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We describe a three-dimensional crystalline topological insulator (TI) phase of matter that exhibits spontaneous polarization. This polarization results from the presence of (approximately) flat bands on the surface of such TIs. These flat…
A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal ($C_4$ in-plane) symmetry is not a necessary condition for the creation of…
Topological semimetals, such as Dirac, Weyl, or line-node semimetals, are gapless states of matter characterized by their nodal band structures and surface states. In this work, we consider layered (topologically trivial) insulating systems…
In higher-order topological insulators (HOTIs), topologically nontrivial phases are usually associated with the shift of Wannier centers to topologically nontrivial positions on the edges of the unit cells, and the emergence of fractional…
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic…
Granular conductors form an artificially engineered class of solid state materials wherein the microstructure can be tuned to mimic a wide range of otherwise inaccessible physical systems. At the same time, topological insulators (TIs) have…
We study stability of multiple conducting edge states in a topological insulator against all multi-particle perturbations allowed by the time-reversal symmetry. We model a system as a multi-channel Luttinger liquid, where the number of…
The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are…
We show that in crystalline insulators point group symmetry alone gives rise to a topological classification based on the quantization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the…
Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…
We demonstrate theoretically an atomic liquid phase that supports topologically nontrivial electronic structure. A minimum two-orbital model of liquid topological insulator in two dimensions is constructed within the framework of…
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…
An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a…
How do we uniquely identify a quantum phase, given its ground state wave-function? This is a key question for many body theory especially when we consider phases like topological insulators, that share the same symmetry but differ at the…
A topological boundary can be formed at the interface between a trivial and a topological insulator. The difference in the topological index across the junction leads to robust gapless surface states. Optical studies of these states are…
The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to 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…
(1) We show that if a presentation of the trivial group is "hard to trivialize", in the sense that lots of Tietze moves are necessary to transform it into the trivial presentation, then the associated presentation complex (which is a…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…