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Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a…
Single-Dirac-cone topological insulators (TI) are the first experimentally discovered class of three dimensional topologically ordered electronic systems, and feature robust, massless spin-helical conducting surface states that appear at…
Hybrid structures between conventional, s-wave superconductors and two-dimensional topological insulators (2D TIs) are a promising route to topological superconductivity. Here, we investigate planar Josephson junctions fabricated from…
Topological photonics and acoustics have recently garnered wide research interests for their topological ability to manipulate the light and sound at surfaces. Conventionally, the supercell technique is the standard approach to calculating…
We investigate interaction effects in three dimensional weak topological insulators (TI) with an even number of Dirac cones on the surface. We find that the surface states can be gapped by a surface charge density wave (CDW) order without…
Aiming at the future spintronics device applications of the spin-polarized surface states in three-dimensional topological insulator, a highly insulating bulk state and a tunable Dirac cone surface state are required. Here we employ a slab…
Three-dimensional topological insulators (3D-TIs) are a new generation of materials with insulating bulk and exotic metallic surface states that facilitate a wide variety of ground-breaking applications. However, utilization of the surface…
Topological insulators (TIs) are a new quantum state of matter. Their surfaces and interfaces act as a topological boundary to generate massless Dirac fermions with spin-helical textures. Investigation of fermion dynamics near the Dirac…
Two-dimensional (2D) topological insulators (TIs) are promising platforms for low-dissipation spintronic devices based on the quantum spin Hall (QSH) effect, but experimental realization of such systems with a large band gap suitable for…
We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling. Higher dimensional generalizations of flat…
We derive a general low-energy theory for twisted moir\'e heterostructures comprised of Dirac materials. We apply our theory to heterostructures on the surface of a three dimensional topological insulator (3D TI). First, we consider the…
Topological materials host fascinating low dimensional gapless states at the boundary. As a prominent example, helical topological edge states (TESs) of two-dimensional topological insulators (2DTIs) and their stacked three-dimensional (3D)…
2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…
Three dimensional (3D) topological insulators are quantum materials with a spin-orbit induced bulk insulating gap that exhibit quantum-Hall-like phenomena in the absence of applied magnetic fields. The proposed applications of topological…
The non-trivial topology of the three-dimensional (3D) topological insulator (TI) dictates the appearance of gapless Dirac surface states. Intriguingly, when a 3D TI is made into a nanowire, a gap opens at the Dirac point due to the quantum…
The electronic states of a single Bi(111) bilayer and its edges, suggested as a two dimensional topological insulator, are investigated by scanning tunneling spectroscopy (STS) and first-principles calculations. Well-ordered bilayer films…
Three-dimensional topological crystalline insulators were recently predicted and observed in the SnTe class of IV-VI semiconductors, which host metallic surface states protected by crystal symmetries. In this work, we study thin films of…
We review the contributions of surface science methods to discover and improve 3D topological insulator materials, while illustrating with examples from our own work. In particular, we demonstrate that spin-polarized angular-resolved…
We have performed scanning tunneling microscopy and differential tunneling conductance ($dI/dV$) mapping for the surface of the three dimensional topological insulator Bi$_{2}$Se$_{3}$. The fast Fourier transformation applied to the $dI/dV$…
We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based…