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The topological response to external perturbations is an effective probe to characterize different topological phases of matter. Besides the Hall conductance, the Hall viscosity is another example of such a response that measures how…
We study the transport properties of topological insulators, encoding them in a generating functional of gauge and gravitational sources. Much of our focus is on the simple example of a free massive Dirac fermion, the so-called Chern…
We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT…
The nondissipative (Hall) viscosity is known to play an interesting role in two-dimensional (2D) topological states of matter, in the hydrodynamic regime of correlated materials, and in classical active fluids with broken time-reversal…
Multi-terminal topological devices are a new generation of electronic devices with quantized properties robust against imperfections. In magnetic topological insulators, dissipationless edge states give functional devices in zero magnetic…
The strong topological insulator in 3D is expected to realize a quantized magneto-electric response, the so-called axion response. However, many of the materials predicted to be topological insulators have turned out to be metallic, with…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
Time Reversal Symmetry (TRS) broken topological phases provide gapless surface states protected by topology, regardless of additional internal symmetries, spin or valley degrees of freedom. Despite the numerous demonstrations of 2D…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
We study a two-dimensional (2D) tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate…
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…
We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic 2D Chern insulator…
Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active…
Thermal noise can destroy topological insulators (TI). However we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian,…
Two-dimensional (2D) topological insulators (TIs) hold promise for applications in spintronics based on the fact that the propagation direction of edge electrons of a 2D TI is robustly linked to their spin origination. Here, with the use of…
Chern insulators, which are the lattice analogs of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices. To date, integer Chern…
We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The…
Considerable efforts have recently been devoted to the experimental realization of a two-dimensional Chern insulator, i.e., a system displaying a quantum anomalous Hall effect. However, existing approaches such as those based on magnetic…
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…
The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions…