skip to main content

Title: Breakdown of conventional winding number calculation in one-dimensional lattices with interactions beyond nearest neighbors

Topological insulators hold promises to realize exotic quantum phenomena in electronic, photonic, and phononic systems. Conventionally, topological indices, such as winding numbers, have been used to predict the number of topologically protected domain-wall states (TPDWSs) in topological insulators, a signature of the topological phenomenon called bulk-edge correspondence. Here, we demonstrate theoretically and experimentally that the number of TPDWSs in a mechanical Su-Schrieffer-Heeger (SSH) model can be higher than the winding number depending on the strengths of beyond-nearest-neighbor interactions, revealing the breakdown of the winding number prediction. Alternatively, we resort to the Berry connection to accurately characterize the number and spatial features of TPDWSs in SSH systems, further confirmed by the Jackiw-Rebbi theory proving that the multiple TPDWSs correspond to the bulk Dirac cones. Our findings deepen the understanding of complex network dynamics and offer a generalized paradigm for precise TPDWS prediction in potential applications involving localized vibrations, such as drug delivery and quantum computing.

more » « less
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Nature Publishing Group
Date Published:
Journal Name:
Communications Physics
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Interest in topological states of matter burgeoned over a decade ago with the theoretical prediction and experimental detection of topological insulators, especially in bulk three-dimensional insulators that can be tuned out of it by doping. Their superconducting counterpart, the fully-gapped three-dimensional time-reversal-invariant topological superconductors, have evaded discovery in bulkintrinsic superconductorsso far. The recently discovered topological metalβ-PdBi2is a unique candidate for tunable bulk topological superconductivity because of its intrinsic superconductivity and spin-orbit-coupling. In this work, we provide experimental transport signatures consistent with fully-gapped 3D time-reversal-invariant topological superconductivity in K-dopedβ-PdBi2. In particular, we find signatures of odd-parity bulk superconductivity via upper-critical field and magnetization measurements— odd-parity pairing can be argued, given the band structure ofβ-PdBi2, to result in 3D topological superconductivity. In addition, Andreev spectroscopy reveals surface states protected by time-reversal symmetry which might be possible evidence of Majorana surface states (Majorana cone). Moreover, we find that the undoped bulk system is a trivial superconductor. Thus, we discoverβ-PdBi2as a unique bulk material that, on doping, can potentially undergo an unprecedented topological quantum phase transition in the superconducting state.

    more » « less
  2. BACKGROUND The past decade has witnessed considerable progress toward the creation of new quantum technologies. Substantial advances in present leading qubit technologies, which are based on superconductors, semiconductors, trapped ions, or neutral atoms, will undoubtedly be made in the years ahead. Beyond these present technologies, there exist blueprints for topological qubits, which leverage fundamentally different physics for improved qubit performance. These qubits exploit the fact that quasiparticles of topological quantum states allow quantum information to be encoded and processed in a nonlocal manner, providing inherent protection against decoherence and potentially overcoming a major challenge of the present generation of qubits. Although still far from being experimentally realized, the potential benefits of this approach are evident. The inherent protection against decoherence implies better scalability, promising a considerable reduction in the number of qubits needed for error correction. Transcending possible technological applications, the underlying physics is rife with exciting concepts and challenges, including topological superconductors, non-abelian anyons such as Majorana zero modes (MZMs), and non-abelian quantum statistics.­­ ADVANCES In a wide-ranging and ongoing effort, numerous potential material platforms are being explored that may realize the required topological quantum states. Non-abelian anyons were first predicted as quasiparticles of topological states known as fractional quantum Hall states, which are formed when electrons move in a plane subject to a strong perpendicular magnetic field. The prediction that hybrid materials that combine topological insulators and conventional superconductors can support localized MZMs, the simplest type of non-abelian anyon, brought entirely new material platforms into view. These include, among others, semiconductor-superconductor hybrids, magnetic adatoms on superconducting substrates, and Fe-based superconductors. One-dimensional systems are playing a particularly prominent role, with blueprints for quantum information applications being most developed for hybrid semiconductor-superconductor systems. There have been numerous attempts to observe non-abelian anyons in the laboratory. Several experimental efforts observed signatures that are consistent with some of the theoretical predictions for MZMs. A few extensively studied platforms were subjected to intense scrutiny and in-depth analyses of alternative interpretations, revealing a more complex reality than anticipated, with multiple possible interpretations of the data. Because advances in our understanding of a physical system often rely on discrepancies between experiment and theory, this has already led to an improved understanding of Majorana signatures; however, our ability to detect and manipulate non-abelian anyons such as MZMs remains in its infancy. Future work can build on improved materials in some of the existing platforms but may also exploit new materials such as van der Waals heterostructures, including twisted layers, which promise many new options for engineering topological phases of matter. OUTLOOK Experimentally establishing the existence of non-abelian anyons constitutes an outstandingly worthwhile goal, not only from the point of view of fundamental physics but also because of their potential applications. Future progress will be accelerated if claims of Majorana discoveries are based on experimental tests that go substantially beyond indicators such as zero-bias peaks that, at best, suggest consistency with a Majorana interpretation. It will be equally important that these discoveries build on an excellent understanding of the underlying material systems. Most likely, further material improvements of existing platforms and the exploration of new material platforms will both be important avenues for progress toward obtaining solid evidence for MZMs. Once that has been achieved, we can hope to explore—and harness—the fascinating physics of non-abelian anyons such as the topologically protected ground state manifold and non-abelian statistics. Proposed topological platforms. (Left) Proposed state of electrons in a high magnetic field (even-denominator fractional quantum Hall states) are predicted to host Majorana quasiparticles. (Right) Hybrid structures of superconductors and other materials have also been proposed to host such quasiparticles and can be tailored to create topological quantum bits based on Majoranas. 
    more » « less
  3. Abstract

    Two-dimensional topological insulators can feature one-dimensional charge transport via edge modes, which offer a rich ground for studying exotic quasi-particles and for quantum materials applications. In this work, we use lateral junction devices, defined by nanoscale finger gates, to study edge mode transport in the two-dimensional topological insulator Cd3As2. The finger gate can be tuned to transmit an integer number of quantum Hall edge modes and exhibits full equilibration in the bipolar regime. When the Fermi level of the channel crosses a Landau level, reflected modes percolate through the channel, resulting in an anomalous conductance peak. The device does not fully pinch off when the channel is tuned into the topological gap, which is a sign of remnant modes in the channel. These modes are expected from band inversion, while residual bulk conduction associated with the disorder potential may also play a role.

    more » « less
  4. Abstract

    Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($${{{{{{{\mathcal{T}}}}}}}}$$T-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and$${{{{{{{\mathcal{T}}}}}}}}$$T-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate thatβ-MoTe2realizes a spin-Weyl state and thatα-BiBr hosts both 3D QSHI and T-DAXI regimes.

    more » « less
  5. Abstract

    The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well‐known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.

    more » « less