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We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multi-valley Dirac fermion surface states. We find that…
Recent years have seen multiple high-throughput studies reveal an immense number of topological materials through use of symmetry indicators. Despite this success, three-dimensional topological insulators (TI) admitting a band-gap larger…
Two new recently proposed classes of topological phases, namely fractons and higher order topological insulators (HOTIs), share at least superficial similarities. The wide variety of proposals for these phases calls for a universal field…
The major breakthroughs in the understanding of topological materials over the past decade were all triggered by the discovery of the Z$_2$ topological insulator (TI). In three dimensions (3D), the TI is classified as either "strong" or…
The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered…
Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been…
Topological insulators materialize a topological quantum state of matter where unusual gapless metallic state protected by time-reversal symmetry appears at the edge or surface. Their discovery stimulated the search for new topological…
Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of…
We construct an interacting lattice model for twisted $\mathrm{MoTe}_{2}$ bilayers at a twist angle of approximately 3.7\degree. We use the infinite density matrix renormalization group (iDMRG) in a cylinder geometry to identify a variety…
Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show that two distinct types of second-order…
The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual…
In two-dimensional electronic lattices, changes in the topology of the Fermi surface (Lifshitz transitions) lead to Van Hove singularities characterized by a divergence in the electronic density of states. Van Hove singularities can enhance…
Recently extended from the modern theory of electric polarization, quantized multipole topological insulators (QMTIs) describe higher-order multipole moments, lying in nested Wilson loops, which are inherently quantized by lattice…
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional…
Topological crystalline insulators (TCI) are a new class of materials which have metallic surface states on select surfaces due to point group crystalline symmetries. In this letter, we consider a model for a three-dimensional (3D)…
The field of topological photonics was initiated with the realization of a Chern insulator phase in a gyromagnetic photonic crystal (PhC) with broken time-reversal symmetry (T), hosting chiral edge states that are topologically protected…
Topological insulator (TI) represents an unconventional quantum phase of matter with insulating bulk bandgap and metallic surface states. Recent theoretical calculations and photoemission spectroscopy measurements show that Group V-VI…
While strong topological insulators (STI) have been experimentally realized soon after their theoretical predictions, a weak topological insulator (WTI) has yet to be unambiguously confirmed. A major obstacle is the lack of distinct natural…
The interplay between topology and correlations can generate a variety of quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe2 as a promising material for doing so in a highly tunable fashion.…