Resolving the Topological Classification of Bismuth with Topological Defects

Abstract

Bulk boundary correspondence in topological materials allows to study their bulk topology through the investigation of their topological boundary modes. However, for classes that share similar boundary phenomenology, the growing diversity of topological phases may lead to ambiguity in the topological classification of materials. Such is the current status of bulk bismuth. While some theoretical models indicate that bismuth possesses a trivial topological nature, other theoretical and experimental studies suggest non-trivial topological classifications such as a strong or a higher order topological insulator, both of which hosts helical modes on their boundaries. Here we use a novel approach to resolve the topological classification of bismuth by spectroscopically mapping the response of its boundary modes to a topological defect in the form of a screw dislocation (SD). We find that the edge mode extends over a wide energy range, and withstands crystallographic irregularities, without showing any signs of backscattering. It seems to bind to the bulk SD, as expected for a topological insulator (TI) with non-vanishing weak indices. We argue that the small scale of the bulk energy gap, at the time reversal symmetric momentum $L$, positions bismuth within the critical region of a topological phase transition to a strong TI with non-vanishing weak indices. We show that the observed boundary modes are approximately helical already on the ${\mathbb{Z}}_2$ trivial side of the topological phase transition. This work opens the door for further possibilities to examine the response of topological phases to crystallographic topological defects, and to uniquely explore their associated bulk boundary phenomena.

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• First Principles Calculations for Topological Quantum Materials
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• Topological dislocation modes in three-dimensional acoustic topological insulators
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• Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators
• Dislocation as a bulk probe of higher-order topological insulators
• Bound states at partial dislocation defects in multipole higher-order topological insulators
• Anomalous and normal dislocation modes in Floquet topological insulators
• Helical Liquids in Semiconductors
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown inside van der Waals materials
• Dislocation defect as a bulk probe of monopole charge of multi-Weyl semimetals
• Symmetry dictated grain boundary state in a two-dimensional topological insulator
• Photo-induced electronic and spin topological phase transitions in monolayer bismuth
• Observation of backscattering induced by magnetism in a topological edge state
• Projected Topological Branes
• $Z_2$ topology of bismuth
• Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction
• Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure
• Boundary conductance in macroscopic bismuth crystals
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• Surface Modification and Subsequent Fermi Density Enhancement of Bi(111)
• Topologically distinct atomic insulators
• Topological field-effect transistor with quantized ON/OFF conductance of helical/chiral dislocation states
• Topological Wannier cycles for the bulk and edges
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Grain-boundary topological superconductor
• Probing fragile topology with a screw dislocation
• Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer
• Dynamic melting and condensation of topological dislocation modes
• Selective branching, quenching, and converting of topological modes
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Hybrid symmetry class topological insulators
• High-field immiscibility of electrons belonging to adjacent twinned bismuth crystals
• Dispersive nodal fermions along grain boundaries in Floquet topological crystals
• Visualizing near-coexistence of massless Dirac electrons and ultra-massive saddle point electrons
• Fragile dislocation modes in obstructed atomic topological phases
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Detecting and Distinguishing Majorana Zero Modes with the Scanning Tunneling Microscope
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Topological Dislocation Response in Elementary Semiconductors
• Intrinsic one-dimensional conducting channels in the Kondo insulator SmB6