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We investigate the stability of the one-dimensional limit of $\nu=1/3$ Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and…
Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
We extend the Berry-phase concept of polarization to insulators having a non-zero value of the Chern invariant. The generalization to such Chern insulators requires special care because of the partial occupation of chiral edge states. We…
The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…
The recent discovery of Dirac semimetals represents a new achievement in our fundamental understanding of topological states of matter. Due to their topological surface states, high mobility, and exotic properties associated with bulk Dirac…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…
Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of…
We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients…
Chern insulator is a building block of many topological quantum matters, ranging from quantum spin Hall insulators to fractional Chern insulators. Here, we discuss a new type of insulator, which consists of two half filled ordinary Chern…
We report anisotropic Dirac-cone surface bands on a side-surface geometry of the topological insulator Bi$_2$Se$_3$ revealed by first-principles density-functional calculations. We find that the electron velocity in the side-surface Dirac…
Fractional Chern insulators arise in topologically nontrivial flat bands, characterized by an integer Chern number C that corresponds to the number of dissipationless edge states in the non-interacting regime. Higher Chern numbers can…
Dirac semimetals are renowned for the host of singular symmetry-protected band degeneracies which can give rise to other exotic phases. In this work, we consider a two-dimensional Dirac semimetal stabilized by PT symmetry and nonsymmorphic…
We re-examine the band structure of the stripe charge ordered state of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure by using an extended Hubbard model within the Hartree mean-field theory. By increasing pressure, we find a topological…
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…
It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges.…
Topological insulators represent a new state of matter where the topological nature of the bulk bands dictates the existence of a surface state with unique properties. These materials are predicted to host exotic states such as Majorana…
We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge". The existence of these edge…
The surface states of the three dimensional (3D) Topological Insulators are described by two-dimensional (2D) massless dirac equation. A gate voltage induced one dimensional potential barrier on such surface creates a discrete bound state…
Topologically protected edge states are the highlight feature of an interface between non-equivalent insulators. The robustness/sensitivity of these states to local single-particle perturbations is well understood, while their stability in…