arXiv subjects

Xun-Jiang Luo

Publications and source records attributed to Xun-Jiang Luo.

At least 19 recordsLinked to original sources

arXiv2026

Phase-Controlled Majorana Zero Modes in Altermagnetic Topological-Insulator Josephson Junctions

We exploit facet-dependent Andreev phase shifts to control topological superconductivity with a phase bias in a three-dimensional altermagnetic topological-insulator Josephson junction. In the weak link between two conventional $s$-wave superconductors, the $d$-wave altermagnetic order produces anisotropic momentum shifts of the surface Dirac cones. The resulting net momentum of the states involved in Andreev reflection generates additional propagation phases that differ between facets. Consequently, the facet-resolved Andreev spectra exhibit gap closings at distinct phase biases, giving rise to topological superconducting regimes that host Majorana zero modes (MZMs). We further show that the spatial locations of the MZMs can be controlled by the phase bias. Moreover, these topological superconducting transitions are only weakly affected by moderate variations in the chemical potential, obviating the need for fine-tuning to the Dirac point. Our results establish a platform for realizing and spatially controlling MZMs by tuning the superconducting phase bias in altermagnetic topological-insulator Josephson junctions.

cond-mat.mes-hall↗

arXiv2026

Néel-Vector Control of the Josephson Diode Effect in $\mathcal{PT}$-symmetric Antiferromagnets

The interplay of superconductivity and magnetism gives rise to rich phenomena in Josephson junctions. In this Letter, we study Josephson junctions formed by conventional $s$-wave superconductors and a $\PT$-symmetric collinear antiferromagnet modeled on CuMnAs. Using microscopic modeling and symmetry analysis, we show that these junctions exhibit both the Josephson diode effect and $φ_{0}$-junction states. Remarkably, both effects are controlled by the Néel vector: rotating it by $90^{\circ}$ switches off both, while reversing it switches the diode polarity. To reveal the microscopic mechanism, we develop a channel-resolved scattering theory that accurately captures the anomalous phases and establishes the exact condition for the diode effect. The interplay of the channel current-phase relations yields a sizable diode efficiency, tunable by both the magnitude and direction of the exchange field. Furthermore, a Green-function reduction identifies a single renormalized $\PT$-degenerate band as the transport carrier and precisely reproduces the full current amplitudes. Our work establishes $\PT$-symmetric antiferromagnets as versatile platforms for field-free, highly tunable Josephson diodes and $φ_{0}$ junctions.

cond-mat.supr-con↗

arXiv2026

A Unified Symmetry Framework For In-plane Anomalous Hall effect

The in-plane anomalous Hall effect (IPAHE), driven by an in-plane net magnetization or an applied magnetic field, challenges the conventional anomalous Hall paradigm. Despite growing interest, a unified symmetry principle governing these phenomena has remained elusive. Here, we establish a comprehensive symmetry framework that bridges the spin space group, which dictates the magnetic geometry, with the magnetic space group, which governs the anomalous Hall response. We show that spontaneous IPAHE can emerge in ferromagnets when spin-orbit-coupling-induced spin-group symmetry breaking permits additional net magnetization directions. For field-induced IPAHE, we analyze how an applied magnetic field reduces the symmetries of all 122 magnetic point groups and identify 54 groups that support IPAHE. Our framework naturally predicts IPAHE in a broad class of unconventional magnets, including altermagnets and odd-parity magnets. In particular, symmetry analysis reveals characteristic one-, two-, or three-fold angular harmonics of the Hall conductance under an in-plane rotating field, providing a symmetry-resolved fingerprint for unconventional magnetism. Using this framework, we screen the MAGNDATA database and identify candidate materials supporting spontaneous or field-induced IPAHE, encompassing ferromagnets, antiferromagnets, and unconventional magnets. Finally, we validate the symmetry predictions through first-principles calculations for two representative materials.

cond-mat.mtrl-sci↗

arXiv2026

Quasi-two-dimensional Majorana zero modes from finite-size-coupled chiral hinge states

Majorana zero modes (MZMs) in topological superconductors have attracted broad research interest for their potential applications in topological quantum computation. In this work, we propose a quasi-two-dimensional route to realize spatially separated MZMs in a chiral higher-order topological insulator (HOTI) proximitized by a conventional $s$-wave superconductor through a theoretical model study. In three dimensions, the chiral HOTI hosts gapless hinge states along the $z$ direction, arising from a mass term that anisotropically gaps the surface Dirac cones of a topological insulator. By confining the sample along the $x$ direction while keeping it extended along $y$ and finite along $z$, opposite $z$-directed chiral hinge states hybridize and effectively form one-dimensional helical channels. Incorporating the superconducting proximity effect into this quasi-two-dimensional system induces effective $p$-wave pairing in these helical channels, thereby opening a topological gap. A fully open-boundary sample then hosts four localized MZMs, one at each endpoint of the helical channels, realizing a second-order topological superconductor characterized by Majorana corner modes. In addition to MZMs, we also find that superconducting pairing in this model produces extended Majorana hinge modes in three dimensions. Furthermore, representative disorder calculations indicate that these Majorana corner modes are robust against weak-to-moderate disorder, provided the excitation gap remains open. These results establish finite-size-coupled chiral hinge states as a promising platform for engineering multiple MZMs via conventional superconducting proximity effect.

cond-mat.mes-hall↗

arXiv2026

Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators

Majorana vortex phases have been extensively studied in topological materials with conventional superconducting pairing. Inspired by recent experimental progress in realizing time-reversal invariant higher-order topological insulators (THOTIs) and inducing superconducting proximity effects, we investigate Majorana vortex phases in these systems. We construct THOTIs as two copies of a topological insulator (TI) with time-reversal symmetry-preserving mass terms that anisotropically gap the surface states. We find that these mass terms have a negligible impact on the vortex phase transitions of double TIs when treated as perturbations, and no additional topological phase transitions are induced. Consequently, $\mathbb{Z}_2$-protected Majorana vortex end modes (MVEMs) emerge when the chemical potential lies between the critical chemical potentials $μ_c^{(1)}$ and $μ_c^{(2)}$ of the two TI vortex phase transitions. We demonstrate this behavior across multiple THOTI models, including rotational symmetry-protected THOTI, inversion symmetry-protected THOTI, rotational and inversion symmetries-protected THOTI bismuth, and extrinsic THOTI. Remarkably, MVEMs persist even when all surfaces are gapped with the same sign, rendering the system topologically trivial in both first- and second-order classifications. Our findings establish that MVEMs can be realized in time-reversal invariant systems with fully gapped surfaces, encompassing both topologically nontrivial and trivial insulators, thus significantly broadening the solid state material platforms for hosting Majorana vortex phases.

cond-mat.supr-con↗

arXiv2026

Unconventional Magnetism: Symmetry Classification, Hybrid-parity and Unconstrained-parity Classes

Unconventional magnetism has emerged as a transformative frontier in condensed matter physics. Such phases are characterized by substantial non-relativistic spin splitting (NSS) in symmetry-compensated magnets. They have been classified by the parity of their spin textures under momentum inversion, leading to the paradigms of altermagnets (even-parity) and odd-parity magnets. However, the full symmetry landscape remains largely unexplored. In this Letter, we present a systematic classification framework for unconventional magnetism based on the representation theory of the spin textures and the associated parity properties. Within this framework, we predict two previously unidentified classes beyond the established pure-parity categories: hybrid-parity magnets (HPMs) and unconstrained-parity magnets (UPMs), where the spin textures exhibit contrasting parities among their Cartesian components and the parity of the spin textures is ill-defined, respectively. We derive universal symmetry criteria that categorize HPMs into three distinct types. Importantly, by combining the spin splitting characteristics of altermagnets and odd-parity magnets, HPMs can enable the coexistence of the spin current and Edelstein effects. Taking FePO4 as an example, we perform first-principles calculations to demonstrate this coexistence. Finally, we discuss the potential applications of HPMs in spintronic devices. Our work provides a comprehensive symmetry classification of unconventional magnetism and establishes HPMs as a promising platform for multi-functional spintronics.

cond-mat.mtrl-sci↗

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

Exact Universal Characterization of Chiral-Symmetric Higher-Order Topological Phases

Utilizing Bott index vectors formulated through a series of polynomials of position operators under open boundary conditions, we establish a universal, rigorous, and complete correspondence between the Bott index vector and topological zero-energy corner states in systems with chiral symmetry. Our framework covers systems of arbitrary shapes, including topological phases that are beyond the characterization by previously proposed invariants such as multipole moments or multipole chiral numbers. A key feature of our approach is its ability to capture the real-space patterns of zero-energy corner states, providing a deeper understanding of higher-order topological phases. We provide a rigorous analytical proof of its higher-order correspondence and sum rules for Bott index vectors under different boundary conditions. To demonstrate the effectiveness of our theory, we examine several model systems with representative patterns of zero-energy corner states that lie outside the scope of previous classification frameworks.

cond-mat.mes-hall↗

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

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.

cond-mat.mes-hall↗

arXiv2025

Signature of gate tunable superconducting network in twisted bilayer graphene

Twisted van der Waals materials provide a tunable platform for investigating two-dimensional superconductivity and quantum phases. Using spectra-imaging scanning tunneling microscopy, we study the superconducting states in twisted bilayer graphene and track their evolution from insulating phases. Gate-dependent spectroscopic measurements reveal two distinct regimes: under-doped (ν = -2.3) and optimally doped (ν = -2.6). In the under-doped regime, partial superconductivity arises, forming a network interspersed with non-gapped regions. At optimal doping, the entire unit cell demonstrates superconductivity, with gap size modulation showing an anti-correlation with the local density of states. This gate-dependent transition from an insulating phase to a modulated superconductor uncovers an unexpected spatial hierarchy in pairing behavior and offers direct microscopic insights to constrain theories of superconductivity in moiré systems.

cond-mat.supr-con↗

arXiv2025

Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes

In a class of systems, there are gapped boundary-localized states described by a boundary Hamiltonian. The topological classification of gapped boundary Hamiltonians, same as the standard tenfold way for gapped bulk states, can lead to the emergence of boundary topological insulators (TIs) and superconductors (TSCs). In this work, we present a theoretical study of boundary TIs and TSCs of the full Altland-Zirnbauer tenfold symmetry classes. Based on the boundary projection analyses for a $d$-dimensional Dirac continuum model, we demonstrate that nontrivial boundary topology can arise at a $(d-n)$-dimensional boundary if the Dirac model incorporates ($n+1$) mass terms with $0<n<d$ although its bulk and $(d-1)$D, $\cdots$, $(d-n+1)$D boundaries are topologically trivial. Furthermore, we present a unified criterion for the emergence of nontrivial boundary topology by extending bulk classification within the context of the Dirac model, which provides a unified framework for nontrivial bulk and boundary topology. Inspired by the Dirac continuum model analysis, we further construct bulk lattice Hamiltonians for realizing boundary TIs and TSCs of the full Altland-Zirnbauer tenfold symmetry classes, which enables the realization of higher-order TIs and TSCs in arbitrary dimensions with arbitrary orders. We analyze some typical examples of the constructed boundary TIs and TSCs in physical dimensions.

cond-mat.mes-hall↗

arXiv2025

Characterization of higher-order topological superconductors using Bott indices

The abundance of bulk and boundary topologies in higher-order topological phases offer remarkable tunability and diversity to boundary states but also pose a challenge to their unified topological characterization. In this work, we propose a theoretical framework to characterize time-reversal invariant topological superconductors hosting Majorana Kramers pairs (MKP) of corner states by using a series of spin Bott indices, which capture both bulk and boundary states topology. The developed invariants can characterize MKP in arbitrarily shaped systems and all distinct spatial distribution patterns of MKP. As an illustrative example, we apply our theory to analyze the Kane-Mele model with sublattice-dependent superconducting pairing potentials. In this representative model, both intrinsic and extrinsic higher-order topological superconductors can be realized and various patterns of MKP can be engineered through edge cleavage. Despite their high sensitivity to boundary terminations, MKP can be faithfully characterized by the proposed topological invariants. We further demonstrate the characterization of higher-order topological superconductors in the BDI symmetry class using Bott indices without resolving the spin degree of freedom.

cond-mat.supr-con↗

arXiv2025

Surface-dependent Majorana vortex phases in topological crystalline insulators

The topological crystalline insulator SnTe exhibits two types of surface Dirac cones: one located at non-time-reversal-invariant momenta on the (001) and (110) surfaces, and the other at time-reversal-invariant momenta on the (111) surface. Motivated by the recent experimental evidence of Majorana vortex end modes (MVEMs) and their hybridization on the (001) surface [Nature 633, 71 (2024)], we present a comprehensive investigation of Majorana vortex phases in SnTe, including topological classification, surface-state Hamiltonians analysis, and lattice model calculations. By utilizing rotational and magnetic mirror symmetries, we present two equivalent methods to reveal the topology of Majorana phases on different surfaces. We find that the MVEMs on the (001) and (110) surfaces are protected by both magnetic group and rotational symmetries. In contrast, the MVEMs on the (111) surface are protected by magnetic group or particle-hole symmetry. Due to the different properties of Dirac fermions in the $\barΓ$ and $\bar{M}$ valleys on the (111) surfaces, including Fermi velocities and energy levels, we find that abundant vortex phase transitions can occur for the [111]-direction vortex. As the chemical potential increases, the number of robust MVEMs can change from $0\rightarrow 1\rightarrow 2$. These vortex transitions are characterized by both $Z$ winding number and $Z_2$ pfaffian topological invariants.

cond-mat.supr-con↗

arXiv2025

Family of third-order topological insulators from Su-Schrieffer-Heeger stacking

We construct a family of chiral symmetry-protected third-order topological insulators by stacking Su-Schrieffer-Heeger (SSH) chains and provide a unified topological characterization by a series of Bott indices. Our approach is informed by the analytical solution of corner states for the model Hamiltonians written as a summation of the extended SSH model along three orthogonal directions. By utilizing the generalized Pauli matrices, an enumeration of the constructed model Hamiltonians generates ten distinct models, including the well-studied three-dimensional Benalcazar-Bernevig-Hughes model. By performing a boundary projection analysis for the ten models, we find that certain surfaces and hinges of the systems can exhibit, respectively, nontrivial second-order and first-order topology in the phase of the third-order topological insulators. Furthermore, we analyze the phase diagram for one of the predicted models and reveal a rich set of topological phases, including the third-order topological insulators, second-order weak topological insulators, and second-order nodal semimetals.

cond-mat.mes-hall↗

arXiv2024

Quantum simulation of honeycomb lattice model by high-order moiré pattern

Moiré superlattices have become an emergent solid-state platform for simulating quantum lattice models. However, in single moiré device, Hamiltonians parameters like lattice constant, hopping and interaction terms can hardly be manipulated, limiting the controllability and accessibility of moire quantum simulator. Here, by combining angle-resolved photoemission spectroscopy and theoretical analysis, we demonstrate that high-order moiré patterns in graphene-monolayered xenon/krypton heterostructures can simulate honeycomb model in mesoscale, with in-situ tunable Hamiltonians parameters. The length scale of simulated lattice constant can be tuned by annealing processes, which in-situ adjusts intervalley interaction and hopping parameters in the simulated honeycomb lattice. The sign of the lattice constant can be switched by choosing xenon or krypton monolayer deposited on graphene, which controls sublattice degree of freedom and valley arrangment of Dirac fermions. Our work establishes a novel path for experimentally simulating the honeycomb model with tunable parameters by high-order moiré patterns.

cond-mat.mtrl-sci↗

arXiv2024

Majorana zero modes in twisted transition metal dichalcogenides homobilayers

Semiconductor moiré superlattices provide a highly tunable platform to study the interplay between electron correlation and band topology. For example, the generalized Kane-Mele-Hubbard model can be simulated by the topological moiré flat bands in twisted transition metal dichalcogenides homobilayers. For this system, we obtain the filling factor, twist angle, and electric field-dependent quantum phase diagrams with a plethora of phases, including the quantum spin Hall insulator, the in-plane antiferromagnetic state, the out-of-plane antiferromagnetic Chern insulator, the spin-polarized Chern insulator, the in-plane ferromagnetic state, and the 120$^\circ$ antiferromagnetic state. We predict that a gate-defined junction formed between the quantum spin Hall insulator phase with proximitized superconductivity and magnetic phases with in-plane magnetization (either ferromagnetic or antiferromagnetic) can realize one-dimensional topological superconductor with Majorana zero modes. Our proposal introduces semiconductor moiré homobilayers as an electrically tunable Majorana platform with no need of an external magnetic field.

cond-mat.supr-con↗