Traditional thermoelectric theory applies to bulk materials and neglects ballistic effects that emerge when the device length approaches the carrier mean free path. This work explores how thermoelectric performance evolves as material length is scaled down, transitioning through diffusive, quasiballistic, and ballistic electron transport regimes. To study this, we develop a coupled electrothermal simulation framework based on the McKelvey-Shockley flux method for modeling ballistic and out-of-equilibrium electron transport, combined with the heat equation and Fourier's law for treating diffusive phonon transport. Using this approach, we simulate thermoelectric generators and coolers with lengths ranging from 1000 nm down to 10 nm. Our results show that ballistic electron transport generally degrades thermoelectric performance relative to bulk materials. However, with the coolers, nonuniform and reduced heat generation associated with nanoscale electron scattering suppresses heat backflow to the cold side, partially offsetting the performance losses. These findings highlight the complex interplay between transport regimes and thermoelectic behavior at the nanoscale.

In this article, we propose a possibility of realizing a distinct family of scale-conformal invariant interacting Hamiltonians in two-dimensional quantum many-body systems. Such phenomena can occur in various interacting systems, including topological surfaces or two-dimensional bulks. Based on a previous study [S. Vijayan and F. Zhou, Phys. Rev. B 111, 174504 (2025) ], here we further demonstrate that a semiclassical conformal manifold can emerge as an exact solution when the number of fermion colors, $N_c$, in our models becomes infinite. We identify distinct exact marginal deformation operators uniquely associated with the semiclassical conformal manifolds. When $N_c$ is set to be finite but large, we also show that quantum fluctuations that induce fermion field renormalization can result in mildly infrared relevant or irrelevant renormalization-group (RG) flow within a semiclassical conformal manifold. These quantum effects lead to standard, isolated, infrared-stable Wilson-Fisher fixed points. These stable fixed points, along with ultraviolet stable fixed points, form a discrete manifold, due to the spontaneous symmetry breaking of an emergent $\mathrm{SO}\left(\mathcal{N}\right)$ dynamical symmetry in the RG flow as $N_c\to \infty$. In addition, we find that along the direction of the RG flow within the manifold, an EPR-like entanglement entropy in the fermion flavor space always increases. The infrared-stable Wilson-Fisher fixed points, induced by quantum fluctuations, are always linked to theories on the manifold where interaction operators are maximally entangled. Our studies provide an effective framework for addressing topological quantum critical points with high-dimensional interaction parameter spaces that potentially host an overwhelmingly large number, often an exponentially large number of fixed points of complex stabilities. They also highlight the central role of entangled conformal operators and their entropy in shaping the universality classes of topological quantum phase transitions on surfaces or in bulk. We conclude our studies with open questions and possible future directions.

We present a framework for investigating the effects of interactions on crystalline symmetry-protected topological (SPT) phases. Within this framework, one can establish a direct connection between the equivalence classes of free-fermion systems and their corresponding interacting classes. A central component of this framework is the Atiyah-Hirzebruch spectral sequence, which provides a systematic way to represent crystalline SPT phases as SPT phases with internal symmetries on subspaces. We demonstrate the application of this approach through examples in various dimensions: $1d$ systems with $U\left(1\right)$ and reflection symmetry, $2d$ systems with $U\left(1\right)$ and $C_n$ rotation symmetry, and $3d$ systems with $U\left(1\right)$ and inversion symmetry.

Flat bands near the Fermi energy ($E_{\mathrm{F}}$) enhance the density of states and promote strong electronic correlations, often driving novel quantum phases. Understanding the microscopic origin of these correlations is essential for uncovering the mechanisms behind correlated phenomena such as superconductivity and magnetism. Here, we investigate the electronic structure of the three-dimensional pyrochlore superconductor ${\mathrm{CeRu}}_2$ using angle-resolved photoemission spectroscopy. The Ru sublattice forms a three-dimensional kagome network, theoretically predicted to host flat bands. While we resolve dispersive Ru $4d$–derived bands near $E_{\mathrm{F}}$, their high band velocities suggest a minimal contribution to low-energy correlations. In contrast, we observed clear signatures of strong hybridization between Ce $4f$ and Ru $4d$ states at $E_{\mathrm{F}}$. Our results identify Ce $4f$ electrons as the primary source of strong correlations in ${\mathrm{CeRu}}_2$, providing crucial insight into the microscopic origin of its superconductivity and magnetic phenomena.

Before assessing the suitability of a semiconductor for specific applications, the first question to ask is whether it possesses a direct or indirect band gap. This distinction is fundamental, as the operation of devices, such as light-emitting diodes, solar cells, and photodetectors, is closely tied to the band gap nature. Semiconductors that exhibit a band gap crossover—indirect to direct or vice versa—offer enhanced versatility for optoelectronic applications. Prominent examples include transition metal dichalcogenides and the subject of this study, ${\mathrm{PbI}}_2$. The nature of the band gap, and its crossover, can only be directly determined in reciprocal space by tracking the valence band maximum and conduction band minimum. Here, we directly visualize the thickness-dependent crossover of ${\mathrm{PbI}}_2$ from an indirect to a direct band gap using angle-resolved photoemission spectroscopy. Our measurements reveal a shift of the valence band maximum toward the Brillouin-zone center as the film thickness exceeds a monolayer. Supported by density functional theory calculations, our results show that this crossover is driven by interlayer interactions and the hybridization of iodine $p_z$ orbitals. These findings demonstrate the tunable electronic structure of ${\mathrm{PbI}}_2$ and its potential for optoelectronic applications.

A polymorph of the bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ that displays an alternating single-layer (SL) and trilayer (TL; 1313) stacking pattern has recently been discovered. Signatures of superconductivity under pressure have been found in this phase. At ambient pressure, ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$-1313 has been reported to crystallize in three different space-group symmetries Cmmm, Imma, and Fmmm. Unlike the commonly observed tilted ${\mathrm{NiO}}_6$ octahedra in perovskite nickelates, the Cmmm phase exhibits no ${\mathrm{NiO}}_6$ tilts, implying that this structural feature alone may be insufficient to give rise to superconductivity in Ruddlesden-Popper nickelates. Here, we employ first-principles calculations and group theory analysis to study the pressure dependence of the structural instabilities in this SL-TL ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ polymorph. At ambient pressure, we identify multiple unstable phonon branches in the highest symmetry (Cmmm) structure at various high-symmetry points of the Brillouin zone. Distortions associated with these instabilities lead to one of the other experimentally reported space groups (Imma) that does display octahedral tilts. The magnetic tendencies indicate that the electronic structure of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$-1313 at ambient pressure is dominated by the TL block, as the SL is in a Mott-insulating regime. Under pressure, a tetragonal $P4/mmm$ structure becomes stable, in agreement with experiments.

Numerical renormalization group (NRG) is formulated for nonequilibrium steady state by converting finite-lattice many-body eigenstates into scattering states. Extension of the full-density-matrix NRG for a biased Anderson impurity model, simplified by using the original orbital basis of the Hamiltonian, enables detailed studies of the sub-Kondo spectral evolution in the zero-temperature limit, confirming the double-resonance structure emerging at bias $V$ equal to the Kondo energy scale $T_K$. The distribution shows distinct multiscale spectral features of population inversion at energy $\omega$ below the Kondo scale ($\omega \lesssim T_K$) and very strong nonequilibrium excitations at energy beyond the bias ($\omega \gtrsim V$). The strong departure from the Fermi-Dirac distribution leads to the local nonequilibrium temperature $T_{\mathrm{loc}}$ scaling as $k_B{T}_{\mathrm{loc}}\approx V$ for $V\gg T_K$. The current-voltage relation at the low temperatures ($T\ll T_K$) in the strong Kondo regime evolves from the unitary limit to the current saturation behavior as the bias increases from zero to beyond the Kondo scale.

Recent studies have demonstrated that topological quantum spin Hall (QSH) states exist in twisted bilayers of transition metal dichalcogenides. However, a comprehensive theoretical characterization of the topological edge states remains a topic of interest and an unresolved issue. Here, the topological transport properties of the twisted ${\mathrm{WSe}}_2$ bilayers are investigated. Beyond the conventional single QSH state, we identify emergent double and fourfold QSH states, hosting two and four pairs of counter-propagating helical edge channels respectively. Furthermore, the charge carriers in these edge states are not localized at the geometric edge but rather the potential maxima of the moiré superlattice boundary, undergoing interlayer transitions and propagating forward continuously. We term these edge states as moiré edge states. These edge states can survive in non-magnetic disorder, with the robustness of double QSH states surpassing that of single QSH states. At a twisting angle of $2.{45}^{\circ }$, the transition between the single and double QSH states can be achieved by adjusting the gate on the surface. Based on this, we propose a five-terminal device as a topological current divider. Our findings provide support for the development of dissipationless spintronics.

We propose a new time ($t$)-resolved method of both vertical- and horizontal-temperature gradients in an orthogonal configuration $\left[t\text{−}\mathrm{resolved}T\right(t\left)\text{−}\mathrm{HVOT}\right]$ to provide real interpretations of the enhancement in the thermoelectric Seebeck effect (SE) observed during the structural phase transition. We apply our new method to superionic-state semiconductors of $p$-type $\mathrm{C}{\mathrm{u}}_2\mathrm{Se}$ and $n$-type $\mathrm{A}{\mathrm{g}}_2\mathrm{S}$. The experimental data differentiate the two types of enhancements during the phase transition: a colossal SE ($S_{\mathrm{colossal}}$), exhibiting an enormous value of 5 to 10 mV/K, and a slight enhancement in SE ($S_{\mathrm{structure}}$), approximately 1.5 to 2.0 times larger than those in the absence of the phase transition. We provide critical insights that the enhancement in $S_{\mathrm{colossal}}$ arising during the structural phase transition is not an intrinsic phenomenon. In addition, $S_{\mathrm{structure}}$ also requires more careful discussion, based on the principle of the Seebeck phenomenon.

Gallium oxide is a promising material for power conversion electronics, yet its widespread application is limited by low carrier mobility. In this work, we investigate the effect of strain on the electron and hole mobilities of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$. Using first-principles calculations, we find that the electron mobility is two orders of magnitude larger than the hole mobility. Furthermore, we show that tensile strain enhances the electron mobility while reducing the hole mobility. To understand this behavior, we analyze the electronic band structure. The lowest conduction bands of $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ are mainly composed of Ga and O $s$ orbitals. Under tensile strain, the electron effective mass and scattering rate decrease, whereas the group velocity increases. In contrast, the valence bands originate primarily from O $p$ states, leading to an increase in the hole effective mass and scattering rate, accompanied by a reduction of the group velocity with strain. We also investigate the long-range interaction between longitudinal optical phonons and charge carriers. At the Brillouin-zone center, polar longitudinal optical phonons dominate electron scattering, while both acoustic and optical phonons contribute significantly to hole scattering. Overall, this study provides a detailed understanding of strain-engineered electron and hole transport in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, offering insights for the design of high-performance semiconductor devices.

Noise is inevitable in realistic quantum circuits. It arises randomly in space. Inspired by the spatial nonuniformity of the noise, we investigate the effects of spatial modulation on quantum phase transitions in a hybrid random Clifford circuit with a mixed initial state. As an efficient observable for extracting quantum entanglement in mixed states, we employ many-body negativity. The behavior of the many-body negativity well characterizes the presence of the phase transitions and its criticality. We find the effect of spatial nonuniformity in measurement probability on the phase transition. The criticality of the phase transition changes from that of uniform probability, which is elucidated by the argument of the Harris criterion. The critical correlation length exponent $\nu$ changes from $\nu <2$ for uniform probability to $\nu >2$ for spatially modulated probability. We further investigate a setting where a two-site random Clifford gate becomes spatially (quasi)modulated. We find that the modulation induces a phase transition, leading to a different pure phase where a short-range quantum entanglement remains.

The amorphous phase of bismuth silicate (${\mathrm{Bi}}_2{\mathrm{SiO}}_5$) is characterized by an exceptionally large dielectric permittivity over a wide temperature range. This study explores the relationship between this remarkable property and the material's atomic-scale structure, which has been modeled from experimental x-ray and neutron scattering as well as x-ray absorption fine structure and nuclear magnetic resonance spectroscopy data in a reverse Monte-Carlo approach. The resulting structural model is analyzed to reveal short- and intermediate-range features on the atomic scale. Our results show that the exceptional dielectric performance stems from the asymmetric coordination of $\mathrm{Bi}\text{−}{\mathrm{O}}_x$ polyhedra as well as a nanosegregation induced by ${\mathrm{SiO}}_4$ chains, which together boost local polarizability. These findings establish a direct link between disordered atomic structures and enhanced dielectric properties, and set a clear benchmark for amorphous materials.

We analyze the interplay of disorder and long-range hopping in a paradigmatic one-dimensional model of quantum transport. While typically the current is expected to decrease as the disorder strength increases due to localization effects, in systems with infinite range hopping, it was shown in Chavez et al. [Phys. Rev. Lett. 126, 153201 (2021)] that the current can increase with disorder in the disorder-enhanced-transport (DET) regime. Here, by analyzing models with variable hopping range decaying as $1/r^{\alpha }$ with the distance $r$ among the sites, we show that the DET regime is a general feature of long-range hopping systems and it occurs, not only in the strong long-range limit $\alpha <1$ but even for weak long range $1\le \alpha \le 3$. Specifically, we show that, after an initial decrease, the current grows with the disorder strength until it reaches a local maximum. Both disorder thresholds at which the DET regime starts and ends are determined. Our results open the path to understand the effect of disorder on transport in many realistic systems where long-range hopping is present.

We investigate the phenomenon of spacetime-localized response in a quantum critical spin system, with particular attention to how it depends on the spatial profile and operator content of the applied perturbation, as well as its robustness against an increase of amplitude and temporal discretization. Motivated by recent theoretical proposals linking such response patterns to the anti-de Sitter/conformal field theory correspondence, we numerically analyze the real-time dynamics of the one-dimensional transverse-field Ising model at criticality using the time-evolving block decimation algorithm. We find that sharply localized and periodically recurring responses emerge only for specific types of perturbations, namely those that correspond to local density fields in the continuum limit. In contrast, perturbations involving other spin components produce conventional propagating excitations without localization. Furthermore, we demonstrate that the response remains qualitatively robust when the time-dependent perturbation is approximated by a piecewise-linear function, highlighting the practical relevance of our findings for quantum simulation platforms with limited temporal resolution. Our results clarify the operator dependence of emergent bulklike dynamics in critical spin chains and offer guidance for probing holographic physics in experimental settings.

We perform a first-principles investigation of electron-phonon interactions in silicon and germanium, uncovering distinct nonpolaronic spectral and transport fingerprints in these archetypal covalent semiconductors. Using many-body perturbation theory with the retarded cumulant expansion, we compute quasiparticle energies, lifetimes, and phonon satellites beyond the Dyson-Migdal approximation. Short-range crystal fields dominate coupling in both materials, yet their low-temperature spectral fingerprints differ: Si exhibits well-resolved satellites at both band edges, whereas Ge displays strong sidebands mainly at the valence-band maximum (VBM) and much weaker features at the conduction-band minimum (CBM). Phonon-induced satellites in both materials broaden and merge with the quasiparticle peak at elevated temperatures. Doping broadens peaks and compresses satellite-quasiparticle separation, with $n$-type carriers affecting the CBM and $p$-type the VBM. Mobility calculations, combining cumulant-derived phonon scattering with experimentally motivated ionized-impurity scattering models, reproduce measured trends and reveal Ge's consistently higher mobilities than Si, stemming from lighter effective masses and weaker coupling. These results link band-edge asymmetries and phonon energetics to measurable transport differences, providing a unified framework for predicting mobility in nonpolar semiconductors.

In this paper, we propose a computational framework, based on the vasp and phono3py computer codes, to obtain the thermoelectric figure of merit from the electron-phonon and phonon-phonon interactions using finite displacements in supercells. Several numerical techniques are developed for efficiency. The method is applied to several thermoelectric materials. We found different behaviors for the lifetimes of the electrons in PbTe, PbSe, and in compounds of the half-Heusler and magnesium silicide family. This is traced back to the different frequencies of the phonons involved in the scattering around the Fermi level. They have a lower frequency in PbTe and PbSe. The magnitude of the thermoelectric figures of merit we computed compare well with experiments, but the agreement is far from perfect. The role of the defects, not explicitly considered in our calculations, but abundant in thermoelectric materials, is discussed as a possible explanation. It is also shown that the choice of the exchange-correlation functional can strongly impact the results.

One–dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a two-dimensional compressible fluid but ignores fluctuations and becomes numerically unwieldy as soon as integrability-breaking perturbations are introduced. We show that GHD can be efficiently simulated as a gas of semiclassical wave packets—a natural generalization of hard-rod particles—whose trajectories are efficiently mapped onto those of point particles. This representation (i) provides a transparent route to incorporate integrability-breaking terms, and (ii) automatically embeds the exact fluctuating-hydrodynamics extension of GHD. The resulting framework enables fast, large-scale simulations of quasi-integrable systems even in the presence of complicated integrability-breaking perturbations. It also manifests the pivotal role of two-point correlations in systems confined by external potentials: we demonstrate that situations where local one-point observables appear thermalized can nevertheless sustain long-lived, far-from-equilibrium long-range correlations for arbitrarily long times, signaling that, differently from what was previously stated, true thermalization is not reached at diffusive time-scales.

“Unconventional magnetism” was proposed to describe the exotic states arising from Landau-Pomeranchuk instabilities in the spin channel nearly two decades ago. Its odd-partial-wave-channel (e.g., $p$-wave) states break parity giving rise to the dynamic generation of spin-orbit coupling, while its even-partial-wave-channel (e.g., $d$-wave) states break time-reversal symmetry. Both types of states can exhibit collinear and noncollinear spin configurations over Fermi surfaces with the former and latter termed as the $\alpha$ and $\beta$ phases, respectively. The collinear states in even partial-wave channels are in the same symmetry class of “altermagnetism”. In this work, we investigate unconventional magnetism in both $p$- and $d$-wave channels within spin-orbit coupled systems with parity and time-reversal symmetries maintained. Based on the Ginzburg-Landau free energy analysis, the $p$-wave channel yields the gyrotropic, Rashba, Dresselhaus-type spin-orbit couplings. They compete and mix evolving from the $\beta$ phase to the $\alpha$ phase with various types of spin-momentum lockings. Analyses are performed in parallel for the $d$-wave unconventional magnetism. We emphasize that the single-particle dispersion is not sufficient to justify the spin-group type symmetry of the full Hamiltonian. Furthermore, Goldstone manifolds and excitations are examined in each unconventional magnetic phase.