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Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing…

We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the…

Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…

Topological insulators (TIs) are a novel class of materials with nontrivial surface or edge states. Time-reversal symmetry (TRS) protected TIs are characterized by the Z2 topological invariant and their helical property becomes lost in an…

In recent years, a class of solid state materials, called three-dimensional topological insulators, has emerged. In the bulk, a topological insulator behaves like an ordinary insulator with a band gap. At the surface, conducting gapless…

A second-order topological insulator on a two-dimensional square lattice hosts zero-dimensional states inside a band gap. They are localized near $90^{\circ}$ and $270^{\circ}$ corners constituting an edge of the system. When the edge is in…

When time reversal symmetry is present there is a sharp distinction between topological and trivial band insulators which ensures that, as parameters are varied, these phases are separated by a phase transition at which the bulk gap closes.…

Topological insulators (TIs) are materials that have a bulk electronic band gap like an ordinary insulator but have protected conducting states on their surface. One of the most interesting properties of TIs is their spin helicity, whereby…

We propose new two-dimensional (2D) topological insulators (TIs) in functionalized germanenes (GeX, X=H, F, Cl, Br or I) using first-principles calculations. We find GeI is a 2D TI with a bulk gap of about 0.3 eV, while GeH, GeF, GeCl and…

The counterpropagating edge states of a two-dimensional topological insulator (TI) carry electrons of opposite spins. We investigate the transport properties of edge states in a two-dimensional TI which is contacted to ferromagnetic leads.…

The prospective of optically inducing a spin polarized current for spintronic devices has generated a vast interest in the out-of-equilibrium electronic and spin structure of topological insulators (TIs). In this Letter we prove that only…

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…

We predict a new class of three-dimensional topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate a large band gap at $\Gamma$ point. The band gap of conventional TI such as Bi$_2$Se$_3$ is mainly…

Topological insulators are new states of matter with a bulk gap and robust gapless surface states protected by time-reversal symmetry. When time-reversal symmetry is broken, the surface states are gapped, which induces a topological…

Topological insulators are insulating in the bulk but possess spin-momentum locked metallic surface states protected by time-reversal symmetry. The existence of these surface states has been confirmed by angle-resolved photoemission…

In magnetic topological insulators, the surface states can exhibit a gap due to the breaking of time-reversal symmetry. Various experiments, while suggesting the existence of the surface gap, have raised questions about its underlying…

Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…

As the thickness of a three-dimensional (3D) topological insulator (TI) becomes comparable to the penetration depth of the surface states, quantum tunneling between surfaces turns their gapless Dirac electronic structure into a gapped…

Topological insulators (TIs) are a unique class of materials characterized by a surface (edge) Dirac cone state of helical Dirac fermions in the middle of bulk (surface) gap. When the thickness (width) of TIs is reduced, however,…

A striking feature of time reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when the surface states are gapped by time reversal breaking…