$m/s, $\sim 10^3$ times lower than the condensate sound speed. This is a record value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of "stopped-sound" based quantum information protocols.

Dramatically reduced lattice thermal conductivity of Mg2Si thermoelectric material from nanotwinning

Tuning phonon transport to reduce the lattice thermal conductivity (κL) is crucial for advancing thermoelectrics (TEs). Traditional strategies on κL reduction focus on introducing scattering sources such as point defects, dislocations, and grain boundaries, that may degrade the electrical conductivity and Seebeck coefficient. We suggest here, a novel twin boundary (TB) strategy that can decrease the κL of Mg2Si by ∼90%, but which may not degrade the electrical properties significantly. We validate this suggestion using density functional theory (DFT). We attribute the mechanism of TB induced κL reduction to (i) the lower phonon velocities and larger Grüneisen parameter, (ii) “rattling” of the MgMg pair induced soft acoustic and optical modes, (iii) shorter phonon lifetime and higher phonon scattering rate. We predict that the size of nanotwinned structure should be controlled between 3 nm and 100 nm in the Mg2Si matrix for the most effective κL reduction. These results should be applicable for other TE or non TE energy materials with desired low thermal conductivity, suggesting rational designs of high-performance Mg2Si TE materials with low κL for the energy conversion applications.

Designing high-performance thermoelectrics in two-dimensional tetradymites

The search for new thermoelectric materials has been of great interest in recent years because thermoelectrics offers useful applications in next-generation vehicles that can directly convert waste heat to electricity. Two-dimensional (2D) tetradymites with M2X3 compounds, in which M (Bi) and X (Te, Se, S) are a group-V metal and group-VI anion, respectivety, are theoretically investigated in this study. Their energy bands are characterized by small energy gaps, high group velocities, small effective masses, nonparabolic bands and multi-valleys convergence at near the center of the Brillouin zone, which are favorable conditions for high power factor with the optimum power factor values can be up to 0.20–0.25 W/mK2 at room temperature. Moreover, the 2D M2X3 contains heavy atomic masses and high polarizability of some chemical bonds, leading to small group velocities of phonons and anharmonic phonon behavior that produce an intrinsic lattice thermal conductivity as low as ∼1.5–2.0 W/mK at room temperature. We find that by mixtures of M and X atoms, such as Bi2Te2Se, the power factor further increases whereas the lattice thermal conductivity decreases. This design gives a high figure of merit of the p-type 2D Bi2Te2Se from 1.4 to 2.0 at operating temperature within 300−500 K.

Elastic constants of single-crystal Pt measured up to 20 GPa based on inelastic X-ray scattering: Implication for the establishment of an equation of state

Phonon velocities and densities for Pt were measured based on inelastic X-ray scattering from ambient pressure to 20GPa in order to independently determine its equation of state (EOS). Phonon velocities were determined with sine dispersion relations. Cij values were obtained by fitting phonon velocities and densities to the Christoffel equation. We found that the obtained Cijs were in good agreement with previously reported Cijs at ambient condition. Based on the Cij values in various conditions, experimental pressures were calculated. The EOS of Pt as a primary pressure scale was determined based on the experimental pressures. We report K’=5.17 with fixed KT=274.1GPa and V0=60.360 Å3 for Vinet EOS. Our scale is in good agreement with several previously published scales based on shock experiments and XRD.

Thermoelectric Material SnPb2Bi2S6: The 4,4L Member of Lillianite Homologous Series with Low Lattice Thermal Conductivity.

Although the binary sulfides Bi2S3, PbS, and SnS have attracted extensive interest as thermoelectric materials, no quaternary sulfides containing Sn/Pb/Bi/S elements have been reported. Herein, we report the synthesis of a new quaternary sulfide, SnPb2Bi2S6, which crystallizes in the orthorhombic space group Pnma with unit cell parameters of a = 20.5458(12) Å, b = 4.0925(4) Å, c = 13.3219(10) Å. SnPb2Bi2S6 has a lillianite-type crystal structure consisting of two alternately aligned NaCl-type structural motifs separated by a mirror plane of PbS7 monocapped trigonal prisms. In the lillianite homologous series, SnPb2Bi2S6 can be classified as 4,4L, where the superscripted numbers indicate the maximum numbers of edge-sharing octahedra in the two adjacent NaCl-shaped slabs along the diagonal direction. The obtained SnPb2Bi2S6 phase exhibited good thermal stability up to 1000 K and n-type degenerate semiconducting behavior, with a power factor of 3.7 μW cm-1 K-2 at 773 K. Notably, this compound exhibited a very low lattice thermal conductivity of 0.69-0.92 W m-1 K-1 at 300-1000 K. Theoretical calculations revealed that the low thermal conductivity is caused by the complex crystal structure and the related elastic properties of a low Debye temperature, low phonon velocity, and large Grüneisen parameters. A reasonable figure of merit (ZT) of ∼0.3 was obtained at 770 K.

High Thermoelectric Performance in the Wide Band‐Gap AgGa1‐xTe2 Compounds: Directional Negative Thermal Expansion and Intrinsically Low Thermal Conductivity

AbstractA deficiency of Ga in wide band‐gap AgGa1‐xTe2 semiconductors (1.2 eV) can be used to optimize the electrical transport properties and reduce the thermal conductivity to achieve ZT > 1 at 873 K. First‐principles density functional theory calculations and a Boson peak observed in the low temperature heat capacity data indicate the presence of strong coupling between optical phonons with low frequency and heat carrying acoustical phonons, resulting in a depressed maximum of Debye frequency in the first Brillouin zone and low phonon velocities. Moreover, the AgTe bond lengths and TeAgTe bond angles increase with rising temperature, leading to a significant distortion of the [AgTe4]7− tetrahedra, but an almost unmodified [GaTe4]5− tetrahedra. This behavior results in lattice expansion in the ab‐plane and contraction along the c‐axis, corresponding to the positive and negative Gruneisen parameters in the phonon spectral calculations. This effect gives rise to the large anharmonic behavior of the lattice. These factors together with the low frequency vibrations of Ag and Te atoms in the structure lead to an ultralow thermal conductivity of 0.18 W m−1 K−1 at 873 K.

Electron Scattering via Interface Optical Phonons with High Group Velocity in Wurtzite GaN-based Quantum Well Heterostructure

Here we present a detailed theoretical analysis of the interaction between electrons and optical phonons of interface and confined modes in a wurtzite AlN/GaN/AlN quantum well heterostructure based on the uniaxial dielectric continuum model. The formalism describing the interface and confined mode optical phonon dispersion relation, electron–phonon scattering rates, and average group velocity of emitted optical phonons are developed and numerically calculated. The dispersion relation of the interface phonons shows a convergence to the resonant phonon frequencies 577.8 and 832.3 cm−1 with a steep slope around the zone center indicating a large group velocity. At the onset of interface phonon emission, the average group velocity is small due to the large contribution of interface and confined mode phonons with close-to-zero group velocity, but eventually increases up to larger values than the bulk GaN acoustic phonon velocity along the wurtzite crystal c-axis (8 nm/ps). By adjusting the GaN thickness in the double heterostructure, the average group velocity can be engineered to become larger than the velocity of acoustic phonons at a specific electron energy. This suggests that the high group velocity interface mode optical phonons can be exploited to remove heat more effectively and reduce junction temperatures in GaN-based heterostructures.

Determination of the lattice thermal conductivity of the TiO2 polymorphs rutile and anatase by molecular dynamics simulation

In this study, the structure of the lattice thermal conductivity of two TiO2 polymorphs, namely rutile and anatase, is determined by using equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism. The most reliable potential parameters are used to describe the interatomic potentials. The results are investigated over a wide temperature range, from 200 to 800 K, with a 100 K temperature step. As titanium dioxide is an anisotropic material, all of the parameters are investigated in both the a- and c-directions. The raw data for the heat current autocorrelation function is analysed to determine the structure of the lattice thermal conductivity. It is revealed that the lattice thermal conductivity of the TiO2 polymorphs can be decomposed into three contributions due to the acoustic short-range and long-range phonon and optical phonon modes. These three contributions can be presented in the form of simple kinetic formulae consisting of the products of the heat capacity, the square of the average phonon velocity and the average relaxation time of the acoustic short- and long-range phonon and optical phonon modes. In particular, it is shown that the average phonon velocities of the acoustic short- and long-range phonon and optical phonon modes are approximately equal to each other and can be expressed through the second-order fluctuations of the heat current vector. The effects of different simulation cell sizes at different temperatures on the lattice thermal conductivity are also investigated. Finally, the results from this work are compared with the experimental data and good agreement is found.

Theoretical predicted high-thermal-conductivity cubic Si3N4 and Ge3N4: promising substrate materials for high-power electronic devices

Ceramic substrates play key roles in power electronic device technology through dissipating heat, wherein both high thermal conductivity and mechanical strength are required. The increased power of new devices has led to the replacement of Al2O3 by high thermal conducting AlN and further β-Si3N4 based substrates. However, the low mechanical strength and/or anisotropic mechanical/thermal properties are still the bottlenecks for the practical applications of these materials in high power electronic devices. Herein, using a combination of density functional theory and modified Debye-Callaway model, two new promising substrate materials γ-Si3N4 and γ-Ge3N4 are predicted. Our results demonstrate for the first time that both compounds exhibit higher room temperature thermal conductivity but less anisotropy in expansion and heat conduction compared to β-Si3N4. The mechanism underpins the high RT κ is identified as relatively small anharmonicity, high phonon velocity and frequency. The suitability of these two nitrides as substrate materials was also discussed.

Commensurate lattice constant dependent thermal conductivity of misoriented bilayer graphene

Misorientation of two layers of bilayer graphene leaves distinct signatures in the electronic properties and the phonon modes. The effect on the thermal conductivity has received the least attention and is the least well understood. In this work, the in-plane thermal conductivity of misoriented bilayer graphene (m-BLG) is investigated as a function of temperature and interlayer misorientation angle using nonequilibrium molecular dynamics (NEMD). The central result is that the calculated thermal conductivities decrease approximately linearly with the increasing lattice constant of the commensurate m-BLG unit cell. Comparisons of the phonon dispersions show that misorientation has negligible affect on the low-energy phonon frequencies and velocities. However, the larger periodicity of m-BLG reduces the Brillouin zone size to the extent that the zone edge acoustic phonons are thermally populated. This allows Umklapp scattering to reduce the lifetimes of the phonons contributing to the thermal transport, and consequently, to reduce the thermal conductivity. This explanation is supported by direct calculation of reduced phonon lifetimes in m-BLG based on density functional theory (DFT).

Evaluating the Relationship between Phonon and Thermal Properties of Group IV Alloys Using Molecular Dynamics Simulation

Introduction Group IV alloy semiconductor material is anticipated to be used for the miniaturized thermoelectric (TE) energy harvester, because it has high TE properties, which is called ZT (= S 2 σTκ -1), is related to the Seebeck coefficient S, the electrical conductivity σ, the thermal conductivity κ, and the temperature T. In the previous study, it was indicated the drastically low thermal conductivity in group IV alloy is mainly caused by the mass disorder scattering of phonon [1]. The low thermal conductivity of group IV alloy was reproduced by our molecular dynamics (MD) simulations [2]. In classical MD simulation, it was considered the difference of the atomic mass and the interatomic potentials. Both mass and potential disorder scattering of phonon is deeply linked with the decreasing thermal conductivity. In this study, we quantitatively investigated which disorder is more affected to thermal conductivity in the group IV alloys whose atomic mass and interatomic potentials were varied independently by MD simulations to clarify. Simulation Procedure The models in MD simulation were 28Si x 73Si(1−x), 28Si x 119Si(1−x), 28Si x 28Ge(1−x), 28Si x 28Sn(1−x), 28Si x 73Ge(1−x), and 28Si x 119Sn(1−x) wire with periodic boundary condition. The initial model length and the one side width of square were 30ai and 4ai Å, respectively. The employed interatomic potential is the Stillinger-Weber (SW) potential, which is defined by the sum of two- and three-body potential energy terms that depend on local geometric positions. This potential was optimized to reproduce the lattice constant and the phonon frequencies in the group IV alloy [2]. The thermal conductivity was calculated by equilibrium MD method. The phonon related properties were conducted from the Fourier analysis. Results and Discussion Fig. 1 shows 28Si concentration dependences of thermal conductivities. Red lines represent results of 28Si x 73Si(1−x) and 28Si x 119Si(1−x) alloys, purple lines represent results of 28Si x 28Ge(1−x) and 28Si x 28Sn(1−x) alloys, blue lines represent results of 28Si x 73Ge(1−x), and orange lines represent calculation results from the research of Khatami et al. [1]. Fig. 2 shows the phonon dispersion of 28Si0.5 73Si0.5, 28Si0.5 28Ge0.5, and 28Si0.5 73Ge0.5 alloys. The changing of the thermal conductivities and the phonon dispersion is caused by mass and potential disorders. The amount of the changing by potential disorder is smaller than that of mass disorder. Fig. 3 shows frequency spectra of vibration density of states (VDOS) and phonon lifetimes in 28Si0.5 73Si0.5, 28Si0.5 28Ge0.5, and 28Si0.5 73Ge0.5 alloys. The VDOS D(ω) is closely related to the phonon lifetime due to alloying τalloy, which is defined as τalloy -1(ω) = (π/6)V 0Γalloy D(ω)ω 2, where V 0 is volume per atom, Γalloy is scattering strength due to the mass and potential disorders, and ω is phonon frequencies. The phonon lifetime in 28Si0.5 28Ge0.5 is almost ten times than that of 28Si0.5 73Si0.5 and 28Si0.5 73Ge0.5. The thermal conductivity is defined as κ(ω) = (1/3)C(ω)v 2(ω)τall(ω), and the phonon lifetime is defined as τall -1(ω) = τpure -1(ω) + τalloy -1(ω) = τpure -1(ω) + τmass -1(ω) + τforce -1(ω), where C is heat capacity, v is phonon velocity, τpure is phonon lifetime in pure crystal, τmass is mass disorder phonon lifetime, and τforce is potential disorder phonon lifetime [1]. When we assumed Cv 2 = 100, τpure = 1, τmass = 1/100, and τforce = 1/10, the thermal conductivity scattered by only potential disorder is 9.09, that scattered by only mass disorder is 0.99, and that scattered by both mass and potential disorder is 0.90. This tendency is agree to the results of MD calculation. The mass disorder is dominant factor for the changing of the thermal and phonon properties. Moreover, the potential disorder is ignorable in phonon and thermal calculation by MD method. Acknowledgements This study was partially supported by the Japan Science and Technology Agency’s (JST) CREST program (JPMJCR15Q7) and the Japan Society for the Promotion of Science (JSAP) through a Grant-in-Aid for JSPS Fellows (15J07583).