Related papers: A mono-atomic orbital-based 1D topological crystal…
In principle the stacking of different two-dimensional (2D) materials allows the construction of 3D systems with entirely new electronic properties. Here we propose to realize topological crystalline insulators (TCI) protected by mirror…
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…
The interplay between topology and crystalline symmetries in materials can lead to a variety of topological crystalline insulator (TCI) states. Despite significant effort towards their experimental realization, so far only…
We present microscopic Hamiltonians that gap the Dirac fermions on the surface of topological crystalline insulators (TCIs) protected by reflection symmetry and create symmetry-preserving states with Abelian topological orders. For TCIs…
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)…
Topological crystalline insulators (TCIs) possess metallic surface states protected by crystalline symmetry, which are a versatile platform for exploring topological phenomena and potential applications. However, progress in this field has…
Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…
The defining feature of topological insulators is that their valence states are not continuously deformable to a suitably defined atomic limit without breaking the symmetry or closing the energy gap. When the atomic limit is given by…
Most topological insulators discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the…
We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…
Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
Understanding crystal shapes is a fundamental subject in surface science. It is now well studied how chemical bondings determine crystal shapes via dependence of surface energies on surface orientations. Meanwhile, discoveries of…
Topological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries \^C$_n$, which have…
Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum…
Higher-order topological insulators (HOTIs) are described by symmetric exponentially decayed Wannier functions at some $necessary$ unoccupied Wyckoff positions and classified as obstructed atomic insulators (OAIs) in the topological quantum…
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…
We study equilibrium crystal shapes of a topological insulator (TI), a topological crystalline insulator (TCI) protected by mirror symmetry, and a second-order topological insulator (SOTI) protected by inversion symmetry. By adding magnetic…
In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological…
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation…