Related papers: Weakly Interacting Topological Insulators: Quantum…
A concrete strategy is presented for generating strong topological insulators in $d+d'$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and $d'$ the virtual dimensions. It consists of seeking…
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 phase transitions in a three-dimensional (3D) topological insulator (TI) with an exchange field of strength $g$ are studied by calculating spin Chern numbers $C^\pm(k_z)$ with momentum $k_z$ as a parameter. When $|g|$ exceeds a…
Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions occurring in 2D Dirac materials like silicene, which is isostructural with…
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of…
We investigate spontaneous and pumped entanglement of two level systems in the vicinity of a photonic topological insulator interface, which supports a nonreciprocal (unidirectional), scattering-immune and topologically-protected surface…
We address the topological classification of one-dimensional chiral symmetric interfaces embedded into a two-dimensional substrate. A proof of the validity of a topological classification based on the Green's function by explicit evaluation…
The defining feature of topological insulators is that their valence states are not continuously deformable to a suitably defined atomic limit without breaking the symmetry or closing the energy gap. When the atomic limit is given by…
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…
Topological Kondo insulator (TKI) is an essential example of interacting topological insulator, where electron's correlation effect plays a key role. However, most of our understanding on this timely issue comes from numerical simulations,…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
We consider a class of {\em quantum Hall topological insulators}: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counter-propagating edge states are protected by a symmetry (spatial or spin)…
In this work, we supply an engineering solution that paves the way to the implementation of the full classification table of topological insulators with passive acoustic crystals. As an example, we design an acoustic crystal displaying the…
Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to…
Recent years witnessed an extensive development of the theory of the critical point in two-dimensional statistical systems, which allowed to prove {\it existence} and {\it conformal invariance} of the {\it scaling limit} for two-dimensional…
We discuss the applicability of elementary band representations (EBRs) to diagnose spatial- and time-reversal-symmetry protected topological phases in interacting insulators in terms of their single-particle Green's functions. We do so by…
The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix…
Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and…
Interactions generically have important effects on the topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change the topological phase diagram which, however, is…
We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak coupling regime, long wavelength phonons may favor topological phases in Dirac insulators with direct and narrow bandgaps. This…