How Do You Want That Insulator?

A normal insulator is turned into an exotic topological insulator by tuning its elemental composition.Comment: Science Perspective article on arXiv:1104.463

Topological phases and phase transitions on the square-octagon lattice

We theoretically investigate a tight binding model of fermions hopping on the square-octagon lattice which consists of a square lattice with plaquette corners themselves decorated by squares. Upon the inclusion of second neighbor spin-orbit coupling or non-Abelian gauge fields, time-reversal symmetric topological Z_2 band insulators are realized. Additional insulating and gapless phases are also realized via the non-Abelian gauge fields. Some of the phase transitions involve topological changes to the Fermi surface. The stability of the topological phases to various symmetry breaking terms is investigated via the entanglement spectrum. Our results enlarge the number of known exactly solvable models of Z_2 band insulators, and are potentially relevant to the realization and identification of topological phases in both the solid state and cold atomic gases.Comment: 12 pages, 9 figure

Coulomb drag between helical edge states

We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall systems. Using an interacting theory of the one-dimensional helical edge modes, we show that the drag vanishes at second order in the inter-edge interaction, where it is typically finite in other systems, due to the absence of backscattering within the edges. However, in the presence of a small external magnetic field the drag is finite and scales as the fourth power of the magnetic field, a behavior that sharply distinguishes it from other systems. We obtain the temperature dependence of the drag for regimes of both linear and quadratic edge dispersion in the presence of a finite field.Comment: 4 pages, 3 figure

Magnetic adatom induced skyrmion-like spin texture in surface electron waves

When a foreign atom is placed on a surface of a metal, the surrounding sea of electrons responds screening the additional charge leading to oscillations or ripples. On surfaces, those electrons are sometimes confined to two-dimensional surface states, whose spin-degeneracy is lifted due to the Rashba effect arising from the spin-orbit interaction of electrons and the inversion asymmetric environment. It is believed that at least for a single adatom scanning tunneling microscopy measurements are insensitive to the Rashba splitting i.e. no signatures in the charge oscillations will be observed. Resting on scattering theory, we demonstrate that, if magnetic, one single adatom is enough to visualize the presence of the Rashba effect in terms of an induced spin-magnetization of the surrounding electrons exhibiting a twisted spin texture described as superposition of two skyrmionic waves of opposite chirality.Comment: 11 pages, 5 figures, accepted in Phys. Rev. Letter

Impact of clustering of substitutional impurities on quasiparticle lifetimes and localization

Motivated by the observation and prediction of clustering behavior for impurities substituted into the host lattice of a real material, and the dramatic impact this can have on electronic properties, we develop a simple approach to describe such an effect via the electron self-energy. We employ a disorder averaged T-matrix expansion taken to second order, which we modify to include a clustering probability parameter. This approach circumvents the need for specific cluster probability distributions, simplifying greatly the analysis of clustered impurities. To gain analytical insights, we study a nearest-neighbor square lattice tight-binding Hamiltonian with clustered impurity substitutions to investigate clustering of off-diagonal hopping impurities. We find that our T-matrix approach is in excellent agreement with exact numerical results from a tight-binding computation performed with the KWANT package. We observe a variety of interesting impurity clustering-induced effects in the self-energy such as the suppression of quasi-particle lifetimes at certain momenta and an increase in localization, as indicated by the inverse participation ratio. The KWANT results are reproduced in our modified T-matrix approach. In addition, our method allows for a full analytical treatment of clustering effects which can aid in physical insight.Comment: 8 pages, 6 figure

Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States

We study the physics of electron tunneling between multiple quantum dots and the edge of a quantum Hall state. Our results generalize earlier work [G. A. Fiete, W. Bishara, C. Nayak, Phys. Rev. Lett. 101, 176801 (2008)] in which it was shown that a single quantum dot tunnel coupled to a non-Abelian quantum Hall state can realize a stable multi-channel Kondo fixed point at low-energy. In this work, we investigate the physics of multiple dots and find that a rich set of possible low-energy fixed points arises, including those with non-Fermi liquid properties. Previously unidentified fixed points may also be among the possibilities. We examine both the situation where the dots are spatially separated and where they are in close proximity. We discuss the relation to previous work on two-impurity Kondo models in Fermi liquids and highlight new research directions in multiple quantum impurity problems.Comment: 12 pages, 2 figure

Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides

The expected phenomenology of non-interacting topological band insulators (TBI) is now largely theoretically understood. However, the fate of TBIs in the presence of interactions remains an active area of research with novel, interaction-driven topological states possible, as well as new exotic magnetic states. In this work we study the magnetic phases of an exchange Hamiltonian arising in the strong interaction limit of a Hubbard model on the honeycomb lattice whose non-interacting limit is a two-dimensional TBI recently proposed for the layered heavy transition metal oxide compound, (Li,Na)$_2$IrO$_3$. By a combination of analytical methods and exact diagonalization studies on finite size clusters, we map out the magnetic phase diagram of the model. We find that strong spin-orbit coupling can lead to a phase transition from an antiferromagnetic Ne\'el state to a spiral or stripy ordered state. We also discuss the conditions under which a quantum spin liquid may appear in our model, and we compare our results with the different but related Kitaev-Heisenberg-$J_2$-$J_3$ model which has recently been studied in a similar context.Comment: 12 pages, 8 figure

Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.Comment: 9 pages, 9 figure

Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

In this paper we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to the spatially proximate bulk non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a $k$-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction $\nu=2+k/(k+2)$ or its particle-hole conjugate at $\nu=2+2/(k+2)$. The $k$-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi liquid and Fermi liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of $k=2$, our results provide a novel venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction $\nu=5/2$. We present numerical estimates for realizing this scenario in experiment.Comment: 18 pages, 2 figures. Clarified final discussio