Publications (100)545.37 Total impact
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ABSTRACT: We propose a platform for interacting topological phases of fermions with time reversal symmetry Θ¯ (such that Θ¯2=1) that can be realized in vortex lattices in the surface state of a topological insulator. The constituent particles are Majorana fermions bound to vortices and antivortices of such a lattice. We explain how the Θ¯ symmetry arises and discuss ways in which interactions can be experimentally tuned and detected. We show how these features can be exploited to realize a class of interactionenabled crystalline topological phases that have no analog in weakly interacting systems.  [Show abstract] [Hide abstract]
ABSTRACT: The effect of boundary disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a threedimensional (3D) topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a method which analytically eliminates the clean bulk and reduces a Ddimensional problem to a Hamiltoniandiagonalization problem within the (D−1)dimensional disordered boundary. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spinHall insulator with nonmagnetic and magnetic edge impurities, and we calculate the disorderinduced redistribution of probability density (or local density of states) in the insulating bulk, as well as the transport effects of edge impurities. The analysis reveals how the edge recovers from disorder scattering as the disorder strength increases. 
Article: Interactionenabled topological phases in topological insulatorsuperconductor heterostructures
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ABSTRACT: Topological phases of matter that depend for their existence on interactions are fundamentally interesting and potentially useful as platforms for future quantum computers. Despite the multitude of theoretical proposals the only interactionenabled topological phase experimentally observed is the fractional quantum Hall liquid. To help identify other systems that can give rise to such phases we present in this work a detailed study of the effect of interactions on Majorana zero modes bound to vortices in a superconducting surface of a 3D topological insulator. This system is of interest because, as was recently pointed out, it can be tuned into the regime of strong interactions. We start with a 0D system suggesting an experimental realization of the interactioninduced $\mathbb{Z}_8$ ground state periodicity previously discussed by Fidkowski and Kitaev. We argue that the periodicity is experimentally observable using a tunnel probe. We then focus on interactionenabled crystalline topological phases that can be built with the Majoranas in a vortex lattice in higher dimensions. In 1D we identify an interesting exactly solvable model which is related to a previously discussed one that exhibits an interactionenabled topological phase. We study these models using analytical techniques, exact numerical diagonalization (ED) and density matrix renormalization group (DMRG). Our results confirm the existence of the interactionenabled topological phase and clarify the nature of the quantum phase transition that leads to it. We finish with a discussion of models in dimensions 2 and 3 that produce similar interactionenabled topological phases.  [Show abstract] [Hide abstract]
ABSTRACT: Certain types of topological superconductors and superfluids are known to host protected Majorana zero modes in cores of Abrikosov vortices. When such vortices are arranged in a dense periodic lattice one expects zero modes from neighboring vortices to hybridize and form dispersing bands. Understanding the structure of these bands is essential for the schemes that aim to employ the zero modes in quantum computation applications and in studies of their strongly interacting phases. We investigate here the band formation phenomenon in two concrete models, describing a two dimensional p + ip superconductor and a superconducting surface of a threedimensional strong topological insulator (FuKane model), using a combination of analytical and numerical techniques. We find that the physics of the Majorana bands is well described by tight binding models of Majorana fermions coupled to a static Z2 gauge field with a nontrivial gauge flux through each plaquette, in accord with expectations based on very general arguments. In the case of the FuKane model we also find that, irrespective of the lattice geometry, the Majorana band becomes completely flat at the so called neutrality point (chemical potential coincident with the Dirac point) where the model exhibits an extra chiral symmetry. In this limit the low energy physics will be dominated by fourfermion interaction terms which are permitted by symmetries and may arise from the Coulomb interaction between the constituent electron degrees of freedom.  [Show abstract] [Hide abstract]
ABSTRACT: The Hubbard chain and spinless fermion chain are paradigms of strongly correlated systems, very well understood using Bethe ansatz, Density Matrix Renormalization Group (DMRG) and field theory/renormalization group (RG) methods. They have been applied to onedimensional materials and have provided important insights for understanding higher dimensional cases. Recently, a new interacting fermion model has been introduced, with possible applications to topological materials. It has a single Majorana fermion operator on each lattice site and interactions with the shortest possible range that involve 4 sites. We present a thorough analysis of the phase diagram of this model in one dimension using field theory/RG and DMRG methods. It includes a gapped supersymmetric region and a novel gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. In addition to a first order transition, three critical points occur: tricritical Ising, Lifshitz and a novel generalization of the commensurateincommensurate transition. We also survey various gapped phases of the system that arise when the translation symmetry is broken by dimerization and find both trivial and topological phases with 0, 1 and 2 Majorana zero modes bound to the edges of the chain with open boundary conditions.  [Show abstract] [Hide abstract]
ABSTRACT: We show that a strongly interacting chain of Majorana fermions exhibits a supersymmetric quantum critical point corresponding to the $c={7\over 10}$ tricritical Ising model, which separates a critical phase in the Ising universality class from a supersymmetric massive phase. We verify our predictions with numerical densitymatrixrenormalizationgroup computations and determine the consequences for tunnelling experiments.  [Show abstract] [Hide abstract]
ABSTRACT: The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a new method which analytically eliminates the clean bulk, and reduces a $D$dimensional problem to a Hamiltoniandiagonalization problem within the $(D1)$dimensional disordered surface. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spinHall insulator with nonmagnetic and magnetic edge impurities, and we calculate the probability density (or local density of states) of the zeroenergy eigenstates as a function of edgeparallel momentum and layer index. Our analysis reveals that the system size needed to reach behavior in the thermodynamic limit increases with disorder. We also compute the edge conductance as a function of disorder strength, and chart a lower bound for the length scale marking the crossover to the thermodynamic limit.  [Show abstract] [Hide abstract]
ABSTRACT: Systems of strongly interacting particles, fermions or bosons, can give rise to topological phases that are not acessible to noninteracting systems. Many such interactionenabled topological phases have been discussed theoretically but few experimental realizations exists. Here we propose a new platform for interacting topological phases of fermions with time reversal symmetry $\bar T$ (such that $\bar T^2=1$) that can be realized in vortex lattices in the surface state of a topological insulator. The constituent particles are Majorana fermions bound to vortices and antivortices of such a lattice. We explain how the $\bar T$ symmetry arises and discuss ways in which interactions can be experimentally tuned and detected. We show how these features can be exploited to realize a class of interactionenabled crystalline topological phases that have no analog in weakly interacting systems.  [Show abstract] [Hide abstract]
ABSTRACT: Interesting phases of quantum matter often arise when the constituent particles  electrons in solids  interact strongly. Such strongly interacting systems are however quite rare and occur only in extreme environments of low spatial dimension, low temperatures or intense magnetic fields. Here we introduce a new system in which the fundamental electrons interact only weakly but the low energy effective theory is described by strongly interacting Majorana fermions. The system consists of an Abrikosov vortex lattice in the surface of a strong topological insulator and is accessible experimentally using presently available technology. The simplest interactions between the Majorana degrees of freedom exhibit an unusual nonlocal structure that involves four distinct Majorana sites. We formulate simple lattice models with this type of interaction and find exact solutions in certain physically relevant one and twodimensional geometries. In other cases we show how our construction allows for the experimental realization of interesting spin models previously only theoretically contemplated.  [Show abstract] [Hide abstract]
ABSTRACT: Electronic states associated with a chain of magnetic adatoms on the surface of an ordinary s wave superconductor have been shown theoretically to form a one dimensional topological phase with unpaired Majorana fermions bound to its ends. In a simple 1D effective model the system exhibits an interesting selforganization property: the pitch of the spiral formed by the adatom magnetic moments tends to adjust itself so that electronically the chain remains in the topological phase whenever such a state is physically accessible. Here we examine the physics underlying this selforganization property in the framework of a more realistic 2D model of a superconducting surface coupled to a 1D chain of magnetic adatoms. Treating both the superconducting order and the magnetic moments selfconsistently we find that the system retains its selforganization property, even if the topological phase extends over a somewhat smaller portion of the phase diagram compared to the 1D model. We also study the effect of imperfections and find that, once established, the topological phase survives moderate levels of disorder.  [Show abstract] [Hide abstract]
ABSTRACT: It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a onedimensional topological superconductor wire. The exchange relies on the concept of ``Majorana shuttle'' whereby a $\pi$ domain wall in the superconducting order parameter which hosts a pair of ancillary Majoranas delivers one zero mode across the wire while the other one tunnels in the opposite direction. The method requires some tuning of parameters and does not, therefore, enjoy the full topological protection. The resulting exchange statistics, however, remains nonAbelian for a wide range of parameters that characterize the exchange.  [Show abstract] [Hide abstract]
ABSTRACT: Most physical systems known to date tend to resist entering the topological phase and must be finetuned to reach that phase. Here, we introduce a system in which a key dynamical parameter adjusts itself in response to the changing external conditions so that the ground state naturally favors the topological phase. The system consists of a quantum wire formed of individual magnetic atoms placed on the surface of an ordinary swave superconductor. It realizes the Kitaev paradigm of topological superconductivity when the wave vector characterizing the emergent spin helix dynamically selftunes to support the topological phase. We call this phenomenon a selforganized topological state.  [Show abstract] [Hide abstract]
ABSTRACT: It has been suggested recently, based on subtle fieldtheoretical considerations, that the electromagnetic response of Weyl semimetals and the closely related Weyl insulators can be characterized by an axion term θE·B with space and time dependent axion angle θ(r,t). Here we construct a minimal lattice model of the Weyl medium and study its electromagnetic response by a combination of analytical and numerical techniques. We confirm the existence of the anomalous Hall effect expected on the basis of the field theory treatment. We find, contrary to the latter, that chiral magnetic effect (that is, ground state charge current induced by the applied magnetic field) is absent in both the semimetal and the insulator phase. We elucidate the reasons for this discrepancy. 
Article: Majorana's wires
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ABSTRACT: Experiments on nanowires have shown evidence of solidstate analogues of the particles predicted by Ettore Majorana more than 70 years ago. Although stronger confirmation is still to come, these first observations have already fuelled expectations of fundamental results and potential applications in quantum information technology.  [Show abstract] [Hide abstract]
ABSTRACT: A surface of a strong topological insulator (STI) is characterized by an odd number of linearly dispersing gapless electronic surface states. It is well known that such a surface cannot be described by an effective twodimensional lattice model (without breaking the timereversal symmetry), which often hampers theoretical efforts to quantitatively understand some of the properties of such surfaces, including the effect of strong disorder, interactions and various symmetrybreaking instabilities. Here we describe a lattice model that can be used to describe a pair of STI surfaces and has an odd number of Dirac fermion states with wavefunctions localized on each surface. The Hamiltonian consists of two planar tightbinding models with spinorbit coupling, representing the two surfaces, weakly coupled to each other by terms that remove the redundant Dirac points from the lowenergy spectrum. The utility of this model is illustrated by studying the magnetic and exciton instabilities of the STI surface state driven by shortrange repulsive interactions.  [Show abstract] [Hide abstract]
ABSTRACT: Twodimensional topological insulators (2D TIs) have been proposed as platforms for many intriguing applications, ranging from spintronics to topological quantum information processing. Realizing this potential will likely be facilitated by the discovery of new, easily manufactured materials in this class. With this goal in mind, we introduce a new framework for engineering a 2D TI by hybridizing graphene with impurity bands arising from heavy adatoms possessing partially filled d shells, in particular, osmium and iridium. Firstprinciples calculations predict that the gaps generated by this means exceed 0.2 eV over a broad range of adatom coverage; moreover, tuning of the Fermi level is not required to enter the TI state. The mechanism at work is expected to be rather general and may open the door to designing new TI phases in many materials.  [Show abstract] [Hide abstract]
ABSTRACT: A surface of a strong topological insulator (STI) is characterized by an odd number of linearly dispersing gapless electronic surface states. It is well known that such a surface cannot be described by an effective twodimensional lattice model (without breaking the timereversal symmetry), which often hampers theoretical efforts to quantitatively understand some of the properties of such surfaces, including the effect of strong disorder, interactions and various symmetrybreaking instabilities. Here we formulate a lattice model that can be used to describe a {\em pair} of STI surfaces and has an odd number of Dirac fermion states with wavefunctions localized on each surface. The Hamiltonian consists of two planar tightbinding models with spinorbit coupling, representing the two surfaces, weakly coupled by terms that remove the extra Dirac points from the lowenergy spectrum. We illustrate the utility of this model by studying the magnetic and exciton instabilities of the STI surface state driven by shortrange repulsive interactions and show that this leads to results that are consistent with calculations based on the continuum model as well as threedimensional lattice models. We expect the model introduced in this work to be widely applicable to studies of surface phenomena in STIs.  [Show abstract] [Hide abstract]
ABSTRACT: It has been shown previously that a finitelength topological insulator nanowire, proximitycoupled to an ordinary bulk swave superconductor and subject to a longitudinal applied magnetic field, realizes a onedimensional topological superconductor with an unpaired Majorana fermion (MF) localized at each end of the nanowire. Here, we study the stability of these MFs with respect to various perturbations that are likely to occur in a physical realization of the proposed device. We show that the unpaired Majorana fermions persist in this system for any value of the chemical potential inside the bulk band gap of order 300 meV in Bi$_2$Se$_3$ by computing the Majorana number. From this calculation, we also show that the unpaired Majorana fermions persist when the magnetic flux through the nanowire crosssection deviates significantly from half flux quantum. Lastly, we demonstrate that the unpaired Majorana fermions persist in strongly disordered wires with fluctuations in the onsite potential ranging in magnitude up to several times the size of the bulk band gap. These results suggest this solidstate system should exhibit unpaired Majorana fermions under accessible conditions likely important for experimental study or future applications. 
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ABSTRACT: We show that a three dimensional topological insulator doped with magnetic impurities in the bulk can have a regime where the surface is magnetically ordered but the bulk is not. This is in contrast to conventional materials where bulk ordered phases are typically more robust than surface ordered phases. The difference originates from the topologically protected gapless surface states characteristic of topological insulators. We study the problem using a mean field approach in two concrete models that give the same qualitative result, with some interesting differences. Our findings could help explain recent experimental results showing the emergence of a spectral gap in the surface state of Bi2Se3 doped with Mn or Fe atoms, but with no measurable bulk magnetism.
Publication Stats
4k  Citations  
545.37  Total Impact Points  
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Institutions

20012015

University of British Columbia  Vancouver
 Department of Physics and Astronomy
Vancouver, British Columbia, Canada


20022012

University of California, Santa Barbara
 Kavli Institute for Theoretical Physics
Santa Barbara, California, United States


19962000

Johns Hopkins University
 Department of Physics and Astronomy
Baltimore, MD, United States


19951997

McMaster University
 Department of Physics and Astronomy
Hamilton, Ontario, Canada


19941995

University of Rochester
 Department of Physics and Astronomy
Rochester, NY, United States
