Related papers: Topological classification of crystalline insulato…
We develop an approach to design, engineer, and measure band structures in a synthetic crystal composed of electric circuit elements. Starting from the nodal analysis of a circuit lattice in terms of currents and voltages, our Laplacian…
A domain wall separating two different topological phases of the same crystal can support the propagation of backscattering-immune guided waves. In valley-Hall and quantum-Hall crystal waveguides, this property stems from symmetry…
Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter…
The topological characterization of nonequilibrium topological matter is highly nontrivial because familiar approaches designed for equilibrium topological phases may not apply. In the presence of crystal symmetry, Floquet topological…
Topological band insulators and (semi-) metals can arise out of atomic insulators when the hopping strength between electrons increases. Such topological phases are separated from the atomic insulator by a bulk gap closing. In this work, we…
We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…
We show that a hierarchy of topological phases in one dimension -- a topological Devil's staircase -- can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a…
Topologically trivial insulators are classified into two primary categories: unobstructed and obstructed atomic insulators. While both types can be described by exponentially localized Wannier orbitals, a defining feature of obstructed…
Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions.…
When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a…
An important aspect in categorizing topological phases is whether the system is spinless or spinful, given that these classes exhibit distinct symmetry algebras, leading to disparate topological classifications. By utilizing the projective…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…
We develop a lattice model which exhibits topological transitions from $Z_2$ topological insulators to mirror symmetry-protected topological crystalline insulators by introducing additional spin-orbit coupling terms. The topological phase…
Topological surface states, a new kind of electronic state of matter, have recently been observed on the cleaved surfaces of crystals of a handful of small band gap semiconductors. The underlying chemical factors that enable these states…
We present the theory and experimental demonstration of a topological classification of finite tight binding Hamiltonians with chiral symmetry. Using the graph-theoretic notion of complete matchings, we show that many chiral tight binding…
The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical…
The theoretical identification of crystalline topological materials has enjoyed sustained success in simplified materials models, often by singling out discrete symmetry operations protecting the topological phase. When band structure…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…