arXiv subjects

Shinsei Ryu

Publications and source records attributed to Shinsei Ryu.

At least 181 records · Page 10Linked to original sources

arXiv2011

Topological phases and surface flat bands in superconductors without inversion symmetry

We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value of any of these topological numbers indicates the appearance of zero-energy Andreev surface states. We find that some of these boundary modes in nodal superconducting phases are dispersionless, i.e., they form a topologically protected flat band. The region where the zero-energy flat band appears in the surface Brillouin zone is determined by the projection of the nodal lines in the bulk onto the surface. These dispersionless Andreev surface bound states have many observable consequences, in particular, a zero-bias conductance peak in tunneling measurements. We also find that in the gapless phase there appear Majorana surface modes at time-reversal invariant momenta which are protected by a $\mathbb{Z}_2$ topological invariant.

cond-mat.mes-hall↗

arXiv2011

Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors

We discuss the effects of disorder in time-reversal invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in symplectic (AII) symmetry class, the phase diagram in the presence of disorder and a mass term, which drives a transition between trivial and topological insulator phases, is computed numerically by the transfer matrix method. The numerics is supplemented by a field theory analysis (the large-$N_f$ expansion where $N_f$ is the number of valleys or Dirac cones), from which we obtain the correlation length exponent, and several anomalous dimensions at a non-trivial critical point separating a metallic phase and a Dirac semi-metal. A similar field theory approach is developed for disorder-driven transitions in symmetry class AIII, CI, and DIII. For these three symmetry classes, where topological superconductors are characterized by integer topological invariant, a complementary description is given in terms of the non-linear sigma model supplemented with a topological term which is a three-dimensional analogue of the Pruisken term in the integer quantum Hall effect.

cond-mat.mes-hall↗

arXiv2011

Holographic Conductivity in Disordered Systems

The main purpose of this paper is to holographically study the behavior of conductivity in 2+1 dimensional disordered systems. We analyze probe D-brane systems in AdS/CFT with random closed string and open string background fields. We give a prescription of calculating the DC conductivity holographically in disordered systems. In particular, we find an analytical formula of the conductivity in the presence of codimension one randomness. We also systematically study the AC conductivity in various probe brane setups without disorder and find analogues of Mott insulators.

hep-th↗

arXiv2010

Topological qubits in graphenelike systems

The fermion-doubling problem can be an obstacle to getting half-a-qubit in two-dimensional fermionic tight-binding models in the form of Majorana zero modes bound to the core of superconducting vortices. We argue that the number of such Majorana zero modes is determined by a Z_2 x Z_2 topological charge for a family of two-dimensional fermionic tight-binding models ranging from noncentrosymmetric materials to graphene. This charge depends on the dimension of the representation (i.e., the number of species of Dirac fermions -- where the doubling problem enters) and the parity of the Chern number induced by breaking time-reversal symmetry. We show that in graphene there are as many as ten order parameters that can be used in groups of four to change the topological number from even to odd.

cond-mat.mes-hall↗

arXiv2010

Topological Insulators and Superconductors from D-branes

Realization of topological insulators (TIs) and superconductors (TSCs), such as the quantum spin Hall effect and the Z_2 topological insulator, in terms of D-branes in string theory is proposed. We establish a one-to-one correspondence between the K-theory classification of TIs/TSCs and D-brane charges. The string theory realization of TIs and TSCs comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature. This sheds light on TIs and TSCs beyond non-interacting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions.

hep-th↗

arXiv2010

Topological Insulators and Superconductors from String Theory

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and supercondutors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K-theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K-theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the $θ$-term in various dimensions. This sheds light on topological insulators and superconductors beyond non-interacting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).

hep-th↗

arXiv2010

Momentum space metric, non-local operator, and topological insulators

Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In particular, we introduce a non-local operator which represents distance square in real space and show that this corresponds to the Laplacian in curved momentum space, and also derive its path integral representation in momentum space. The quantum metric itself measures the second cumulant of the position operator in real space, much like the Berry gauge potential measures the first cumulant or the electric polarization in real space. By using the non-local operator and the metric, we study some aspects of topological phases such as topological invariants, the cumulants and topological phase transitions. The effect of interactions to the momentum space geometry is also discussed.

cond-mat.mes-hall↗

arXiv2010

Topological insulators and superconductors: ten-fold way and dimensional hierarchy

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a Z or a Z_2 topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via dimensional reduction by compactifying one or more spatial dimensions (in Kaluza-Klein-like fashion). For Z-topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The Z_2-topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent Z-topological insulators in the same class, from which they inherit their topological properties. The 8-fold periodicity in dimension d that exists for topological insulators (superconductors) with Hamiltonians satisfying at least one reality condition (arising from time-reversal or charge-conjugation/particle-hole symmetries) is a reflection of the 8-fold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). We derive a relation between the topological invariant that characterizes topological insulators/superconductors with chiral symmetry and the Chern-Simons invariant: it relates the invariant to the electric polarization (d=1), or to the magnetoelectric polarizability (d=3). Finally, we discuss topological field theories describing the space time theory of linear responses, and study how the presence of inversion symmetry modifies the classification.

cond-mat.mes-hall↗

arXiv2010

Chiral Topological Insulators, Superconductors and other competing orders in three dimensions

We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette $π$-flux as a model, we find, among others phases, a chiral topological insulator and singlet topological superconductor. While the former requires a special "chiral" symmetry, the latter is stable as long as time reversal and SU(2) spin rotation symmetry are present. These phases are characterized by stable surface Dirac fermion modes, and by an integer topological invariant in the bulk. The key features of these phases are readily understood in a two dimensional limit with an appropriate pairing of Dirac nodes between layers. This Dirac node-pairing picture is also shown to apply to $Z_2$ topological insulators protected by time-reversal symmetry (TRS). The nature of point-like topological defects in these phases is also investigated, revealing an interesting duality relation between these topological phases and the Neel phase.

cond-mat.mtrl-sci↗

arXiv2010

High-gradient operators in perturbed Wess-Zumino-Witten field theories in two dimensions

Many classes of non-linear sigma models (NLSMs) are known to contain composite operators with an arbitrary number 2s of derivatives ("high-gradient operators") which appear to become strongly relevant within RG calculations at one (or fixed higher) loop order, when the number 2s of derivatives becomes large. This occurs at many conventional fixed points of NLSMs which are perturbatively accessible within the usual epsilon-expansion in d=2+εdimensions. Since such operators are not prohibited from occurring in the action, they appear to threaten the very existence of such fixed points. At the same time, for NLSMs describing metal-insulator transitions of Anderson localization in electronic conductors, the strong RG-relevance of these operators has been previously related to statistical properties of the conductance of samples of large finite size ("conductance fluctuations"). In this paper, we analyze this question, not for perturbative RG treatments of NLSMs, but for 2d Wess-Zumino-Witten (WZW) models at level k, perturbatively in the current-current interaction of the Noether current. WZW models are special ("Principal Chiral") NLSMs on a Lie Group G with a WZW term at level k. In these models the role of high-gradient operators is played by homogeneous polynomials of order 2s in the Noether currents, whose scaling dimensions we analyze. For the Lie Supergroup G=GL(2N|2N) and k=1, this corresponds to time-reversal invariant problems of Anderson localization in the so-called chiral symmetry classes, and the strength of the current-current interaction, a measure of the strength of disorder, is known to be completely marginal (for any k). We find that all high-gradient (polynomial) operators are, to one loop order, irrelevant or relevant depending on the sign of that interaction.

cond-mat.mes-hall↗

arXiv2010

Holographic Superconductor/Insulator Transition at Zero Temperature

We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2+1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-Tc superconductors via an emergent gauge symmetry.

hep-th↗

arXiv2009

The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality

The quantum spin Hall effect shares many similarities (and some important differences) with the quantum Hall effect for the electric charge. As with the quantum (electric charge) Hall effect, there exists a correspondence between bulk and boundary physics that allows to characterize the quantum spin Hall effect in diverse and complementary ways. In this paper, we derive from the network model that encodes the quantum spin Hall effect, the so-called Z_2 network model, a Dirac Hamiltonian in two dimensions. In the clean limit of this Dirac Hamiltonian, we show that the bulk Kane-Mele Z_2 invariant is nothing but the SU(2) Wilson loop constructed from the SU(2) Berry connection of the occupied Dirac-Bloch single-particle states. In the presence of disorder, the non-linear sigma model (NLSM) that is derived from this Dirac Hamiltonian describes a metal-insulator transition in the standard two-dimensional symplectic universality class. In particular, we show that the fermion doubling prevents the presence of a topological term in the NLSM that would change the universality class of the ordinary two-dimensional symplectic metal-insulator transition. This analytical result is fully consistent with our previous numerical studies of the bulk critical exponents at the metal-insulator transition encoded by the Z_2 network model. Finally, we improve the quality and extend the numerical study of boundary multifractality in the Z_2 topological insulator. We show that the hypothesis of two-dimensional conformal invariance at the metal-insulator transition is verified within the accuracy of our numerical results.

cond-mat.mes-hall↗

arXiv2009

Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene

At the charge neutral point, graphene exhibits a very unusual high resistance metallic state and a transition to a complete insulating phase in a strong magnetic field. We propose that the current carriers in this state are the charged vortices of the XY valley pseudospin order-parameter, a situation which is dual to a conventional thin superconducting film. We study energetics and the stability of this phase in the presence of disorder.

cond-mat.mes-hall↗

arXiv2009

Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics

We classify all possible 36 gap-opening instabilities in graphene-like structures in two dimensions, i.e., masses of Dirac Hamiltonian when the spin, valley, and superconducting channels are included. These 36 order parameters break up into 56 possible quintuplets of masses that add in quadrature, and hence do not compete and thus can coexist. There is additionally a 6th competing mass, the one added by Haldane to obtain the quantum Hall effect in graphene without magnetic fields, that breaks time-reversal symmetry and competes with all other masses in any of the quintuplets. Topological defects in these 5-dimensional order parameters can generically bind excitations with fractionalized quantum numbers. The problem simplifies greatly if we consider spin-rotation invariant systems without superconductivity. In such simplified systems, the possible masses are only 4 and correspond to the Kekulé dimerization pattern, the staggered chemical potential, and the Haldane mass. Vortices in the Kekulé pattern are topological defects that have Abelian fractional statistics in the presence of the Haldane term. We calculate the statistical angle by integrating out the massive fermions and constructing the effective field theory for the system. Finally, we discuss how one can have generically non-Landau-Ginzburg-type transitions, with direct transitions between phases characterized by distinct order parameters.

cond-mat.str-el↗

arXiv2009

Holographic Entanglement Entropy: An Overview

In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.

hep-th↗

arXiv2009

Classification of topological insulators and superconductors in three spatial dimensions

We systematically study topological phases of insulators and superconductors (SCs) in 3D. We find that there exist 3D topologically non-trivial insulators or SCs in 5 out of 10 symmetry classes introduced by Altland and Zirnbauer within the context of random matrix theory. One of these is the recently introduced Z_2 topological insulator in the symplectic symmetry class. We show there exist precisely 4 more topological insulators. For these systems, all of which are time-reversal (TR) invariant in 3D, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. 3 of the above 5 topologically non-trivial phases can be realized as TR invariant SCs, and in these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a 2D surface, they support a number (which may be an arbitrary non-vanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations that preserve the characteristic discrete symmetries. In particular, these surface modes completely evade Anderson localization. These topological phases can be thought of as 3D analogues of well known paired topological phases in 2D such as the chiral p-wave SC. In the corresponding topologically non-trivial and topologically trivial 3D phases, the wavefunctions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the SC phases with non-vanishing winding number possess non-trivial topological ground state degeneracies.

cond-mat.mes-hall↗

arXiv2009

Three-dimensional topological phase on the diamond lattice

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a non-zero winding number introduced in A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786. The topological character of the weak pairing phase is protected by a discrete symmetry.

cond-mat.mes-hall↗

arXiv2009

Classification of Topological Insulators and Superconductors

An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically non-trivial state. Our approach consists in reducing the problem of classifying topological insulators (superconductors) in d spatial dimensions to the problem of Anderson localization at a (d-1) dimensional boundary of the system. We find that in each spatial dimension there are precisely five distinct classes of topological insulators (superconductors). The different topological sectors within a given topological insulator (superconductor) can be labeled by an integer winding number or a Z_2 quantity. One of the five topological insulators is the 'quantum spin Hall' (or: Z_2 topological) insulator in d=2, and its generalization in d=3 dimensions. For each dimension d, the five topological insulators correspond to a certain subset of five of the ten generic symmetry classes of Hamiltonians introduced more than a decade ago by Altland and Zirnbauer in the context of disordered systems (which generalizes the three well known "Wigner-Dyson'' symmetry classes).

cond-mat.mes-hall↗