We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the Ansatz expressiveness without accumulating errors from iterative imaginary-time evolution. We employ a variety of trial states—both tensor networks as well as neural networks—as variational Ansätze for our numerical optimization. We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to $N=100$ spins. Our results demonstrate that while restricted Boltzmann machines show limitations, string bond tensor network states exhibit systematic improvements with increasing bond dimensions and the number of strings.

Materials with large spin injection efficiency and long spin relaxation time are highly desirable for spintronic devices with low-power consumption, high-speed operation, and long-distance spin information transmission. With strong spin-orbit coupling (SOC), large spin injection efficiency and spin-charge interconversion can be achieved as an enhancement of damping factor ${\alpha }_{\mathrm{sp}}$ induced by spin pumping in ferromagnet/nonmagnetic material heterojunctions, whereas the spin relaxation time $\left({\tau }_{\mathrm{s}}\right)$ will be greatly diminished, which makes it contradictory to combine long ${\tau }_{\mathrm{s}}$ and large ${\alpha }_{\mathrm{sp}}$ in one material. Here, we utilized the topologically protected surface states to enhance damping factor $\alpha$ and prolong spin relaxation time ${\tau }_{\mathrm{s}}$ simultaneously by delicately altering the thickness of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ in $\mathrm{Fe}/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ heterostructures. The linear correlation between $\alpha$ and ${\tau }_{\mathrm{s}}$ is originated from the spin-momentum locking and the robustness against backscattering of topological surface states (TSSs), resulting in a longer ${\tau }_{\mathrm{s}}$ even with strong SOC. The interplay between damping factor, spin relaxation, and band structure of topological insulators could shed deep insights on spin relaxation mechanism of TSSs. Our work will provide opportunities on designing spintronic devices for spin-encoded information transmission over macroscopic distances based on topological-band engineering.

Nonlinear electronic excitation in laser-irradiated silicon at finite electron temperatures is numerically investigated by first-principles calculations based on the time-dependent density functional theory. In bulk silicon at finite temperatures under near-infrared laser irradiation, we found that the absorbed energy is saturated when using a certain laser intensity even with a few-cycle pulse. Although one-photon processes of conduction-to-conduction and valence-to-valence transitions are dominant at such a laser intensity, the Pauli blocking inhibits further one-photon transition. With higher intensities, multiphoton excitation across the bandgap overwhelms the one-photon excitation and the saturable absorption disappears. At the surface of finite-temperature silicon, the Pauli blocking is suppressed by the symmetry breaking and the absorbed energy is relatively enhanced from the energy of the saturable absorption in the bulk region.

Optimizing the magnetic Zeeman-splitting term, specifically the magnetic gap of the topological surface states (TSSs), is a crucial issue and central challenge in advancing higher-temperature quantum anomalous Hall (QAH) states. In this work, we demonstrate a counterintuitive, nonmonotonic relationship between the magnetic gap and the hybridization strength in ferromagnetic-insulator (FMI)/topological-insulator (TI) sandwich structures. Concretely, insufficient hybridization strength fails to induce a substantial magnetic gap; while excessive hybridization incandesces the competition between kinetic and Coulomb exchange interactions, thereby reducing the gap. Strong hybridization strength also spatially delocalizes the TSSs, diminishing the effective orbital coupling between TSS-based $p$ and magnetic $d$ orbitals, which further weakens kinetic and Coulomb exchange interaction strength. Moreover, modifying the stacking order offers an experimentally viable approach to optimizing magnetic gaps, enabling the tunability of Chern numbers, chirality, and maximizing global gaps. These findings unveil a universal guiding principle for optimizing magnetic gaps in FMI-TI proximity-based QAH systems, offering valuable insights for advancing experimental implementations in this field.

The high-efficiency generation and dynamic control of nonlinear harmonics at the nanoscale are crucial for integrated nanophotonics. Herein, we theoretically propose a permittivity-asymmetry lithium niobite dimer metasurface and numerically investigate the photonic spin as a degree of freedom for tailoring high-efficiency second-order nonlinear frequency conversion, based on a chiral quasibound state in the continuum (quasi-BIC) with a quality factor approaching 7.5 × ${10}^3$ and circular dichroism (CD) of 0.91. Finite-element method simulations exhibit that this chiral quasi-BIC enables the difference in second-harmonic generation efficiency exceeding three orders of magnitude under the illumination of left- and right-circularly polarized light, leading to a nonlinear CD approaching 1. Importantly, in combination with an achiral magnetic dipole resonance, the photonic-spin-controlled sum-frequency generation and photon-pair generation from spontaneous parametric downconversion are also observed. In this paper, we suggest that the chiral quasi-BICs open an avenue for controlling nonlinear frequency conversion by using the photonic spin, without reconfiguring structure using external stimuli. Our results provide insights for both linear and nonlinear photonic-spin-dependent applications such as chiral sensing, chiral light sources, and chiral filters.

Interface engineering has become a new research field recently. Transition metal dichalcogenides, as a kind of graphenelike two-dimensional semiconductor layered material, can be constructed as rich heterostructures with various other materials, which helps to fully explore the modulation effect of interlayer interaction. Based on first-principles calculation, it is found that ${\mathrm{MoS}}_2$/${\mathrm{FeCl}}_2$ is a typical metal-semiconductor contact heterostructure with a variety of novel physical properties, including unconventional band alignment, the coexistence of spintronics and valleytronics, and the abnormal valley Hall effect. The change of interlayer interaction leads to the effective regulation of band structure in the system, and the interlayer coupling transforms between weak vdWs force and covalentlike quasibonding interaction depending on the interlayer distance. The transition from $n$-type to $p$-type Schottky contact at the interface of the system is also achieved by interlayer engineering. Meanwhile, under the influence of magnetic proximity effect, the heterostructure presents a robust ferromagnetic ground state, but the magnetic anisotropy energy can be transferred from in-plane to out-of-plane. Remarkably, manipulating interlayer coupling through magnetization direction or interlayer proximity can result in alterations of spin and valley polarization. Once synthesized, the ${\mathrm{MoS}}_2$/${\mathrm{FeCl}}_2$ heterostructure is a potential candidate for multifunctional applications.

This work explores the impact of geometry on viscous electron flow in graphene channels. We demonstrate that structural modifications of the material edges distinctly influence its electrical resistance. As a general trend, we observe that softening the edges reduces the resistance in both the hydrodynamic and the ballistic regimes. Our simulations are based on a two-dimensional hydrodynamic model, which is compared with those obtained by the Boltzmann transport equation in some representative cases. In both formalisms, the scattering length due to electron-electron collisions and due to momentum-relaxing collisions of electrons with impurities and phonons are taken into account. A minimization algorithm was employed to optimize the channel geometry of the minimal resistance. Our findings emphasize the critical role of the channel geometry in graphene, presenting significant implications for the design of advanced electronic devices based on two-dimensional materials.

We investigate the wave function of electrons and holes injected by voltage pulses with noninteger flux quantum. We find that the wave function can be delocalized in the time domain, which is measured by using the inverse participation ratio. As the flux approaches an integer multiples of flux quantum, the wave function can either remain delocalized or undergo a localization-delocalization transition. The former case occurs for the neutral electron-hole pairs, while the latter case occurs for electrons and holes which are injected individually. We perform the finite-size scaling analysis of the inverse participation ratio to further clarify the nature of the localization-delocalization transition. The scaling function and correlation length are determined numerically by the data collapse method. We find that the localization-delocalization transition is universal in the sense that the scaling function and correlation length is insensitive to the pulse profile when the pulse is sufficiently sharp. In contrast, they exhibit quantitatively different behavior for the Lorentzian pulse, indicating the corresponding localization-delocalization transition belongs to a different universality class.

Light sources and photodetectors operating in the far- to midinfrared (FIR/MIR) band (8–12 µm, 0.15–0.1 eV) remain relatively poorly developed compared to their counterparts operating in the visible and near-infrared ranges, despite extensive application potential for thermal imaging, standoff sensing, and other technologies. This is attributable in part to the lack of narrow-gap materials (<0.1 eV) with high optical gain and absorption. In this work, a narrow-gap semiconductor, ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$, is demonstrated to exhibit an optical response >10× larger than that of ${\mathrm{Hg}}_x{\mathrm{Cd}}_{1-x}\mathrm{Te}$ (MCT), the dominant material for FIR/MIR photodetectors. A previous theoretical investigation indicated that chalcogen $p$ and metal $d$ band inversion in this material creates a Mexican hat band structure (MHBS), which results in a dramatic increase in the joint density of states at the optical transition edge compared to typical semiconductors. This prediction is experimentally validated here using single-crystal specimens of ${\mathrm{Pb}}_{0.7}{\mathrm{Sn}}_{0.3}\mathrm{Se}$ measured using temperature-dependent spectroscopic ellipsometry over a wavelength range 1.7–20 µm (0.73–0.062 eV). These measurements demonstrate a large enhancement in extinction coefficient and refractive index, which are characteristic of a MHBS in the vicinity of the absorption edge, in agreement with theoretical predictions. The realization of topological semiconductors with a MHBS is expected to lead to high-efficiency detectors operating in the FIR/MIR range.

Nonreciprocal hopping and balanced gain and loss are two regular approaches to revolutionize new physics individually within the scope of a non-Hermitian system. In stark contrast to prior studies, wherein non-Hermitian skin effects (NHSEs) typically arise from asymmetry nearest-neighboring (NN) hopping, here we show that NHSEs can also be enabled and steered in a modified Su-Schrieffer-Heeger (SSH) model with nonreciprocal long-range coupling, i.e., next-nearest-neighboring (NNN) hopping in the presence of balanced gain and loss. It can be found that NHSEs survive in most of the parameter spaces spanned by NN hopping ratio, non-Hermitian strength, and NNN hopping phase. The skin modes vary greatly in various schemes with NHSEs whether in amount or the concentrated degree. For fixed NNN hopping and non-Hermitian strength, the localization length of skin modes can be amplified by increasing the NN hopping amplitude. Beyond critical NN hopping ratio, all bulk states become localized along with the highest concentration degree at the same time. Our paradigm presents an alternative proposal to effectively design and manipulate NHSEs, highlighting the intricate interplay between nonreciprocal hopping and non-Hermitian strengths, which holds promise for future applications in topological non-Hermitian devices.

We consider a fermionic quantum system exchanging particles with an environment at a fixed temperature and study its reduced evolution by means of a Redfield-I equation with time-dependent (non-Markovian) coefficients. We find that the description can be efficiently reduced to a standard-form Redfield-II equation, however, with a time-dependent effective bath temperature obeying a universal law. At early times, after the system and environment start in a product state, the effective temperature appears to be very high, yet eventually it settles down towards the true environment value. In this way, we obtain a time-local master equation, offering high accuracy at all times and preserving the crucial properties of the density matrix. It includes non-Markovian relaxation processes beyond the secular approximation and time-averaging methods and can be further applied to various types of Gorini-Kossakowski-Sudarshan-Lindblad equations. We derive the theory from first principles and discuss its application using a simple example of a single quantum dot.

Advances in engineering mesoscopic quantum devices have led to new material platforms where electronic transport can be achieved on foldable structures. In this respect, we study quantum phases and their transitions on a kirigami structure—a Japanese craft form—where its individual building blocks are topologically nontrivial. In particular, we find that by mechanically deforming the kirigami structure one can engineer topological phase transitions in the system. Using a multipronged approach, we show that the physics of the system can be captured within a transfer matrix formalism, akin to Chalker-Coddington networks, where the junctions describe scattering between effective non-Hermitian one-dimensional edge channels. We further show that the nature of the kirigami structure can affect the critical folding angles where the topological phase transitions occur. Our study shows the rich interplay between topological quantum phenomena and structural configuration of an underlying kirigami network reflecting its potential as an intriguing platform.

The vitality of topological insulators (TIs) arises in large part from the conducting edge states, which support the dissipationless transport along the edge. Whereas chiral edge states have been identified by electrical transport measurements, observations that capture the topological order of the insulating bulk states are rather scarce. Instead, contributions from bulk states are assumed to behave like those of ordinary insulators, and are thus undesirable. Here, we theoretically demonstrate that in nanosized TIs, the topological order of bulk states can be manifested by the distinct circular dichroism of the dipole transition in high harmonic generation (HHG), even though the energy band structure changes negligibly compared to the trivial one in bulk TIs. The circular dichroism is mapped onto the large ellipticity of HHG, which keeps the same sign as the Chern number of TIs despite fluctuations of driving laser ellipticity, defects, and doping of TIs. It also enables a micromagnetic trap that realizes magnetic confinement more than three orders of magnitude stronger than that generated by the conventional method. Our results reveal a counterintuitive feature of dynamic responses in nanosized TIs and provide additional degrees of freedom for the design of novel TI-based devices.

We have performed large-scale density-matrix renormalization group studies of the lightly doped Hubbard model on the honeycomb lattice on long three- and four-leg cylinders. We find that the ground state of the system upon lightly doping is consistent with that of a superconducting state with coexisting quasi-long-range superconducting and charge density wave orders. Both the superconducting and charge density wave correlations decay as a power law at long distances with corresponding exponents $K_{sc}<2$ and $K_c<2$. On the contrary, the spin-spin and single-particle correlations decay exponentially, although with relatively long correlation lengths.

Ferroelectric materials underlie key optical technologies in optical communications, integrated optics, and quantum computing. Yet, there is a lack of a consistent thermodynamic framework to predict the optical properties of ferroelectrics and the mutual connections among ferroelectric polarization, optical properties, and optical dispersion. For example, there is no existing thermodynamic model for establishing the relationship between the ferroelectric polarization and the optical properties in the visible spectrum. Here we present a thermodynamic theory of the linear optical and electro-optic properties of ferroelectrics by separating the lattice and electronic contributions to the total polarization. We introduce a biquadratic coupling between the lattice and electronic contributions validated by both first-principles calculations and experimental measurements. As an example, we derive the temperature and wavelength-dependent anisotropic optical properties of $\mathrm{BaTi}{\mathrm{O}}_3$, including the full linear optical dielectric tensor and the linear electro-optic (Pockels) effect through multiple ferroelectric phase transitions, which are in excellent agreement with existing experimental data and first- principles calculations. We further demonstrate the validity by comparing our predictions to the experimental temperature- and wavelength-dependent optical properties of $\mathrm{LiNb}{\mathrm{O}}_3$. This general framework incorporates essentially all optical properties of materials, including coupling between the ionic and electronic order parameters, as well as their dispersion and temperature dependence, and thus offers a powerful theoretical tool for analyzing light-matter interactions in ferroelectrics-based optical devices.

The coloring triangular (CT) lattice, which is equivalent to the kagome lattice, incorporates van Hove singularities, flat bands, and Dirac states, significantly advancing the field of materials discovery in kagome physics. Using first-principles calculations, this study identifies six stable bilayer borophene structures composed of two CT-latticed ${\mathrm{B}}_9$ monolayers arranged in three distinct stacking modes. These six bilayer structures can be categorized into two classes based on their interlayer interactions: three van der Waals-bonded and three covalently bonded bilayers. Interestingly, bilayer structures of the same stacking mode can interchange between vdW-bonded and covalently bonded forms under suitable conditions, such as biaxial strain or external pressure. As anticipated, the vdW-bonded bilayer structures display the characteristic kagome band topology, attributed to their weak interlayer interactions. In contrast, the covalently bonded bilayers exhibit versatile properties, including ideal Dirac semimetal behavior and phonon-mediated superconductivity, with a maximum $T_{\text{c}}$ of 17.96 K. This superconducting phase features Dirac states and van Hove singularities near the Fermi level, indicating the potential for realizing a topological superconductor. These findings offer valuable insights and opportunities for the design of CT-latticed materials and to create a platform to investigate the interplay between band topology, electron correlation, and superconductivity.

Subjecting a massive two-dimensional Dirac material to a vortex light beam provides a mechanism for the photo-induction of multiply quantized vortices. Using Floquet theory, we show that electronic vortices, characterized by their total angular momentum, are exclusive to circularly polarized vortex beams. The equations for the driven system at the one photon-resonance are mapped to the Bogoliubov–de Gennes equations of $s$-wave superconductors with multiply quantized vortices. This mapping provides valuable analytical tools for the analysis of the system's spectral properties.

While graphene is known for its high thermal conductivity at room temperature, the thermal conductivity near its edges (armchair and zigzag)—where phonon-boundary scattering becomes significant—remains less explored. Microscopic roughness at the boundaries of exfoliated graphene flakes often leads to dominant diffuse reflections. Recent theoretical studies have suggested that such diffuse reflections can significantly reduce thermal conductivity in low-dimensional crystals. In this work, we experimentally investigate the thermal conductivity and interface thermal conductance near the armchair and zigzag edges of supported monolayer graphene using optothermal Raman spectroscopy. Additionally,we perform simulations based on a two-dimensional finite difference model to understand the temperature distribution and the heat flow near the edges, comparing the results with the interior region. Our results show a significant change in the temperature distribution near the edges, leading to a substantial reduction ($\sim 50\%$) in in-plane thermal conductivity. This reduction is attributed to a shorter phonon mean free path due to increased phonon-boundary scattering. Notably, despite the localized electronic states at the zigzag edge, we observe no significant differences in the thermal transport properties between the armchair and zigzag edges. Furthermore, in most samples, the interface thermal conductance per unit area decreases at the edges, indicating reduced adhesion to the substrate.