A pointlike defect in a uniform current-carrying conductor induces a dipole in the electrochemical potential, which counteracts the original transport field. If the mean free path of the carriers is much smaller than the size of the defect, then the dipole results from the purely diffusive motion of the carriers around the defect. In the opposite limit, ballistic carriers scatter from the defect—for this situation, Landauer postulated the emergence of residual resistivity dipoles that are independent of the defect size and thus impose a fundamental limit on the resistance of the parent conductor. Here, we study resistivity dipoles around holes of different sizes in two-dimensional Bi films on Si(111). Using scanning tunneling potentiometry to image the dipoles, we find a crossover from linear to constant scaling behavior of their amplitudes with defect size, manifesting the transition from diffusive to Landauer dipoles. The extracted parameters of the transition allow us to estimate the Fermi wave vector and the carrier mean free path in our Bi films.

An excitonic insulator represents a quantum phase in which spontaneous condensation of excitons leads to novel many-body phenomena. ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ (TNSe), a layered narrow-gap semiconductor, has emerged as a model platform to probe these correlated excitonic phases and their underlying dynamics below 327 K. In this work, we investigate the nonequilibrium dynamics of TNSe using temperature-dependent, nondegenerate optical pump-probe spectroscopy with a 3.14 eV pump and a 1.57 eV probe, extending the accessible pump-probe delay window up to 500 ps. In addition to the well-established subpicosecond relaxation channel ($\sim 0.7-0.9$ ps) associated with carrier cooling and recombination, accompanied by exciton reformation, we uncover a much slower recovery process with a decay time of $\sim 280-600$ ps, significantly longer than previously reported. We attribute this unusually prolonged recovery to enhanced scattering between excitons and nonequilibrium phonons, which delays the reestablishment of equilibrium excitonic correlations. On top of this biexponential background, we observe two coherent phonon modes at 1.0 and 2.9 THz with distinctly different coupling behaviors. The 1.0 THz mode exhibits an order-parameter-like temperature dependence, consistent with strong coupling to the excitonic condensate in TNSe. In contrast, the 2.9 THz mode does not exhibit any discernible coupling to the excitonic order parameter, and appears to arise from anharmonic lattice dynamics associated with the structural phase transition. Together, these results elucidate the hierarchy of relaxation pathways in TNSe and highlight the importance of extending the temporal detection window in pump-probe measurements to fully capture long-lived exciton-phonon dynamics.

Fe-based superconductors are derived from metallic parent compounds with nematic and stripe magnetic orders, which lead to two types of magnetic domains. Recently, it was found that ${\mathrm{K}}_5{\mathrm{Fe}}_4{\mathrm{Ag}}_6{\mathrm{Te}}_{10}$ (KFAT), an Fe-based semiconductor, exhibits similar nematic and stripe magnetic orders, and is thus an analog to the Fe-based superconductors in the limit of localized electrons. In this work, the superstructure and magnetic domains of KFAT are elucidated by fully mapping the reciprocal space using time-of-flight single crystal neutron diffraction. In KFAT, Fe and Ag atoms order to form a $\sqrt{5}\times \sqrt{5}$ superstructure containing $2\times 2$ Fe blocks, which leads to two superstructure domains with identical main Bragg peaks but distinct superstructure peaks. Below $T_{\mathrm{N}}\approx 35\mathrm{K}$, magnetic and nematic orders break in-plane rotational symmetry of the tetragonal $\sqrt{5}\times \sqrt{5}$ superstructure, and further give rise to two magnetic domains. These four equally populated domains account for the complex scattering pattern observed in our time-of-flight elastic neutron scattering measurements. Using polarized neutron scattering, we demonstrate a prominent spin anisotropy with an easy-plane spanned by the $c$ axis and the intrablock antiferromagnetic Fe-Fe bond direction. Such an anisotropy at $\mathbf{q}\ne 0$ persists well above $T_{\mathrm{N}}$, accounts for the in-plane $\mathbf{q}=0$ magnetic anisotropy observed in uniaxial-strained KFAT, and offers an indicator for discovering similar piezomagnetic effects in other materials.

Quantum spin liquids (QSLs) are magnetic phases that evade long-range order down to the lowest temperatures due to strong quantum fluctuations. Their lack of conventional order parameters, however, makes experimental identification challenging. In this work, we investigate how distinct QSL phases affect phonon dynamics through spinon-phonon coupling. By computing the phonon self-energy, we show that the phonon spectrum remains unrenormalized by spinon interactions, while sound attenuation exhibit distinct signatures of the underlying QSL phase. Furthermore, the phonon thermal conductivity generally exhibits a linear-in-temperature dependence at low temperatures, in stark contrast to the $T^2$ behavior expected when the scattering is due to ordinary electrons. These response functions therefore provide experimentally accessible fingerprints for distinguishing different QSL backgrounds. Remarkably, we find that a chiral QSL coupled to phonons does not generate a phonon thermal Hall effect despite explicitly breaking time-reversal symmetry. Our results establish phonon transport as a potential probe for identifying and characterizing quantum spin liquids.

Altermagnets, collinear antiferromagnets with vanishing net magnetization yet momentum-dependent spin splitting, open a new route to topology and strong correlations. In this work, we propose a general framework to construct nearly topological flat-band (TFB) models in $d$-wave altermagnets via stacking bilayer Chern insulators with spin flip and intralayer rotation. This framework is concretely realized on altermagnetic checkerboard and Lieb lattices. By tuning hopping parameters, we obtain TFBs with a flatness ratio exceeding 10, whose topology is fully captured by the spin Chern number. These altermagnetic TFB models support a stable fractional quantum spin Hall state, thereby realizing the coexistence of altermagnetic symmetry and topological order. Our work not only provides a unified scheme for constructing altermagnetic TFB models but also establishes a platform for exploring fractionalization in altermagnetic materials.

Simultaneous control over the directionality and spin of light at the nanoscale is a central goal in nanophotonics with applications ranging from quantum information to advanced biosensing. We introduce the concept of the Circular Huygens dipole and numerically demonstrate its realization in a single Si nanocuboid. We show that the polarization of an incident linear wave controls the interference between colocated circular electric and magnetic dipoles excited in phase quadrature. This enables deterministic switching of the forward-scattered radiation between purely right- and left-circularly polarized states. The system also functions as a directional spin-to-linear polarization converter. Our findings establish a robust, passive method for reconfigurable spin-directional control in a simple, monolithic silicon nanostructure, opening avenues for chip-scale spin optics, chiral quantum interfaces, and novel sensing platforms.

Surface charge transfer doping (SCTD) preserves the pristine crystal structure and allows precise tuning of the doping level, making it a promising strategy for modulating the properties of low-dimensional materials. In this work, we investigate the effect of surface ${\mathrm{MoO}}_3$ molecular doping on the thermal transport properties of monolayer ${\mathrm{MoS}}_2$. Density functional theory calculations reveal that surface-adsorbed ${\mathrm{MoO}}_3$ enables the injection of holes ($0.331\mathrm{e}{\mathrm{molecule}}^{-1}$) into monolayer ${\mathrm{MoS}}_2$, providing $p$-type doping. The charge transfer also leads to strong adsorption of the ${\mathrm{MoO}}_3$ molecule on the ${\mathrm{MoS}}_2$, with adsorption energies below –1.85 eV. Based on a developed neuroevolution potential and homogeneous nonequilibrium molecular dynamics simulations, we demonstrate that ${\mathrm{MoO}}_3$ adsorption significantly reduces the lattice thermal conductivity (LTC) of monolayer ${\mathrm{MoS}}_2$. At 300 K, the LTC decreases from $163.9\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ in pristine ${\mathrm{MoS}}_2$ to $47.3\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at a doping level of $1.82\times {10}^{13}\mathrm{molecule}{\mathrm{cm}}^{-2}$. The LTC is further reduced to $28.3\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ when the concentration of ${\mathrm{MoO}}_3$ increases to 7.29×${10}^{13}\mathrm{molecule}{\mathrm{cm}}^{-2}$. The introduction of surface ${\mathrm{MoO}}_3$ dopants generates resonant flat bands at various frequencies in the phonon dispersion curves. These resonant modes interact with propagating modes in ${\mathrm{MoS}}_2$, which not only reduce phonon group velocities but also enhance phonon–phonon scattering by increasing the number of scattering channels. The resonant effect is particularly pronounced in the low-frequency regime, where the phonon mean free path is reduced by more than one order of magnitude when the doping concentration exceeds 1.82×${10}^{13}\mathrm{molecule}{\mathrm{cm}}^{-2}$. This work demonstrates that SCTD not only enables efficient carrier modulation in 2D semiconductors but also provides precise control over thermal transport through the phonon resonance effect, offering a strategy for the design of high-performance 2D thermoelectric materials.

The lowest-energy exciton in some two-dimensional (2D) materials can be optically dark owing to spin, momentum, or spatial-symmetry selection rules, which suppresses its direct radiative recombination. Controlling the relative energy ordering of bright and dark states in the exciton spectrum is therefore important for engineering the direct optical response of 2D materials. In this work, using the α/β structural difference and Janus Si/Ge substitution as two theoretical symmetry-breaking design dimensions, we construct 2D α- and β-phase CSiN and their Janus derivative CSiGeN. Their electronic structures and excitonic properties are then systematically studied using the $\mathit{GW}$-BSE method within many-body perturbation theory. The results reveal that the lowest singlet exciton in α-CSiN is optically dark because of spatial-symmetry selection rules. The built-in electric field induced by the Janus configuration modifies the momentum-space distribution and relative energies of low-energy singlet excitons. The structural change from the α to the β phase alters the relative energy ordering of low-energy dark and bright singlet excitons, making an optically allowed state the lowest-energy state in the singlet exciton spectrum. The two mechanisms act synergistically in β-CSiGeN, making the lowest singlet exciton, dominated by transitions near the $M$ point, optically bright. This singlet exciton has an exciton binding energy of 1.03 eV and an intrinsic radiative lifetime of 0.50 ps. This study clarifies the independent and synergistic roles of the structural phase transition and the built-in electric field induced by the Janus configuration in controlling the energy-level ordering of bright and dark singlet excitons, providing a theoretical basis for tuning radiative transitions and luminescent properties in low-dimensional materials through the relative energy reordering of bright and dark excitons.

We extend the equation of state and phase stability of body-centered cubic (bcc) antimony (Sb) into the multimegabar regime using both first-principles calculations up to 436 GPa and experimental synchrotron x-ray diffraction in the diamond-anvil cell up to 258(6) GPa using Ne as a soft pressure-transmitting medium. We observe the complete sequence of pressure-induced phase transitions from Sb's A7 rhombohedral phase through the intermediate pressure incommensurate structures, including evidence for Sb-IV, and identify the onset of the bcc phase between 28.9(5) and 30.3(6) GPa. The high-pressure volumetric response of the bcc phase was fit to a third-order Vinet equation of state with parameters of $V_0=26.28\left(32\right){\AA }^3/\mathrm{atom}, K_0=66.50\left(47\right)\mathrm{GPa}$, and $K^{\prime }=4.97\left(2\right)$. Density-functional theory confirms the stability and characterizes the elastic properties of bcc Sb up to 436 GPa. A Comparison with bcc As and Bi highlights the systematic trends in compressibility and electronic structure across these group-15 elements.

Hidden altermagnetism was theoretically proposed and then experimentally confirmed in the metal ${\mathrm{Cs}}_{1-\delta }{\mathrm{V}}_2{\mathrm{Te}}_2\mathrm{O}$, which exhibits two nearly degenerate ground-state magnetic configurations ($C$ type and $G$ type), corresponding, respectively, to apparent and hidden altermagnetism. Here, we propose that in-plane uniaxial strain can be utilized to distinguish apparent and hidden altermagnetism. Under uniaxial strain, apparent altermagnetism exhibits an obvious net magnetic moment, whereas hidden altermagnetism maintains zero net magnetic moment. The magnetic moment induced by uniaxial strain here, namely, the piezomagnetic effect, differs from that in semiconductors, where strain must be applied first, followed by carrier doping, to generate net magnetism. First-principles calculations verify our proposal, revealing that the magnetic moment induced by uniaxial strain in $C$-type antiferromagnetic ${\mathrm{CsV}}_2{\mathrm{Te}}_2\mathrm{O}$ is much larger than that in previously studied altermagnetic semiconductors. Furthermore, we also investigate the electronic state transitions of semiconductors featuring a crystal structure analogous to ${\mathrm{CsV}}_2{\mathrm{Te}}_2\mathrm{O}$ under uniaxial strain and verify our proposal for specific materials via first-principles calculations. Upon application of uniaxial strain, $C$-type ${\mathrm{CsV}}_2{\mathrm{Te}}_2\mathrm{O}$ exhibits the anomalous Hall effect via the piezomagnetic effect, while $G$-type ${\mathrm{CsV}}_2{\mathrm{Te}}_2\mathrm{O}$ shows no anomalous Hall response. Our work provides an experimentally feasible strategy to distinguish apparent and hidden altermagnetism in the ${\mathrm{CsV}}_2{\mathrm{Te}}_2\mathrm{O}$ family.

Silver niobate is a conventional perovskite oxide compound, known to exhibit a rich polymorphism. Although often classified as antiferroelectric, its low-temperature structure remains unclear. Here, first-principles calculations reveal a previously overlooked and unusual rhombohedral ferroelectric phase with $R3$ symmetry that emerges as the thermodynamic ground state despite its almost degenerate energy and close energetic competition with previously proposed structures. Remarkably, this phase is structurally chiral, with chirality emerging improperly from the coupling between polarization and in-phase rotations of the oxygen octahedra along [111], producing a ferrichiral state with incomplete cancellation of local chiral motifs. As a consequence, the phase exhibits significant natural optical activity comparable to that of quartz. Although energetically favored, its experimental observation may be hindered by kinetic limitations, potentially contributing to the ongoing controversy surrounding the low-temperature structure of silver niobate.

We report a comprehensive study of single-crystal ${\mathrm{BaNd}}_2{\mathrm{PdS}}_5$, a Shastry-Sutherland lattice (SSL) antiferromagnet. Thermodynamic and magnetization measurements identify an AFM transition at $T_N\approx 3.6\mathrm{K}$. The ${\mathrm{Nd}}^{3+}$ local-crystal-field environment imposes a rigid, mutually orthogonal Ising anisotropy, effectively splitting the SSL into two perpendicular magnetic sublattices. This orthogonal spin texture is demonstrated by a pronounced in-plane anisotropy: the saturation magnetization and the critical fields for suppressing AFM order along [100] and [110] directions differ by a factor of about $\sqrt{2}$, in close agreement with a minimal two-sublattice model. The low-temperature phase diagram for $B\parallel \left[110\right]$ reveals a field-induced quantum critical point near 2.2 T and a sublattice-selective partially polarized ordered state, in which the field-coupled sublattice is polarized while the orthogonal sublattice remains antiferromagnetically ordered. Together, these results establish ${\mathrm{BaNd}}_2{\mathrm{PdS}}_5$ as a platform to explore how lattice and site symmetries constrain collective magnetism in frustrated insulators and to guide engineering of sublattice-selective quantum criticality.

Transport properties of strongly correlated materials have contributions from quasiparticle excitations such as electrons and holes as well as emerging collective excitations such as plasmonic soundlike modes which are sustained by interactions. It was previously shown by Pongsangangan et al. [Phys. Rev. B 106, 205127 (2022)] that the thermal excitation of the long-lived plasmons in graphene provides a substantial contribution to heat and momentum transport in the interaction-dominated regime. Detailed information on these excitations is therefore necessary for the understanding of hydrodynamic transport with quantitative precision. On the other hand, dynamics of graphene plasmons is usually studied using perturbation theory within the Dirac cone approximation, thus neglecting the effects of a finite Brillouin zone (BZ) and higher-order perturbative corrections. Both these effects can be, however, significant for strong-interacting systems including free-standing graphene, where the effective coupling constant can reach values up to $\alpha =\frac{e^2}{\hslash v_{\mathrm{F}}}=2$. Consequently, in this paper, we study the behavior of plasmons in half-filled free-standing graphene using unbiased quantum Monte Carlo (QMC) calculations. We confirm the existence of well-defined resonance peaks for plasmons around the $\mathrm{\Gamma }$ point. Comparison with the random phase approximation (RPA) calculation for the honeycomb lattice shows qualitative agreement with QMC. However, RPA yields more stable plasmon modes, while QMC shows enhanced broadening due to nonperturbative interaction effects naturally included in the simulations. To account for this effect, we generalize the calculation of lattice RPA by dressing the fermionic propagator by a constant lifetime. As a result, the plasmon frequencies are shifted toward higher energies, and the spectrum is broadened, yielding better agreement with QMC. Our findings highlight the need to account for both a finite BZ and strong interaction effects when developing theories of electronic transport in free-standing graphene.

The interplay between chemical bonding, lattice anharmonicity, and thermal transport plays a central role in determining the thermoelectric performance of crystalline solids. Here, we systematically investigate the structural stability, lattice dynamics, thermal transport, and thermoelectric properties of the $M\mathrm{Ag}C{h}_2$ ($M=\mathrm{Sc}$, Y; $Ch=\mathrm{S}$, Se, Te) family. The calculated formation energies, phonon dispersions, and finite-temperature radial distribution functions confirm the thermodynamic, dynamical, and thermal stability of all six compounds. Furthermore, the predicted lattice parameters show excellent agreement with available experimental measurements, supporting the reliability of the theoretical framework. Chemical-bonding analysis reveals a distinct bonding hierarchy characterized by strong $M$–$\mathit{Ch}$ interactions and substantially weaker Ag–$\mathit{Ch}$ bonds. This weakly bonded Ag sublattice gives rise to highly anisotropic atomic vibrations, large mean-square displacements, and dense low-frequency optical phonon modes. As a result, pronounced acoustic–optical phonon overlap and strong anharmonicity emerge throughout the series. The lattice thermal conductivity decreases systematically from sulfides to tellurides and remains below 1 W/mK at elevated temperatures. Notably, wave-like phonon transport contributes significantly to the lattice thermal conductivity, accounting for approximately 45–56% of the heat conduction at 900 K, highlighting the breakdown of a purely particle-like phonon picture. Electronic structure calculations reveal progressive band gap narrowing and reduced carrier effective masses from S to Te, leading to enhanced carrier transport in the tellurides. Owing to the combination of intrinsically low lattice thermal conductivity and favorable electronic transport properties, ${\mathrm{ScAgTe}}_2$ and ${\mathrm{YAgTe}}_2$ exhibit the best thermoelectric performance, with predicted peak $\mathit{zT}$ values approaching 3.5 and 3.0 along the preferred transport direction, respectively. These findings identify $M\mathrm{Ag}C{h}_2$ as a promising thermoelectric material family and demonstrate the critical role of weak Ag-centered bonding, higher-order anharmonicity, and coherent phonon transport in achieving ultralow thermal conductivity.

Two-dimensional (2D) semi-Dirac bands hybridize Schrödinger and Dirac fermions, exhibiting quadratic dispersion along the $k_x$ direction and linear dispersion along the $k_y$ direction. Tilting along either direction enhances band anisotropy and can drive the corresponding Lifshitz transition when the tilt is tuned appropriately. To characterize the two fundamentally distinct Lifshitz transitions in 2D semi-Dirac bands, we propose for the first time a chemical-potential-dependent tilt parameter ($t_x=v_{tx}/\sqrt{4a\mu }$) for tilting solely along the quadratic dispersion direction ($k_x$ direction), in stark contrast to the conventional tilt parameter ($t_y=v_{ty}/v_F$) for tilting purely along the linear dispersion direction ($k_y$ direction). Within linear response theory, we rigorously prove the particle-hole symmetry of optical conductivities in 2D tilted semi-Dirac bands, and analytically compute, at zero temperature, the corresponding longitudinal optical conductivities (LOCs) and the joint density of states. The interband LOCs exhibit characteristic piecewise line shapes, critical frequencies, and high-frequency backgrounds for different tilting directions, especially in the type-II phase. Remarkably, we find a robust fixed point at $\omega =2\mu$ for both tilting directions, where the interband LOC and the joint density of states become exactly half of their untilted values. However, the range of tilt parameter for this fixed point differs markedly: $0<t_x\le 1$ for tilting along the $k_x$ direction versus $0<t_y\le 2$ for tilting along the $k_y$ direction. Furthermore, for tilting along the $k_x$ direction, the Drude weight is always cutoff independent (for $t_x>0$); whereas for tilting along the $k_y$ direction, the Drude weight is cutoff-free for $0\le t_y<1$ but cutoff dependent for $t_y\ge 1$. All of the piecewise line shapes, high-frequency asymptotic background, and range of tilt parameter for the fixed point in the interband LOCs serve as distinctive fingerprints for identifying the tilting direction and Lifshitz transitions in future optical experiments on semi-Dirac materials.

Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a nonequilibrium setting. For a Hamiltonian composed of strictly short-range interactions, the Suzuki-Trotter decomposition is the main technique for obtaining such a representation. Vanhecke et al. [Phys. Rev. A 103, L020402 (2021)] introduced an alternative strategy—the cluster expansion. This approach naturally preserves internal and lattice symmetries and can more easily be extended to higher-order representations or longer-range interactions. We extend the cluster expansion to two-dimensional fermionic systems and employ it to construct projected entangled-pair operator (PEPO) approximations of Gibbs states. We also discuss and benchmark different truncation schemes for multiplying layers of PEPOs together. Applying the resulting framework to a two-dimensional spinless fermion model with attractive interactions, we resolve a clear phase boundary at finite temperature.

The dual localized-itinerant character of uranium $5f$ electrons governs the electronic and magnetic properties of many actinide materials, yet the microscopic mechanisms controlling their tunable itinerancy remain incompletely understood. Here we investigate the uranium dipnictides $\mathrm{U}{X}_2$ ($X=\mathrm{P},\mathrm{As},\mathrm{Sb}$) using fully charge-self-consistent density functional theory combined with dynamical mean-field theory including spin–orbit coupling (SOC) in the paramagnetic (PM) state at $T=300\mathrm{K}$. The calculations reveal that the uranium $5f$ shell resides in a mixed-valence configuration with occupancies $\langle n_{5f}\rangle \approx 2.6-2.8$, dominated by $5f^2-5f^3$ states. Momentum-resolved spectra and hybridization functions show that decreasing $5f-p$ hybridization along the $\mathrm{P}\to \mathrm{As}\to \mathrm{Sb}$ series enhances correlation effects and strengthens $5f$ localization, whereas hydrostatic pressure increases hybridization and quasiparticle (QP) coherence, driving the system toward greater itinerancy. The Matsubara self-energy indicates coherent Fermi-liquid behavior at 300 K with pronounced spin–orbit-driven orbital differentiation, where the $j=5/2$ manifold is more strongly renormalized than the $j=7/2$ states. Local susceptibilities reveal sizable fluctuating $5f$ moments in the PM phase at room temperature, providing a qualitative—necessarily speculative—connection to magnetic scales inferred from previous static DFT calculations of the antiferromagnetic ground state. Additional calculations for ${\mathrm{UP}}_2$ in its experimentally established tetragonal $I4/mmm$ phase show that the key features identified in the $P4/nmm$ reference structure—including the SOC-split $5f$ manifold, the dominance of $j=5/2$ states near the Fermi level, and pressure-enhanced QP coherence—remain qualitatively preserved, with only moderate quantitative differences arising from the distinct crystallographic environment. Together these results establish a clear microscopic mechanism: ligand chemistry sets the baseline uranium–ligand hybridization and degree of $5f$ localization, while pressure continuously tunes the same control parameter, providing a unified framework for understanding how correlations, SOC, and hybridization govern $5f$ itinerancy in uranium intermetallic compounds.

In the natural chalcopyrite mineral ${\mathrm{Cu}}_{1+x}{\mathrm{Fe}}_{1-x}{\mathrm{S}}_2$ ($x=0.08$), a huge Seebeck effect was reported around room temperature [Ang et al., Angew. Chem. Int. Ed. 54, 12909 (2015)]. In this paper, we suggest that the observed huge Seebeck coefficient is due to antiferromagnetic magnon drag collaborated with an impurity band. First, we show that the temperature dependences of the electrical resistivity and Hall coefficient are in good agreement with the theoretical results based on the self-consistent $t$-matrix approximation, considering the impurity band. Secondly, by deducing the lifetime of the magnon from the experimental result of the thermal conductivity, we evaluate the Seebeck coefficient due to antiferromagnetic magnon drag collaborating with the impurity band by the linear response theory based on the Kubo-Luttinger formalism. Finally, we find that the obtained theoretical result is quantitatively consistent with the experimental one near room temperature.