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The bulk-boundary correspondence is a key concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z2 topology.…
The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I…
In the two-dimensional case the transition between ordinary and topological insulator states can be described by a massive Dirac model with the mass term changing its sign at the transition point. We theoretically investigate how such a…
Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such…
The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for…
Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
Energy dispersion and spin orientation of the protected states at interfaces between topological insulators (TIs) and non-topological materials depend on the charge redistribution, strain, and atomic displacement at the interface. Knowledge…
The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases and quantum information. While recent studies suggest that…
This paper discusses the topological and transport properties of binary heterostructures of different topological materials. The creation of multilayer devices is an alternative to building synthetic topological materials. By adjusting the…
Topological insulators are a class of solids in which the nontrivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity scattering. In three-dimensional (3D) topological insulators, however,…
Topological phases of matter are classified based on symmetries, with nonsymmorphic symmetries like glide reflections and screw rotations being of particular importance in the classification. In contrast to extensively studied glide…
Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be…
Topological superconductors (TSCs) in superconducting hybrid heterostructures, which integrate superconducting and non-superconducting materials, have been intensely investigated with the hope of discovering exotic non-Abelian anyons for…
The bulk-boundary correspondence plays a crucial role in topological quantum systems, however,this principle is broken in non-Hermitian systems. The breakdown of the bulk-boundary correspondence indicates that the global phase diagrams…
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving Dirac fermions that behave as massless relativistic particles. These Dirac fermions are responsible for achieving a…
The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It…
The interface between topological and normal insulators hosts metallic states that appear due to the change in band topology. While these topological states at a surface, i.e., a topological insulator-air/vacuum interface, have been studied…
A topological pump enables robust transport of quantized particles when the system parameters are varied in a cyclic process. In previous studies, topological pump was achieved inhomogeneous systems guaranteed by a topological invariant of…
We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. We present a formalism for…