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Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting…
Motivated by recent advances in digital quantum emulation using noisy intermediate-scale quantum (NISQ) devices and an increased interest in topological Green's function zeros in condensed matter systems, we here study Green's function…
This paper analyzes Floquet topological insulators resulting from the time-harmonic irradiation of electromagnetic waves on two dimensional materials such as graphene. We analyze the bulk and edge topologies of approximations to the…
Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground…
We apply mean-field theory and Hirsch-Fye quantum Monte Carlo method to study the spin-spin interaction in the bulk of three-dimensional topological insulators. We find that the spin-spin interaction has three different components: the…
We study the Haldane model with nearest-neighbor interactions. This model is physically motivated by the associated ultracold atoms implementation. We show that the topological phase of the interacting model can be characterized by a…
We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A…
Ultracold atom experiments allow the study of topological insulators, such as the noninteracting Haldane model. In this work we study a generalization of the Haldane model with spin-spin on-site interactions that can be implemented on such…
We study one-dimensional topological superconductivity in the presence of time-reversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zero-energy Majorana bound states at each of its ends.…
We study interaction induced topological phase transition in Bernevig-Hughes-Zhang model. Topological nature of the phase transition is revealed by directly calculating the Z2 index of the interacting system from the single-particle Green's…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
The poor performance of copper interconnects at the nanometer scale calls for new material solutions for continued scaling of integrated circuits. We propose the use of three dimensional time-reversal-invariant topological insulators (TIs),…
We discuss detection strategies for fractional topological insulators (FTIs) realizing time-reversal invariant analogues of fractional quantum Hall systems in the Laughlin universality class. Focusing on transport measurements, we study the…
The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a $p$-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench…
Topological insulators can be generally defined by a topological field theory with an axion angle theta of 0 or pi. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that…
We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion…