Related papers: Type-II quadrupole topological insulators
Three-dimensional topological insulators are characterized by the presence of protected gapless spin helical surface states. In realistic samples these surface states are extended from one surface to another, covering the entire sample.…
The interface between a superconductor and a topological insulator has been proposed to harbor novel quasiparticles that realize physical schemes for fault-tolerant quantum computation. Here, we present high resolution angle-resolved…
Although topological materials have recently seen tremendous development, their applications have remained elusive. Simultaneously, there exists considerable interest in pushing the limits of topological materials, including the exploration…
We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…
The topology of the Brillouin zone, foundational in topological physics, is always assumed to be a torus. We theoretically report the construction of Brillouin real projective plane ($\mathrm{RP}^2$) and the appearance of quadrupole…
Quantized bulk quadrupole moment has unveiled a nontrivial boundary state, exhibiting lower-dimensional topological edge states and simultaneously hosting the in-gap corner modes of zero dimension. All state-of-the-art strategies for…
A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…
Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
Insulating systems are characterized by their insensitivity to twisted boundary conditions as quantified by the charge stiffness and charge localization length. The latter quantity was shown to be related to the expectation value of the…
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically…
Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological…
Chiral surface states in topological insulators are robust against interactions, non-magnetic disorder and localization, yet topology does not yield protection in transport. This work presents a theory of interacting topological insulators…
Recent advancements in quantum polarization theory have propelled the exploration of topological insulators (TIs) into the realm of higher-order systems, leading to the study of the celebrated two-dimensional (2D) quadrupole and…
The modern theory of polarization allows for the determination of the macroscopic end charge of a truncated one-dimensional insulator, modulo the charge quantum $e$, from a knowledge of bulk properties alone. A more subtle problem is the…
The discovery of the topological insulators has fueled a surge of interests in the topological phases in periodic systems. Topological insulators have bulk energy gap and topologically protected gapless edge states. The edge states in…
Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian {topologies that thrive on involving multiple gaps} were studied, unveiling a new horizon {in topological…
Existence of robust edge modes at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, topological insulators. Such electronic states were originally predicted…
Type-II hyperbolic lattices constitute a new class of hyperbolic structures that are projected onto the Poincar\'{e} ring and possess both an inner and an outer boundary. In this work, we reveal the higher-order topological phases in…