Topological quantum materials

Surfaces and edges are often used for characterizing the nontrivial topological properties in the bulk materials. The conventional wisdom tells us that such nontrivial edge and surface states can not be localized by elastic disorder scattering alone. I have been working on examples that show localized edge/surface states due to interplays of disorder and interaction. Surprisingly, the novel properties of localization (e.g., half-charge localization, localized Majorana zero modes, etc) exhibits the strong side of topological phases. Potential experimental signatures are discussed in our recent works. One of the key messages to experimentalists is that the trivial-looking surfaces/edges may turn out to be the exotic orders from interacting topological materials.

Phys. Rev. B 103, 075120 (2021)

Phys. Rev. B 99, 165108 (2019); Editors' suggestion.

Phys. Rev. B 98, 054205 (2018)

Also see a youtube video for a poster presentation in Localisation 2020

https://youtu.be/2C1mFhCh1fU

Recently, we study how does the anomaly of topological insulator coexists with the localized boundary. The relation to an unconventional low energy localization is also discussed.

Phys. Rev. B 101, 035131 (2020) 

Another important question is if the delocalized surface and edge states are stable against arbitrary small disorder and interaction. This was first undertaken by Foster and Yuzbashyan in 2012. It's demonstrated that the absence of delocalized surface state of 3D topological superconductor of class CI. The mechanism is known as the multifractal enhancement - interactions get stronger in certain critically delocalized single particle states. We numerically confirm multifractal spectra of the surface states follow conformal field theory predictions. In addition, we predict the absence of Altshuler-Aronov corrections on the interacting disordered surfaces. In the absence of such a mechanism, the surface quasiparticle transport is expected to be quantized - reminiscent of integer quantum Hall effect but in 3D.

Phys. Rev. B 89, 155140 (2014); Editors' suggestion.

Phys. Rev. B 89, 165136 (2014)

Phys. Rev. B 91, 024203 (2015)

A  somewhat controversial question is if the topological insulator edges can be affected by random Rashba spin orbit coupling. From the point of view from topology, the weak random Rashba spin orbit coupling should not affect the phase. However, there exists studies that advocate nontrivial corrections based on bosonization analysis. To settle this issue, we demonstrate that the low energy theory in the presence of random Rashba scatterings can be mapped to an exactly solvable model. Perfect ballistic conduction is predicted via transfer matrix formalism. We also argue that the Luttinger liquid interaction will not give any conductance correction.

Phys. Rev. Lett. 116, 086603 (2016)

At the boundary of two-dimensional time-reversal topological insulators, the robust gapless edge modes can be characterized by helical Luttinger liquid theory. Since the edge state is immuned from elastic impurity scatterings, they are expected to be better quantum wires for transport studies. In 2015, we suggested that a novel two-terminal measurement can reveal Luttinger liquid effect via  conductance. More recently, I pointed out a possibility of negative drag  among two dirty interacting helical Luttinger liquids. Finite temperature conductivity is also discussed.

Phys. Rev. B 99, 045125 (2019)

Phys. Rev. Lett. 115, 186404 (2015)

We also study the momentum resolved tunneling spectroscopy of the topological insulator edges. We provide a systematic theory incorporating disorder, interaction, and various other experimentally relevant features.

Phys. Rev. B 102, 085152 (2020)

Strong electron–electron interactions between adjacent nanoscale wires can lead to one-dimensional Coulomb drag, where current in one wire induces a voltage in the second wire via Coulomb interactions. This effect creates challenges for the development of nanoelectronic devices. Quantum spin Hall (QSH) insulators are a promising platform for the development of low-power electronic devices due to their topological protection of edge states from non-magnetic disorder. However, although Coulomb drag in QSH edges has been considered theoretically, experimental explorations of the effect remain limited. Here, we show that one-dimensional Coulomb drag can be observed between adjacent QSH edges that are separated by an air gap. The pair of one-dimensional helical edge states is created in split H-bar devices in inverted InAs/GaSb quantum wells. Near the Dirac point, negative drag signals dominate at low temperatures and exhibit a non-monotonic temperature dependence, suggesting that distinct drag mechanisms compete and cancel out at higher temperatures. The results suggest that QSH effects could be used to suppress the impact of Coulomb interactions on the performance of future nanocircuits.

https://www.nature.com/articles/s41928-021-00603-y

Theory is based on

Phys. Rev. B 99, 045125 (2019)

The stability of the Weyl point in the presence of disorder has been discussed extensively since the discovery of Weyl semimetal. From perturbative RG analysis, the nodal density of state is zero until the disorder exceeds a certain threshold. However, rare configuration of disorder can give an exponentially small but finite contribution in the density of states, A.K.A rare region effect. My contribution is to study the rare region effect via an analytical T-matrix technique. The self energy correction due to rare region can be obtained in the dilute impurity limit. With Kernel polynomial method, T matrix, and renormalization group analysis, we provide predictions of Green function which are related to ARPES and STM experiments. 

Phys. Rev. B 95, 235101 (2017); Editors' suggestion