arXiv subjects

W. B. Rui

Publications and source records attributed to W. B. Rui.

17 recordsLinked to original sources

arXiv2025

Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones

Exceptional points (EPs) are prominent non-Hermitian band degeneracies that give rise to a variety of intriguing and unconventional phenomena. Similar to Weyl and Dirac points, EPs carry topological charges and comply with the celebrated fermion doubling theorems in lattices. Beyond these characteristics, EPs exhibit more exotic topological properties, particularly non-Abelian braiding topologies not seen in conventional degeneracies. Here, we investigate these foundational concepts of EPs in two-dimensional non-Hermitian lattices where the fundamental domain of the Brillouin zone is a Klein bottle, rather than a torus assumed in previous studies. We find that EPs do not necessarily appear in pairs with opposite topological charges in the Brillouin Klein bottle, thus violating the fermion doubling theorem. The violation occurs because, without crossing the boundary, the sum of the topological charges of EPs is in fact an even number rather than zero. Moreover, we uncover unique braiding topologies of EPs that cannot be captured by existing theories. Specifically, the composite braidings around all EPs equals the braiding along the boundary of the Brillouin Klein bottle. This novel braiding topology further confirms the failure of the fermion doubling theorem, and allows us to explore the non-Abelian braidings of EPs beyond the scope of topological charges. Our work highlights the fundamental role of Brillouin-zone topology in non-Hermitian systems.

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arXiv2025

Instanton-Induced Supersymmetry Breaking in Topological Semimetals

Supersymmetry (SUSY) proposed as an elementary symmetry for physics beyond the Standard Model has found important applications in various areas outside high-energy physics. Here, we systematically implement supersymmetric quantum mechanics -- exhibiting fundamental SUSY properties in the simple setting of quantum mechanics -- into a wide range of topological semimetals, where the broken translational symmetry, e.g., by a magnetic field, is effectively captured by a SUSY potential. We show that the dynamical SUSY breaking via the instanton effect over the SUSY potential valleys works as the underlying mechanism for the gap opening of the topological semimetallic phases, and the magnitude of the instanton effect is proportional to the energy gap. This instanton mechanism provides a simple criterion for determining whether the energy gap has been opened, without resorting to detailed calculations, i.e., a finite energy gap is opened if and only if the SUSY potential has an even number of zeros. Our theory leads to previously unexpected results: even an infinitesimal magnetic field can open a gap in topologically robust Dirac, Weyl, and nodal-line semimetallic phases due to the dynamical SUSY breaking. Overall, the revealed connection between SUSY quantum mechanics and non-uniform topological semimetals can elucidate previously ambiguous phenomena, provide guidance for future investigations, and open a new avenue for exploring topological semimetals.

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arXiv2025

Non-Hermitian Dirac cones with valley-dependent lifetimes

Relativistic quasiparticles emerging from band degeneracies in crystals play crucial roles in the transport and topological properties of materials and metamaterials. Quasiparticles are commonly described by Hermitian Hamiltonians, with non-Hermiticity usually considered detrimental. In this work, we show that such an assumption of Hermiticity can be lifted to bring quasiparticles into non-Hermitian regime. We propose a concrete lattice model containing two Dirac cones with valley-dependent lifetimes. The lifetime contrast enables an ultra-strong valley selection rule: only one valley can survive in the long-time limit regardless of the excitation, lattice shape and other details. This property leads to an effective parity anomaly with a single Dirac cone and offers a simple way to generate vortex states. Additionally, extending non-Hermitian features to boundaries generates valley kink states with valley-locked lifetimes, making them effectively unidirectional and more resistant against inter-valley scattering. All these phenomena are experimentally demonstrated in a non-Hermitian electric circuit lattice.

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arXiv2024

Quantized Hall conductance in 3D topological nodal-line semimetals without chiral symmetry

A quantized Hall conductance (not conductivity) in three dimensions has been searched for more than 30 years. Here we explore it in 3D topological nodal-line semimetals, by using a model capable of describing all essential physics of a semimetal, in particular the drumhead surface states protected by a momentum-dependent winding number. We develop a microscopic theory to demonstrate that the drumhead surface states can host quantized Hall conductance in this 3D material. We stress that breaking chiral symmetry is necessary for the quantum Hall effect of the drumhead surface states. The analytic theory can be verified numerically by the Kubo formula. There may also be trivial quantum Hall effects from the bulk states. We propose an experimental setup to distinguish the surface and bulk quantum Hall effects. The theory will be useful for ongoing explorations on nodal-line semimetals.

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arXiv2023

Projective symmetry determined topology in flux Su-Schrieffer-Heeger model

In the field of symmetry-protected topological phases, a common wisdom is that the symmetries fix the topological classifications, but they alone cannot determine whether a system is topologically trivial or not. Here, we show that this is no longer true in cases where symmetries are projectively represented. Particularly, the Zak phase, a topological invariant of a one-dimensional system, can be entirely determined by the projective symmetry algebra (PSA). To demonstrate this remarkable effect, we propose a minimal model, termed as flux Su-Schrieffer-Heeger (SSH) model, where the bond dimerization in the original SSH model is replaced by a flux dimerization. We present experimental realization of our flux SSH model in an electric-circuit array, and our predictions are directly confirmed by experimental measurement. Our work refreshes the understanding of the relation between symmetry and topology, opens up new avenues for exploring PSA determined topological phases, and suggests flux dimerization as a novel approach for designing topological crystals.

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arXiv2023

Making topologically trivial non-Hermitian systems nontrivial via gauge fields

Non-Hermiticity significantly enriches the concepts of symmetry and topology in physics. Particularly, non-Hermiticity gives rise to the ramified symmetries, where the non-Hermitian Hamiltonian $H$ is transformed to $H^\dagger$. For time-reversal ($T$) and sublattice symmetries, there are six ramified symmetry classes leading to novel topological classifications with various non-Hermitian skin effects. As artificial crystals are the main experimental platforms for non-Hermitian physics, there exists the symmetry barrier for realizing topological physics in the six ramified symmetry classes: While artificial crystals are in spinless classes with $T^2=1$, nontrivial classifications dominantly appear in spinful classes with $T^2=-1$. Here, we present a general mechanism to cross the symmetry barrier. With an internal parity symmetry $P$, the square of the combination $\tilde{T}=PT$ can be modified by appropriate gauge fluxes. Using the general mechanism, we systematically construct spinless models for all non-Hermitian spinful topological phases in one and two dimensions, which are experimentally realizable. Our work suggests that gauge structures may significantly enrich non-Hermitian physics at the fundamental level.

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arXiv2023

Hermitian Topologies originating from non-Hermitian braidings

The complex energy bands of non-Hermitian systems braid in momentum space even in one dimension. Here, we reveal that the non-Hermitian braiding underlies the Hermitian topological physics with chiral symmetry under a general framework that unifies Hermitian and non-Hermitian systems. Particularly, we derive an elegant identity that equates the linking number between the knots of braiding non-Hermitian bands and the zero-energy loop to the topological invariant of chiral-symmetric topological phases in one dimension. Moreover, we find an exotic class of phase transitions arising from the critical point transforming different knot structures of the non-Hermitian braiding, which are not included in the conventional Hermitian topological phase transition theory. Nevertheless, we show the bulk-boundary correspondence between the bulk non-Hermitian braiding and boundary zero-modes of the Hermitian topological insulators. Finally, we construct typical topological phases with non-Hermitian braidings, which can be readily realized by artificial crystals.

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arXiv2022

Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals

We study non-Hermitian spatial symmetries -- a class of symmetries that have no counterparts in Hermitian systems -- and study how normal and exceptional semimetals can be stabilized by these symmetries. Different from internal ones, spatial symmetries act nonlocally in momentum space and enforce global constraints on both band degeneracies and topological quantities at different locations. In deriving general constraints on band degeneracies and topological invariants, we demonstrate that non-Hermitian spatial symmetries are on an equal footing with, but are essentially different from Hermitian ones. First, we discover the nonlocal Hermitian conjugate pair of exceptional or normal band degeneracies that are enforced by non-Hermitian spatial symmetries. Remarkably, we find that these pairs lead to the symmetry-enforced violation of the Fermion doubling theorem in the long-time limit. Second, with the topological constraints, we unravel that certain exceptional manifold is only compatible with and stabilized by non-Hermitian spatial symmetries but is intrinsically incompatible with Hermitian spatial symmetries. We illustrate these findings using two three-dimensional models of a non-Hermitian Weyl semimetal and an exceptional unconventional Weyl semimetal. Experimental cold-atom realizations of both models are also proposed.

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arXiv2022

Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry

We discover three-dimensional intertwined Weyl phases, by developing a theory to create topological phases. The theory is based on intertwining existing topological gapped and gapless phases protected by the same crystalline symmetry. The intertwined Weyl phases feature both unconventional Weyl semimetallic (monopole charge>1) and higher-order topological phases, and more importantly, their exotic intertwining. While the two phases are independently stabilized by the same symmetry, their intertwining results in the specific distribution of them in the bulk. The construction mechanism allows us to combine different kinds of unconventional Weyl semimetallic and higher-order topological phases to generate distinct phases. Remarkably, on 2D surfaces, the intertwining causes the Fermi-arc topology to change in a periodic pattern against surface orientation. This feature provides a characteristic and feasible signature to probe the intertwining Weyl phases. Moreover, we provide guidelines for searching candidate materials, and elaborate on emulating the intertwined double-Weyl phase in cold-atom experiments.

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arXiv2020

Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.

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arXiv2020

Higher-order Weyl superconductors with anisotropic Weyl-point connectivity

Weyl superconductors feature Weyl points at zero energy in the three-dimensional (3D) Brillouin zone and arc states that connect the projections of these Weyl points on the surface. We report that higher-order Weyl superconductors can be realized in odd-parity topological superconductors with time-reversal symmetry being broken by periodic driving. Different from conventional Weyl points, the higher-order Weyl points in the bulk separate 2D first- and second-order topological phases, while on the surface, their projections are connected not only by conventional surface Majorana arcs, but also by hinge Majorana arcs. We show that the Weyl-point connectivity via Majorana arcs is largely enriched by the underlying higher-order topology and becomes anisotropic with respect to surface orientations. We identify the anisotropic Weyl-point connectivity as a characteristic feature of higher-order Weyl materials. As each 2D subsystem can be singled out by fixing the periodic driving, we propose how the Majorana zero modes in the 2D higher-order topological phases can be detected and manipulated in experiments.

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arXiv2020

Topological and holonomic quantum computation based on second-order topological superconductors

Majorana fermions feature non-Abelian exchange statistics and promise fascinating applications in topological quantum computation. Recently, second-order topological superconductors (SOTSs) have been proposed to host Majorana fermions as localized quasiparticles with zero excitation energy, pointing out a new avenue to facilitate topological quantum computation. We provide a minimal model for SOTSs and systematically analyze the features of Majorana zero modes with analytical and numerical methods. We further construct the fundamental fusion principles of zero modes stemming from a single or multiple SOTS islands. Finally, we propose concrete schemes in different setups formed by SOTSs, enabling us to exchange and fuse the zero modes for non-Abelian braiding and holonomic quantum gate operations.

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arXiv2020

Phenomenology of the chiral $d$-wave state in the hexagonal pnictide superconductor SrPtAs

The pairing symmetry of the hexagonal pnictide superconductor SrPtAs is discussed with taking into account its multiband structure. The topological chiral $d$-wave state with time-reversal-symmetry breaking has been anticipated from the spontaneous magnetization observed by the muon-spin-relaxation experiment. We point out in this paper that the recent experimental reports on the nuclear-spin-lattice relaxation rate $T_1^{-1}$ and superfluid density $n_s(T)$, which seemingly support the conventional $s$-wave pairing, are also consistent with the chiral $d$-wave state. The compatibility of the gap and multiband structures is crucial in this argument. We propose that the measurement of the bulk quasiparticle density of states would be useful for the distinction between two pairing states.

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arXiv2019

$\mathcal{PT}$-symmetric non-Hermitian Dirac semimetals

Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems $\mathcal{PT}$ symmetry gives rise to stable and protected Dirac points. Here, we study a $\mathcal{PT}$-symmetric system which is both non-Hermitian and topological, namely a $\mathcal{PT}$-symmetric Dirac semimetal with non-Hermitian perturbations in three dimensions. We find that, in general, there are only two types of symmetry allowed non-Hermitian perturbations, namely non-Hermitian kinetic potentials, and non-Hermitian anti-commuting potentials. For both of these non-Hermitian potentials we investigate the band topology for open and periodic boundary conditions, determine the exceptional points, and compute the surface states. We find that with periodic boundary conditions, the non-Hermitian kinetic potential leads to exceptional rings, while the non-Hermitian anti-commuting potential generates exceptional spheres, which separate regions with broken $\mathcal{PT}$ symmetry from regions with unbroken $\mathcal{PT}$ symmetry. With open boundary conditions, the non-Hermitian kinetic potential induces a non-Hermitian skin effect which is localized on both sides of the sample due to symmetry, while the non-Hermitian anticommuting potential leads to Fermi ribbon surface states.

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arXiv2019

Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations

Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general classification and characterization of non-Hermitian Dirac models that describe the experimental systems is missing. Here, we present a systematic investigation of massive Dirac models on periodic lattices, perturbed by general non-Hermitian terms. We find that there are three different types of non-Hermitian terms. For each case we determine the bulk exceptional points, the boundary modes, and the band topology. Our findings serve as guiding principles for the design of applications, for example, in photonic lattices. For instance, periodic Dirac systems with non-Hermitian mass terms can be used as topological lasers. Periodic Dirac systems with non-Hermitian anti-commuting terms, on the other hand, exhibit exceptional points at the surface, whose non-trivial topology could be utilized for optical devices.

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arXiv2018

Topological transport in Dirac nodal-line semimetals

Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$. The stability of these Dirac rings is guaranteed by a quantized $\pm π$ Berry phase and their low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. Here we study the Berry-phase supported topological transport of $\mathcal{P}\mathcal{T}$ invariant nodal-line semimetals. We find that small inversion breaking allows for an electric-field induced anomalous transverse current, whose universal component originates from the parity anomaly. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, we propose a dumbbell device, which uses surface states to filter charges based on their momenta. Suggestions for experiments and device applications are discussed.

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arXiv2017

Surface magnetism in a chiral d-wave superconductor with hexagonal symmetry

Surface properties are examined in a chiral d-wave superconductor with hexagonal symmetry, whose one-body Hamiltonian possesses the intrinsic spin-orbit coupling identical to the one characterizing the topological nature of the Kane-Mele honeycomb insulator. In the normal state spin-orbit coupling gives rise to spontaneous surface spin currents, whereas in the superconducting state there exist besides the spin currents also charge surface currents, due to the chiral pairing symmetry. Interestingly, the combination of these two currents results in a surface spin polarization, whose spatial dependence is markedly different on the zigzag and armchair surfaces. We discuss various potential candidate materials, such as SrPtAs, which may exhibit these surface properties.

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