arXiv subjects

Longjun Xiang

Publications and source records attributed to Longjun Xiang.

At least 19 recordsLinked to original sources

arXiv2026

Lindbladian Phase Geometry and Hall Transport in Open Bloch Systems

Quantum geometry underlies a wide range of transport phenomena in Bloch systems. How quantum-geometric transport is modified when Bloch electrons are coupled to an environment, however, remains largely unexplored, even though the environment can alter both the electronic state and the physical current operator. Here we formulate dc linear response within a trace-preserving Lindblad kinetic theory by defining the physical velocity as the Liouvillian time derivative of the position operator. This construction reveals an environment-induced contribution to the current vertex whose momentum-space curl generates new Hall responses governed by the gauge-invariant phase geometry encoded by Lindblad jump amplitudes, which characterize electron-environment coupling. To leading order in the dissipative coupling, this geometry gives rise to interband shift-vector and diagonal-vorticity Hall responses arising from off-diagonal and diagonal jump amplitudes, respectively. Remarkably, both mechanisms can produce a finite Hall conductivity even when the conventional Berry-curvature anomalous Hall effect vanishes identically. Our work establishes Lindbladian phase geometry as an independent geometric origin of transverse transport in open quantum matter.

cond-mat.mes-hall↗

arXiv2026

Dissipationless Photovoltaic Spin Hall Effect from Spin-current Vorticity

Spin-current vorticity (SCV) can generate the linear magnetic spin Hall effect [\href{https://doi.org/10.1038/s41586-018-0853-0}{Nature \textbf{565}, 627 (2019)}], yet its role in nonlinear spin Hall transport has been much less explored. Here, we show that, under a dc electric field, SCV can deflect optically excited electrons to drive a dissipationless photovoltaic spin Hall effect (PSHE), in which optical excitation by circularly and linearly polarized light is governed by the Berry curvature and quantum metric, respectively. Because the Berry curvature is $\mathcal{T}$-odd whereas the quantum metric is $\mathcal{T}$-even, their respective combinations with the $\mathcal{T}$-odd SCV give rise to $\mathcal{T}$-even and $\mathcal{T}$-odd PSHEs, where $\mathcal{T}$ denotes time-reversal symmetry. Remarkably, we find that the spin current of the $\mathcal{T}$-even PSHE can be reversed by switching the light helicity, as illustrated in monolayer WTe$_2$. By contrast, the $\mathcal{T}$-odd PSHE in altermagnets changes sign upon N\'eel-vector reversal, as demonstrated in a $d$-wave altermagnetic model. Beyond the PSHE, we show that the SCV dipole governs both the Drude and intrinsic nonlinear spin Hall effects proposed recently. Our results reveal two switchable spin Hall mechanisms and establish SCV as a unifying concept for understanding dissipationless nonlinear spin Hall transport.

cond-mat.mtrl-sci↗

arXiv2026

Third-order intrinsic anomalous Hall effect as a transport fingerprint of altermagnets

The intrinsic anomalous Hall effect (IAHE) provides a powerful transport fingerprint of quantum magnets, with its linear and second-order responses distinguishing ferromagnets and $\mathcal{P}\mathcal{T}$-symmetric antiferromagnets, respectively. Altermagnets, as an emergent class of quantum magnets, have recently been shown to host a third-order extrinsic anomalous Hall effect, raising a question of whether an \textit{intrinsic} counterpart can serve as a diagnostic of altermagnetic order. Based on spin-group symmetry analysis, we demonstrate that the third-order IAHE is generically allowed in the ten spin Laue groups relevant to altermagnets when spin-orbit coupling (SOC) is taken into account. By combining these symmetry constraints with the anomalous velocity induced by the second-order Berry curvature, we uncover a resonant third-order IAHE arising near the altermagnetic band crossings at generic momenta in both the Lieb-lattice altermagnet and the experimentally realized altermagnet V$_2$Se$_2$O. Notably, we identify the Berry curvature quadrupole, encoded in the second-order Berry curvature and activated by finite SOC, as the microscopic quantum geometric origin of this resonance. Our results establish the third-order IAHE as an intrinsic quantum geometric transport fingerprint of altermagnets and extend the hierarchy of IAHE across collinear quantum magnets.

cond-mat.mtrl-sci↗

arXiv2026

Dual Quantum Geometric Tensors and Local Topological Invariant

The conventional quantum geometric tensor (QGT) is Hermitian, with a real symmetric quantum metric and an imaginary antisymmetric Berry curvature. We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition into normal and anomalous metric-curvature sectors. The normal sector reduces to the conventional Hermitian structure, whereas the anomalous sector contains an imaginary symmetric metric-like tensor and a real antisymmetric curvature-like tensor with no counterpart in the standard QGT. In a two-dimensional Dirac system, the anomalous Zeeman curvature develops a radial flux singularity that is Hodge-dual to the tangential winding field of the Dirac node. This recasts the same local $\pi_1$ topology into a curvature-flux language, analogous to the flux representation of global $\pi_2$ topology by the conventional Berry curvature. At the level of linear response, the four symmetry-resolved components of the gyrotropic conductivity are in one-to-one correspondence with the four components of the Zeeman QGT, while their distinct low-frequency scalings provide an additional diagnostic for isolating the underlying geometric sector. The reciprocal kinetic magnetoelectric response offers a complementary experimental route to probe the same structure. These results establish a unified framework connecting non-Hermitian Zeeman quantum geometry, local Dirac-node topology, and measurable transport signatures.

quant-ph↗

arXiv2026

Quantum Geometric Entropy Production and Entropy Hall Effect

Quantum geometry, encoded in the Berry curvature and quantum metric, has unified diverse anomalous transport phenomena in solids, yet a microscopic quantum-geometric theory of entropy transport for Bloch electrons is still lacking. We formulate an entropy continuity equation for noninteracting fermions driven by an electric field, starting from the von Neumann entropy, and obtain quantum-mechanical expressions for the entropy current density and entropy production rate. Introducing relaxation through a relaxation-time dissipator, we identify the quantum metric as the origin of the leading entropy production, providing a direct microscopic diagnostic of dissipation in both the extrinsic Drude response and an intrinsic nonlinear Ohmic contribution controlled by quantum metric. We further predict an entropy Hall effect arising from the Berry curvature and show that it obeys an Onsager reciprocal relation with the anomalous Nernst effect under a temperature gradient. Finally, we establish universal relations connecting entropy and charge currents under DC and AC driving, offering experimentally accessible probes of quantum geometry through nonequilibrium entropy flow.

cond-mat.stat-mech↗

arXiv2025

Quantum geometric map of magnetotransport

We propose a quantum geometric map for the magnetononlinear Hall effect (MNHE), the planar Hall effect (PHE), and the ordinary Hall effect (OHE). These magnetotransport phenomena originate from the bilinear charge current of Bloch electrons in electromagnetic fields, incorporating both spin Zeeman coupling and orbital minimal coupling to the applied magnetic field. Benchmarked against Onsager reciprocity, we demonstrate that the spin- and orbital-induced MNHEs are governed by the time-reversal-even Zeeman quantum metric dipole and conventional quantum metric quadrupole, respectively; the spin- and orbital-induced PHEs are dominated by the time-reversal-odd Zeeman Berry curvature dipole and conventional Berry curvature quadrupole, respectively. We further show that the OHE contains an interband contribution that is related to the quantum metric quadrupole, contrary to conventional wisdom. Navigated by this map, we study the previously unexplored spin-induced PHE in the surface Dirac cone of topological insulators, where we uncover a step-like PHE. Our work offers a unified quantum geometric framework for understanding magnetotransport experiments.

cond-mat.mes-hall↗

arXiv2025

Nonlinear Magnetoelectric Edelstein Effect

The linear Edelstein effect is a cornerstone phenomenon in spintronics that describes the generation of spin magnetization in response to an applied electric field. Recent theoretical advances have reignited interest in its nonlinear counterpart, the nonlinear Edelstein effect, in which spin magnetization is induced by a second-order electric field. However, the intrinsic contribution to both effects is generally forbidden in systems preserving time-reversal symmetry ($\mathcal{T}$) or composite symmetries such as $\mathcal{T}\tau_{1/2}$, where $\tau_{1/2}$ denotes a half-lattice translation. In such systems, spin magnetization typically emerges either from extrinsic mechanisms but limited to metals due to their Fermi-surface property, or from dynamical electric fields with a terahertz driving frequency. Here, we propose a new mechanism for spin magnetization, arising from the interplay of magnetic and electric fields, termed the nonlinear magnetoelectric Edelstein effect. Remarkably, its intrinsic component, determined purely by the material's band structure, can appear even in $\mathcal{T}$-invariant materials, but lacking inversion symmetry ($\mathcal{P}$), including insulators. On the other hand, we illustrate that its extrinsic component can serve as a sensitive indicator of the N\'eel vector reversal in $\mathcal{P}\mathcal{T}$-symmetric antiferromagnetic materials, offering a novel route for antiferromagnetic order detection. To validate our theory, we perform explicit calculations using a two-band Dirac model and a tight-binding model on a honeycomb lattice, finding that both effects yield sizable spin magnetization. Our findings establish the nonlinear magnetoelectric Edelstein effect as a versatile platform for both exploring nonlinear spin physics and enabling symmetry-based detection of antiferromagnetic order.

cond-mat.mes-hall↗

arXiv2025

Unconventional Hall Effect in Gapless Superconductors: Transverse Supercurrent Converted from Normal Current

A normal metallic system proximitized by a superconductor can exhibit a gapless superconducting state characterized by segmented Fermi surfaces, as confirmed experimentally. In such a state, quasiparticle states remain gapless along one direction, while a superconducting gap opens in the perpendicular direction. This anisotropy enables a novel Hall effect in gapless superconductors, termed the superconducting Hall effect (ScHE), where a longitudinal normal current carried by quasiparticles is converted into a dissipationless transverse supercurrent. Employing both the thermodynamic approach for bulk systems and quantum transport theory for a four-probe setup, we demonstrate the existence of this effect and reveal its intrinsic origin as the quasiparticle Berry curvature. The predicted ScHE can be experimentally verified via the standard angular-dependent Hall measurements performed on gapless superconductors.

cond-mat.mes-hall↗

arXiv2024

Light-induced thermal noise \textit{anomaly} governed by quantum metric

Traditionally, thermal noise in electric currents, arising from thermal agitation, is expected to increase with temperature $T$ and disappear as $T$ approaches zero. Contrary to this expectation, we discover that the resonant DC thermal noise (DTN) in photocurrents not only persists at $T=0$ but also exhibits a divergence proportional to $1/T$. This thermal noise \textit{anomaly} arises from the unique electron-photon interactions near the Fermi surface, manifesting as the interplay between the inherent Fermi-surface property and the resonant optical selection rules of DTN, and thereby represents an unexplored noise regime. Notably, we reveal that this \textit{anomalous} DTN, especially in time-reversal-invariant systems, is intrinsically linked to the quantum metric. We illustrate this \textit{anomalous} DTN in massless Dirac materials, including two-dimensional graphene, the surfaces of three-dimensional topological insulators, and three-dimensional Weyl semimetals, where the quantum metric plays a pivotal role. Finally, we find that the total noise spectrum at low temperatures, which includes both the DC shot noise and the \textit{anomalous} DTN, will universally peak at $\omega_p=2|\mu|$ with $\omega_p$ the frequency of light and $\mu$ the chemical potential of the bulk crystals.

cond-mat.mes-hall↗

arXiv2024

Pseudo-Riemannian metric: a new perspective on the quantum realm

As a fundamental concept in condensed matter physics, quantum geometry within the Riemannian metric elucidates various exotic phenomena, including the Hall effects driven by Berry curvature and quantum metric. In this work, we propose novel quantum geometries within a pseudo-Riemannian framework to explore unique characteristic of quantum matter. By defining distinct distances on pseudo-Riemannian manifolds and incorporating spin degree of freedom, we introduce the Pauli quantum geometric tensor. The imaginary part of this tensor corresponds to the Pauli Berry curvature, leading to the discovery a novel quantum phase: Pauli semimetal in PT-symmetric systems. This phase, characterized by the topological Pauli Chern number, manifests as a two-dimensional Pauli Chern insulator with helical edge states. These topological phases, uniquely revealed by the Pauli-Riemannian metric, go beyond the familiar Riemannian metric, where Berry curvature vanishes due to PT-symmetry. Pauli Chern number can classify helical topological insulator with or without time reversal symmetry. Pseudo-Riemannian metrics offer new insights into quantum materials and extend the scope of quantum geometry.

cond-mat.mes-hall↗

arXiv2024

Quantum intrinsic ${\cal T}$-odd spin Hall effect in altermagnets

Drude weight, historically associated with the longitudinal Drude conductivity, can be generalized to describe the transverse or Hall component of the extrinsic conductivity tensor. In particular, transverse Drude weights, such as band geometric quantities Berry curvature dipole and spin vorticity, manifest themselves through the \textit{extrinsic} second-order nonlinear Hall effect and \textit{extrinsic} linear spin Hall effect (SHE) in diffusive transport, respectively. In this work, we uncover a new class of intrinsic Hall effects in quantum transport regime, termed as quantum intrinsic Hall effect (QIHE), which is the manifestation of system symmetry through intrinsic transport phenomena. For a given Hamiltonian, its transport characteristics can be revealed either intrinsically through QIHE in ballistic regime or extrinsically via the transverse Drude weight in diffusive transport, where both intrinsic and extrinsic effects share the same salient transport features governed by symmetry of the Hamiltonian. The physical origin of QIHE is attributed to quantum boundary scattering of the measurement setup that respects the system symmetry, as exemplified by the contact resistance of a two-terminal ballistic conductor. We demonstrate our finding by studying the quantum ${\cal T}$-odd ($\mathcal{T}$, time-reversal) SHE in altermagnets. Our work paves a way towards the quantum transport manifestation of band geometric characteristics.

cond-mat.mes-hall↗

arXiv2024

Spin transport revealed by the spin quantum geometry

We present the framework of \textit{spin quantum geometry}, which is fundamentally linked to the spin degree of freedom of Bloch electrons and incorporates both the spin quantum geometric tensor (QGT) and the recently introduced Zeeman QGT, to elucidate the spin transport. We show that the spin and Zeeman QGTs, respectively, provide a unified framework for revealing known spin currents, such as the intrinsic spin Hall effect, and spin magnetization, such as the Edelstein effect, of Bloch electrons under an electric field. In addition, we predict the linear displacement spin Hall effect, wherein an AC electric field induces a transverse spin current in insulating systems. Furthermore, we propose two novel nonlinear spin responses: the nonlinear Drude spin current (NDSC) and the nonlinear Drude spin magnetization (NDSM), both of which exhibit a quadratic dependence on the relaxation time, like the nonlinear Drude charge current, and are governed by the \textit{spin quantum geometry}. Finally, we evaluate the NDSC and NDSM with Dirac models of topological insulators and find that, in the moderately dirty regime, the NDSC and NDSM can exceed their respective nonlinear intrinsic counterparts, which have recently garnered significant interest in spintronics.

cond-mat.mtrl-sci↗

arXiv2024

Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects

It has been known that the semiclassical theory and the response theory can equivalently give the Drude and the intrinsic anomalous Hall conductivities in the linear order of electric field. However, recent theoretical advances implied that the second-order nonlinear conductivities calculated with both approaches are no longer equivalent, which leads to various experimental explanations even in a similar experimental setup conducted in \href{https://www.science.org/doi/10.1126/science.adf1506}{[\textit{Science \textbf{381}, 181 (2023)}]} and \href{https://www.nature.com/articles/s41586-023-06363-3}{[\textit{Nature \textbf{621}, 487 (2023)}]}, respectively. Herein, by extending the AC semiclassical theory up to the second order of electric field, we show that the semiclassical theory is still equivalent to the response theory in the second order of electric field when the relaxation is taken into account on the same footing. In particular, we show that the familiar second-order nonlinear current responses, including the nonlinear Drude current and the Berry curvature (quantum metric) dipole driven extrinsic (intrinsic) nonlinear Hall current, can be derived by both approaches. Further, we show that the quantum-corrected intrinsic nonlinear longitudinal current, as recently proposed by the response theory or in a similar manner, can also be reproduced by the semiclassical theory. Beyond those known second-order current responses, with both approaches, we uncover two previously overlooked nonlinear displacement currents unique to the AC electric field. As a consequence of this equivalence,...

cond-mat.mes-hall↗

arXiv2023

Intrinsic gyrotropic magnetic current from Zeeman quantum geometry

Quantum geometric tensor (QGT), which is usually obtained by evaluating the quantum distance between Bloch states parametrized by momentum, plays a key role in exploring the exotic responses of quantum materials. Herein, we revisit the concept of QGT by further taking into account the spin degree of freedom. Besides the conventional QGT relating to momentum translation, we uncover a new QGT (termed Zeeman QGT) relating to momentum translation as well as spin rotation, whose imaginary (real) part gives the Zeeman Berry curvature (quantum metric). Notably, we show that these novel quantum geometric quantities can drive an intrinsic gyrotropic magnetic current (IGMC) in spin-orbit coupled materials when the electron spin is steered by an oscillating magnetic field. With symmetry analysis, we show that a wide range of materials can support the IGMC, as illustrated by model calculations. Finally, we discuss the experimental aspects of detecting the IGMC driven by Zeeman QGT.

cond-mat.mes-hall↗

arXiv2023

Classification of spin Hall effect in two-dimensional systems

Physical properties such as the conductivity are usually classified according to the symmetry of the underlying system using Neumann's principle, which gives an upper bound for the number of independent components of the corresponding property tensor. However, for a given Hamiltonian, this global approach usually can not give a definite answer on whether a physical effect such as spin Hall effect (SHE) exists or not. It is found that the parity and types of spin-orbit interactions (SOIs) are good indicators that can further reduce the number of independent components of the spin Hall conductivity for a specific system. In terms of the parity as well as various Rashba-like and Dresselhaus-like SOIs, we propose a local approach to classify SHE in two-dimensional (2D) two-band models, where sufficient conditions for identifying the existence or absence of SHE in all 2D magnetic point groups are presented.

cond-mat.mes-hall↗

arXiv2023

Gapless superconducting state and mirage gap in altermagnets

The interplay between spin-orbit interaction (SOI) and magnetism produces interesting phenomena in superconductors. When a two-dimensional (2D) system with strong SOI is coupled to an $s$-wave superconductor, an in-plane magnetic field can drive the system into a gapless superconducting state and induce a mirage gap at finite energies for an Ising superconductor. In this work, we demonstrate that when an $s$-wave superconductor is proximitized to an altermagnet, the intrinsic anisotropic spin splitting of the altermagnet can result in a gapless superconducting state and a pair of mirage gaps at finite energy. The gapless superconductivity exhibits spin-polarized segmented Fermi surfaces, with coexisting spin-singlet and spin-triplet pairings that have a $d$-wave character. Importantly, the gapless superconducting and mirage gap features are quantified through quantum transport. Our results suggest that altermagnet is an ideal platform for studying gapless superconducting states and mirage gap physics.

cond-mat.supr-con↗

arXiv2023

Linear displacement current solely driven by the quantum metric

Quantum metric and Berry curvature are the real part and imaginary part of the quantum geometric tensor, respectively. The T-odd (T: time-reversal) nonlinear Hall effect driven by the quantum metric dipole, recently confirmed in Science 381, 181 (2023) and Nature 621, 487 (2023), established the geometric duality to the T-even nonlinear Hall effect that driven by the Berry curvature dipole. Interestingly, a similar geometric duality between the quantum metric and the Berry curvature, particularly for the linear response of Bloch electrons, has not been established, although the T-odd linear intrinsic anomalous Hall effect (IAHE) solely driven by the Berry curvature has been known for a long time. Herein, we develop the quantum theory for displacement current under an AC electric field. Particularly, we show that the T-even component of the linear displacement current conductivity (LDCC) is solely determined by the quantum metric, by both the response theory and the semiclassical theory. Notably, with symmetry analysis we find that the T-even LDCC can contribute a Hall current in T-invariant systems but with low symmetry, while its longitudinal component is immune to symmetry. Furthermore, employing the Dirac Hamiltonian, we arrive at a $1/\mu$ ($\mu$: chemical potential) experimental observable enhancement of the displacement current owing to the divergent behavior of quantum metric near Dirac point, similar to the IAHE at Weyl point. Our work reveals the band geometric origin of the linear displacement current and establishes, together with the IAHE, the geometric duality for the linear response of Bloch electrons. Additionally, our work offers the very first intrinsic Hall effect in T-invariant materials, which can not be envisioned in DC transport in both linear and nonlinear regimes.

cond-mat.mes-hall↗

arXiv2023

Quantifying the photocurrent fluctuation in quantum materials by shot noise

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS$_2$ with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase.

cond-mat.mtrl-sci↗