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The bulk-boundary correspondence of the second-order topological insulator (SOTI) has been well established, but a universal transport signature for open systems is still absent. For a variety of SOTIs induced by applying in-plane magnetic…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
Two-dimensional topological insulators are central to our understanding of the connection between topological symmetries in a material and its band electronics. Within this class of materials, a breadth of complex quantum behaviors, such as…
Topological insulators (TIs) are characterized by an insulating bulk and symmetry protected bound state on their boundaries. A "strong" topological insulator is characterized by robust conducting states on \emph{all} boundaries protected by…
We study the effects of strong electron-electron interactions on the surface of cubic topological Kondo insulators (such as samarium hexaboride, SmB$_6$). Cubic topological Kondo insulators generally support three copies of massless Dirac…
We report on the site-resolved observation of characteristic states of the two-dimensional repulsive Fermi-Hubbard model, using ultracold $^{40}$K atoms in an optical lattice. By varying the tunneling, interaction strength, and external…
Quantum spin Hall edge transport in two-dimensional transition-metal dichalcogenides depends on whether their one-dimensional edge channels are preserved under realistic substrates and device boundaries. Here we implement spin-orbit…
The surface of a 3D topological insulator is conducting and the topologically nontrivial nature of the surface states is observed in experiments. It is the aim of this paper to review and analyze experimental observations with respect to…
Presence of entangled states is explicitly shown in Topological insulator (TI) $Bi_2Te_3$. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the…
We investigate the influence of nuclear spins on the resistance of helical edge states of two-dimensional topological insulators (2DTIs). Via the hyperfine interaction, nuclear spins allow electron backscattering, otherwise forbidden by…
We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of 7 families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric/magnetic charges. We show…
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
We theoretically investigate a two-dimensional heterostructure composed of a topological insulator (TI) and a Mott insulator (MI), and clarify what kind of electronic states can be realized at the interface. By using inhomogeneous dynamical…
Topological band insulators have recently been discovered in spin-orbit coupled two and three dimensional systems. In this work, we theoretically predict a class of topological Mott insulators where interaction effects play a dominant role.…
Shortly after the discovery of topological band insulators, topological Kondo insulators (TKIs) have also been theoretically predicted. The latter has ignited revival interest in the properties of Kondo insulators. Currently, the…
Topologically-protected edge states are dissipationless conducting surface states immune to impurity scattering and geometrical defects that occur in electronic systems characterized by a bulk insulating gap. One example can be found in a…
Recently, the field of strongly correlated electrons has begun an intense search for a correlation induced topological insulating phase. An example is the quadratic band touching point which arises in a checkerboard lattice at half-filling,…
We present a microscopic model for a strongly repulsive electron gas on a 2D square lattice. We suggest that nearest neighbor Coulomb repulsion stabilizes a state in which electrons undergo a "somersault" in their internal spin-space…
Heavy fermion materials naturally combine strong spin-orbit interactions and electronic correlations. When there is precisely one conduction electron per impurity spin, the coherent heavy fermion state is insulating. This Kondo insulating…