arXiv subjects

K. T. Law

Publications and source records attributed to K. T. Law.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Geometric Friedel Oscillations

In conventional Friedel oscillations, the real-space charge density oscillations induced by an impurity are characterized by an oscillation period set by the Fermi momentum. In this work, we demonstrate that in metals with an isolated (nearly) flat band at the Fermi energy, quantum geometry induces a distinct type of oscillations, which we call the \emph{quantum geometric Friedel oscillations} (QGFOs). The period of the QGFOs is set by the momentum-space separation of the quantum metric hot spots of the isolated band. The conventional and quantum metric-induced oscillations can coexist at low temperatures. At higher temperatures, the conventional Friedel oscillation amplitudes away from the impurity site are set by the thermal length such that the oscillations can be easily washed out by temperature effects. Remarkably, the QGFOs decay length is set by the quantum metric length which is defined by the integration of the quantum metric of the isolated band. As a result, the QGFOs can persist even at temperatures much larger than the bandwidth of the isolated flat band. Moreover, the decay length is invariant for a wide range of temperature which is a striking result. In conclusion, we show that the quantum metric induces novel Friedel oscillations. Our work suggests that the measurement of the QGFOs is a powerful way to detect the quantum metric length (which is associated with the integral of the quantum metric) and the quantum metric hot spot separations (which are associated with the distribution of the quantum metric in the momentum space).

cond-mat.mes-hall↗

arXiv2026

Quantum Geometric Kondo Cloud

A magnetic impurity embedded in a metal is collectively screened by Fermi-surface quasiparticles into a many-body spin-singlet ground state, forming a Kondo cloud of size $ξ_{\rm K}\sim\hbar v_F/(k_B T_{\rm K})$. This kinematic picture collapses in flat bands, where $v_F=0$ and the hierarchy of dispersive energy shells is absent. Here we show that the missing organizing principle is quantum geometry. A magnetic impurity coupled to an isolated flat band selects a single active bath mode: a coherent superposition of flat-band Bloch states weighted by the hybridization factor $v(\mathbf{k})$, while all orthogonal flat-band modes remain dark. The resulting flat-band Kondo problem is a quantum geometric molecule, with an algebraic Kondo scale set by the total projected hybridization strength rather than a logarithmic-renormalization scale. In real space, the impurity-bath spin correlation defines a quantum geometric Kondo cloud. Its cloud-size tensor admits a gauge-invariant decomposition into a hybridization-weighted quantum metric, a dressed Berry-connection covariance, and a positive hybridization-gradient term, yielding the lower bound $ξ_{\rm K}^2\geq \sum_{\mathbf{k}}ρ(\mathbf{k}){\rm Tr}\,g(\mathbf{k})$, where $ρ(\mathbf{k})=|v(\mathbf{k})|^2/\sum_{\mathbf{k}}|v(\mathbf{k})|^2$. Our result reveals that, in flat bands, Kondo screening is governed by the quantum geometry and interference structure of the impurity-selected Bloch wave packet, rather than Fermi-surface kinematics.

cond-mat.str-el↗

arXiv2026

Quantum Metric Induced Critical Current Anomaly in Flat Band Josephson Junctions

In well-established theories of Josephson junctions, the superconducting critical current $ I_\mathrm{c} $ increases as the normal state conductance $ \mathcal{G} $ increases. However, in a recent experiment in twisted bilayer graphene (TBG) based Josephson junctions, unexpectedly, it was observed that the increase of the critical current is accompanied by a decrease of the normal state conductance. We call this phenomenon the critical current anomaly. In this work, we point out that in the TBG-based Josephson junction, due to the suppression of the conventional Josephson current by the flatness of the band and the quantum metric enabled Josephson current (QMJC), the critical current anomaly can occur. The QMJC appears if the quantum metric length is comparable or longer than the junction length. We show that both $ \mathcal{G} $ and $ I_\mathrm{c} $ have the conventional and the quantum metric contributions, and there are parameter regimes in which $ I_\mathrm{c} $ increases even when $ \mathcal{G} $ decreases. We first demonstrate the critical current anomaly by a simple modified Lieb-lattice model both analytically and numerically. The incredible consistency with the experimental results is demonstrated using a realistic six-band model of twisted bilayer graphene. Therefore, we suggest that the critical current anomaly observed in the experiment provide strong evidence of QMJC which were ignored in well-established theories of Josephson junctions.

cond-mat.supr-con↗

arXiv2026

Quantum Metric Localization and Quantum Metric Protection

The study of disorder effects in electronic systems is one of the central themes in physics. It is well established that in the Anderson localization regime, the localization length of electrons decreases monotonically as the disorder strength increases. Here, we demonstrate that the conventional Anderson localization paradigm fails completely in describing an isolated band with quantum metric, where the quantum metric of the band defines a length scale called the quantum metric length. For an isolated band with a finite bandwidth separated from other bands by a band gap $Δ$, weak disorder results in conventional Anderson localization behavior. However, as the disorder increases, the localization length ceases to decrease and becomes pinned at a value proportional to the quantum metric length, forming a localization length plateau. We term the regime within this localization length plateau as the quantum metric localization regime. Remarkably, the localization length does not deviate from the plateau until the disorder strength far exceeds $Δ$. We refer to this strong protection against disorder, characterized by the quantum metric length, as quantum metric protection. In this work, we first numerically demonstrate quantum metric localization using a 1D Lieb lattice. We then provide a simple physical picture based on the properties of Wannier functions to explain the origin of the localization length plateau. A supersymmetric field theory approach explains why the localization length is proportional to the quantum metric length and captures the crossover from Anderson localization to quantum metric localization. Our conclusions are broadly applicable to disordered electronic, photonic, and acoustic systems.

cond-mat.mes-hall↗

arXiv2026

Quantum Metric Bound State of Light

The spatial confinement of defect-induced bound states is conventionally governed by the effective mass in dispersive bands. More recently, Compact Localized States (CLSs) arising from exact destructive interference have been utilized to achieve confinement in flat bands. However, CLSs rely on pristine lattice symmetries and fine-tuned defect profiles. The introduction of a generic local impurity inevitably breaks these strict phase-matching conditions, resulting in extensive bound states whose fundamental length scale has remained an open question. Here, we establish a third regime of confinement: the quantum metric bound state. We provide a rigorous mathematical proof demonstrating that in the absence of kinetic energy and CLS protection, the exponential decay length of these states is lower-bounded by the quantum metric of the unperturbed flat band. We demonstrate the tightness of this geometric limit by constructing a family of highly tunable flat-band generators, and we verify its universality across diverse realistic architectures. Ultimately, this classification establishes the independently measurable quantum metric as a predictive design principle for engineering confined modes in synthetic wave platforms.

cond-mat.mes-hall↗

arXiv2026

Quantum-Geometric Fingerprints of Altermagnetic Order in Planar Magnetotransport

Identifying altermagnetic order through transport requires signatures that are sensitive to magnetic symmetry but do not rely on a net magnetization. Here we show that planar magnetotransport provides such quantum-geometric fingerprints. In two-dimensional altermagnets with $C_n\mathcal{T}$ magnetic symmetry, an in-plane Zeeman field explicitly breaks the mirror and emergent $C_{2z}$ symmetries that otherwise suppress intrinsic Hall and second-order transport responses. The resulting magnetic field susceptibilities of the Berry curvature and quantum metric produce linear planar Hall, nonlinear planar Hall, and nonreciprocal longitudinal responses. Crucially, the leading magnetic field powers and angular periodicities of these responses are fixed by the underlying altermagnetic order. For $d$-, $g$-, and $i$-wave altermagnets, we find distinct fingerprint patterns associated with quantum geometric susceptibilities. Our results establish planar magnetotransport as a symmetry selective probe of both band quantum geometry and altermagnetic order.

cond-mat.mes-hall↗

arXiv2026

Superconductivity from Quasiparticle Pairing of Intervalley Coherent State in Rhombohedral Trilayer Graphene

Superconductivity is observed in rhombohedral trilayer graphene in a narrow regime between the flavor-symmetric state and the symmetry breaking phase, which cannot be described by the conventional Bardeen-Cooper-Schrieffer theory. The measured coherence length, for instance, is roughly two orders of magnitude shorter than the value predicted by the Bardeen-Cooper-Schrieffer relation based on the large fermi velocity and an extremely low charge carrier density of the flavor-symmetric phase. To resolve the discrepancies, we propose that the rhombohedral trilayer graphene superconducting phase arises from the pairing of quasiparticles of the adjacent inter-valley coherent state. We illustrate the superconducting phenomenology using gapped Dirac cones with the chemical potential $μ$ close to the valence band's edge. Our findings indicate that the transition temperature $T_c$ obeys $T_c\propto ε_D\exp(-2/ρ_\mathrm{qp}U)$ with the density of states $ρ_\mathrm{qp}$ of intervalley coherent state quasiparticles, which is much suppressed compared to predictions from the Bardeen-Cooper-Schrieffer theory. The coherence length $ξ$ we predict behaves according to $ξ\sim v/\sqrt{μT_c}$ with $v$ being the velocity of Dirac cone. Applying our assumption to a microscopic model, our predictions align well with experimental data and effectively capture key measurable quantities such as the transition temperature $T_c$ and the coherence length $ξ$ without parameter fine-tuning.

cond-mat.supr-con↗

arXiv2026

Quantum-metric-nematicity induced Kerr-like polarization rotation without time-reversal symmetry breaking

The magneto-optic Kerr effect (MOKE), which describes the rotation and ellipticity of linearly polarized light upon reflection, is conventionally associated with time-reversal symmetry breaking. Here, we theoretically demonstrate that a Kerr-like polarization rotation can emerge even in nonmagnetic systems with time-reversal symmetry, owing to the nontrivial quantum metric of electronic bands. We show that the nematicity of the quantum metric, which captures the anisotropy of the quantum metric tensor due to the breaking of $n$-fold (with $n \ge 3$) rotational symmetry, gives rise to an incident-polarization-dependent reflected-polarization rotation. Notably, this mechanism requires neither magnetic order nor spin-orbit coupling, which are conventionally considered essential for MOKE. We illustrate the effect using a minimal tight-binding model and a model for strained MoS$_2$. This work reveals a quantum-geometric origin of the polarization rotation effects beyond conventional MOKE and suggests a new experimental approach to detect quantum metric nematicity.

cond-mat.mes-hall↗

arXiv2026

Pseudo-spin-polarized topological superconductivity in kagome RbV$_3$Sb$_5$

Kagome superconductors AV$_3$Sb$_5$ (A=K, Rb, Cs) have sparked considerable interest due to the presence of several intertwined symmetry-breaking phases within a single material. Interestingly, in a recent experiment, magnetic hysteresis was observed in the superconducting state through magnetoresistance measurements in RbV$_{3}$Sb$_{5}$ [Nature Comm \textbf{17}, 1310 (2026)], providing strong evidence of a spontaneous time-reversal symmetry breaking superconducting state. The magnetic hysteresis, combined with crystalline symmetry, imposes strong constraints on the possible pairing symmetries of the superconducting state. In this work, we propose that RbV$_3$Sb$_5$ is a nodal topological superconductor with pseudo-spin-polarized Cooper pairs. The pseudo-spin-polarized superconducting domains resemble the properties of ferromagnetic domains and induce hysteresis. Moreover, the nodal topological superconducting state possesses Majorana flat band modes at the sample boundary, which can be detected by tunneling experiments.

cond-mat.supr-con↗

arXiv2026

Hidden Zeeman Field in Odd-Parity Magnets: An Ideal Platform for Topological Superconductivity

Odd-parity magnets (OPMs) have emerged as a fundamental class of unconventional magnetisms, characterized by time-reversal-preserving non-relativistic spin splitting (NSS). Despite growing interest, the fundamental understanding of OPMs remains critically incomplete, as previous studies have focused exclusively on NSS while overlooking the intrinsically broken time-reversal symmetry ($\mathcal{T}$) inherent to magnetic order. In this work, we reveal that OPMs universally host a hidden Zeeman field rooted in this $\mathcal{T}$-breaking, which fundamentally reshapes their band structure. Through an analytical $f$-wave magnet model, we show that NSS microscopically originates from an emergent gauge field, manifesting as a real-space spin loop current order. Crucially, the large NSS (eV scale) enables conventional superconductivity to coexist robustly with the hidden Zeeman field, with Zeeman splitting reaches hundreds of meV. This unique band structure establishes OPMs as an ideal platform for topological superconductors (TSCs), supporting large topological regions. Based on OPMs, we engineer a series of TSCs hosting distinct Majorana boundary modes, including unidirectional Majorana edge states. Our work corrects a fundamental misconception about OPMs and establishes them as a versatile platform for field-free and robust TSCs.

cond-mat.supr-con↗

arXiv2026

Spin Group Symmetry Criteria For Unconventional Magnetism

Unconventional magnetism has typically been classified into two fundamental classes: even-parity magnets (EPMs) and odd-parity magnets (OPMs). These two classes exhibit identical and opposite spin splittings, respectively, under momentum inversion, while both maintain symmetry-compensated magnetization. In this Letter, we present a unified spin space group-based framework that establishes comprehensive symmetry criteria for both classes. Our framework not only yields a complete classification of EPMs and OPMs but also uncovers a wealth of new symmetry-driven mechanisms for them. Specifically, we classify both classes into three types based on their spin textures: collinear (type-I), coplanar (type-II), and noncoplanar (type-III), and we demonstrate that both classes can be realized across collinear, coplanar, and noncoplanar magnetic orders. We identify eight distinct symmetry-driven mechanisms for OPMs and seven for EPMs, among which some paradigms of unconventional magnetism, for instance, altermagnets naturally emerge as one specific mechanism of EPMs. Using these established criteria, we identify numerous candidate materials from the Magndata database, realizing some new symmetry mechanisms for OPMs and EPMs. Our work establishes a foundational symmetry framework for understanding, predicting, and designing unconventional magnetic materials.

cond-mat.str-el↗

arXiv2026

Quantum Metric Length as a Fundamental Length Scale in Disordered Flat Band Materials

Our previous understanding of electronic transport in disordered systems was based on the assumption that there is a finite Fermi velocity for the relevant electrons. The Fermi velocity determines important length scales in disordered systems such as the diffusion length and the localization length. However, in disordered systems with vanishing or nearly vanishing Fermi velocity, it is uncertain what determines the important length scales in such systems. In this work, we use the 1D Lieb lattice with isolated flat bands as an example to show that the quantum metric length (QML) is a fundamental length scale in the ballistic, diffusive and localization regimes. The QML is defined through the Bloch state wave functions of the flat bands. In the ballistic regime with short junctions, the QML controls the finite energy transport properties. In the localization regime with long junctions, the localization length is determined by the QML and remarkably, independent of disorder strength over a wide range of disorder strength. We call this unconventional localization regime, the quantum metric localization regime. In the diffusive regime, we demonstrate that the diffusion coefficient is linearly proportional to the QML via the wave-packet dynamics numerically. Importantly, the numerical results are consistent with the analytical results obtained through the Bethe-Salpeter equation. We conclude that the QML is a fundamentally important length scale governing the properties of disordered flat band materials.

cond-mat.mes-hall↗

arXiv2026

Unconventional Josephson effects in {\it PT}-symmetric antiferromagnetic bilayers

We propose that unconventional Josephson effects can typically emerge in {\it PT}-symmetric antiferromagnetic (AFM) bilayer systems. When proximitized by a conventional superconductor, these heterostructures host dominant interlayer Cooper pairing that features a distinctive spin texture enabled by the strong exchange field. Specifically, we demonstrate a novel mechanism for electrically tunable 0-$π$ oscillations in lateral Josephson junctions, controlled by an out-of-plane electric displacement field. This behavior originates from field-induced finite-momentum Cooper pairing, a hallmark of the unique layer-pseudospin structure in {\it PT}-symmetric AFM bilayers. Furthermore, we introduce a Josephson giant magnetoresistor based on these exotic spin-layer-locked Cooper pairs, in which the supercurrent exhibits a strong dependence on the internal Néel order. Our findings establish {\it PT}-symmetric AFM bilayers as a versatile platform for phase-controllable Josephson junctions and superconducting magnetic random-access memory, with promising applications in superconducting circuits and ultralow-power computing.

cond-mat.supr-con↗

arXiv2026

Spin Group Symmetry Criteria for Odd-parity Magnets

Odd-parity magnets (OPMs) have recently emerged as a new magnetic class, but their general symmetry criteria remain elusive. In this Letter, we establish these criteria through a comprehensive spin group symmetry analysis. Concretely, we identify eight distinct symmetry-driven cases that support OPMs with collinear, coplanar, or noncoplanar magnetic order. These are classified into three classes based on their spin textures: collinear (type-I), coplanar (type-II), and noncoplanar (type-III). From the Magndata database, we identify 33 candidate OPM materials and diagnose their spin-splitting character ($p$- or $f$-wave) by analyzing the representation of spin textures within an emergent Laue group derived from the spin space group, which reveals a variety of novel spin textures. To validate the symmetry criteria, we construct and analyze two theoretical models. Furthermore, we demonstrate that OPMs can host an intrinsic $\mathbb{Z}_2$ topology and propose a model for their realization. Our work provides a foundational framework for the future exploration of OPMs.

cond-mat.other↗

arXiv2025

Universal Boundary-Modes Localization from Quantum Metric Length

The presence of localized boundary modes is an unambiguous hallmark of topological quantum matter. While these modes are typically protected by topological invariants such as the Chern number, here we demonstrate that the {\it quantum metric length} (QML), a quantity inherent in multi-band topological systems, governs the spatial extent of flat-band topological boundary modes. We introduce a framework for constructing topological flat bands from degenerate manifolds with large quantum metric and find that the boundary modes exhibit dual phases of spatial behaviors: a conventional oscillatory decay arising from bare band dispersion, followed by another exponential decay controlled by quantum geometry. Crucially, the QML, derived from the quantum metric of the degenerate manifolds, sets a lower bound on the spatial spread of boundary states in the flat-band limit. Applying our framework to concrete models, we validate the universal role of the QML in shaping the long-range behavior of topological boundary modes. Furthermore, by tuning the QML, we unveil extraordinary non-local transport phenomena, including QML-shaped quantum Hall plateaus and anomalous Fraunhofer patterns. Our theoretical framework paves the way for engineering boundary-modes localization in topological flat-band systems.

cond-mat.mes-hall↗

arXiv2025

Second Harmonic Hall Response in Insulators: Inter-band Quantum Geometry and Breakdown of Kleinman's Conjecture

The nonlinear Hall effect has recently garnered significant attention as a powerful probe of Fermi surface quantum geometry in metals. While current studies mainly focus on the nonlinear Hall response driven by quasi-static electric fields of low frequencies, the extension of the response to higher frequencies is another promising frontier, which introduces quantum geometry into inter-band transitions. Here, we demonstrate that a specific nonlinear Hall response, namely the second harmonic Hall (SHH) response, can arise from inter-band transitions. We establish the quantum geometric origin of the SHH response and show that inter-band quantum geometry dominates the SHH response when driven near inter-band resonance. Crucially, we find that the inter-band SHH response in insulators exhibits strong frequecy dispersion, manifesting the breakdown of Kleinman's conjecture in nonlinear optics. This connects the SHH response to the breakdown of Kleinman's conjecture and reveals that frequency dispersive insulators generally allow the SHH response. Furthermore, we predict a giant SHH susceptibility in gated strained bilayer graphene and propose that one can apply the polarization resolved second harmonic microscopy to detect the SHH response there.

cond-mat.mes-hall↗

arXiv2025

Nonreciprocal Current-Induced Zero-Resistance State in Valley-Polarized Superconductors

The recently observed nonreciprocal current-induced zero-resistance state (CIZRS) in twisted trilayer graphene/WSe$_2$ heterostructure has posed a significant theoretical challenge. In the experiment, the system shows a zero-resistance state only when a sufficiently large current is applied in a particular direction, while stays in an incipient superconducting state with small resistance when the current is small or flows in the opposite direction. In this Letter, we provide a theory of CIZRS. We show that the threefold degenerate Fulde-Ferrell (FF) states are stabilized by the valley polarization and trigonal warping effects of twisted trilayer graphene/WSe$_2$ heterostructures. Moreover, a current flowing in a particular direction breaks the threefold degeneracy and favors a particular FF pairing domain. We therefore propose that the incipient superconducting state is naturally understood as a multidomain state where the interdomain supercurrent is difficult to flow due to the tiny Josephson coupling caused by the mismatch of Cooper-pair momenta between different FF domains. Nevertheless, a sufficiently large current in a particular direction can selectively populate a certain FF state and create monodomain pathways with zero resistance. Crucially, due to the threefold symmetry of the system, a current flowing in the opposite direction can fail to generate the zero-resistance pathways, thus giving rise to the observed nonreciprocity. Finally, we suggest that the long-sought-after triangular finite-momentum state can also be realized in valley-polarized superconductors.

cond-mat.supr-con↗

arXiv2025

Tunable quantum metric and band topology in bilayer Dirac models

Quantum metric, a fundamental component of quantum geometry, has attracted broad interest in recent years due to its critical role in various quantum phenomena. Meanwhile, band topology, which serves as an important framework in condensed matter physics, has led to the discovery of various topological phases. In this work, we introduce a bilayer Dirac model that allows precise tuning of both properties. Our approach combines two Dirac Hamiltonians with distinct energy scales; one producing relatively dispersive bands and the other yielding relatively flat bands. The dispersive and flat bands are weakly coupled via hybridization $λ$. By inducing a band inversion in the layer subspace, we achieve flexible tuning of band topology across all Altland-Zirnbauer symmetry classes and quantum metric scaling as $g \propto 1/λ^2$ near band inversion point. Using the bilayer Su-Schrieffer-Heeger model, we investigate the localization properties of gapless boundary states, which are affected by quantum metric. Our work lays a foundation for exploring the interplay between band topology and quantum metric.

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