arXiv subjects

Shinsei Ryu

Publications and source records attributed to Shinsei Ryu.

At least 163 records · Page 9Linked to original sources

arXiv2013

Protected boundary states in gapless topological phases

We systematically study gapless topological phases of (semi-)metals and nodal superconductors described by Bloch and Bogoliubov-de Gennes Hamiltonians. Using K-theory, a classification of topologically stable Fermi surfaces in (semi-)metals and nodal lines in superconductors is derived. We discuss a generalized bulk-boundary correspondence that relates the topological features of the Fermi surfaces and superconducting nodal lines to the presence of protected zero-energy states at the boundary of the system. Depending on the case, the boundary states are either linearly dispersing (i.e., Dirac or Majorana states) or are dispersionless, forming two-dimensional surface flat bands or one-dimensional arc surface states. We study examples of gapless topological phases in symmetry class AIII and DIII, focusing in particular on nodal superconductors, such as nodal non-centrosymmetric superconductors. For some cases we explicitly compute the surface spectrum and examine the signatures of the topological boundary states in the surface density of states.

cond-mat.supr-con↗

arXiv2013

Classification of topological insulators and superconductors in the presence of reflection symmetry

We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using the structure of bulk Dirac Hamiltonians of minimal matrix dimensions and explicit constructions of topological invariants, we provide the complete classification, which still has the same dimensional periodicities with the original Altland-Zirnbauer classification. The classification of reflection-symmetry-protected topological insulators and superconductors depends crucially on the way reflection symmetry operation is realized. When a boundary is introduced, which is reflected into itself, these non-trivial topological insulators and superconductors support gapless modes localized at the boundary.

cond-mat.mes-hall↗

arXiv2013

Effective field theories for topological insulators by functional bosonization

Effective field theories that describes the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension $D=d+1$ using the functional bosonization technique. For non-interacting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII) and in the "primary series" of topological insulators in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when $D$ is odd) or the $θ$-term (when $D$ is even). For topological insulators characterized by a $\mathbb{Z}_2$ topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for non-interacting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these non-trivial quantum phases.

cond-mat.str-el↗

arXiv2012

Stability of edge states in strained graphene

Spatially inhomogeneous strains in graphene can simulate the effects of valley-dependent magnetic fields. As demonstrated in recent experiments, the realizable magnetic fields are large enough to give rise to well-defined flat pseudo-Landau levels, potentially having counter-propagating edge modes. In the present work we address the conditions under which such edge modes are visible. We find that, whereas armchair edges do not support counter-propagating edge modes, zigzag edges do so, through a novel selective-hybridization mechanism. We then discuss effects of interactions on the stability of counter-propagating edge modes, and find that, for the experimentally relevant case of Coulomb interactions, interactions typically decrease the stability of the edge modes. Finally, we generalize our analysis to address the case of spontaneous valley polarization, which is expected to occur in charge-neutral strained graphene.

cond-mat.mes-hall↗

arXiv2012

Electromagnetic and thermal responses in topological matter: topological terms, quantum anomalies and D-branes

We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological insulators and superconductors beyond the single-particle picture. In two-dimensional topological phases, the Strěda formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the angular momentum and thermal polarization (entropy polarization). We also discuss a use of D-branes in string theory as a systematic tool to derive all such topological terms and topological responses. In particular, we relate the $\mathbb{Z}_2$ index of topological insulators introduced by Kane and Mele (and its generalization to other symmetry classes and to arbitrary dimensions) to the K-theory charge of non-BPS D-branes, and vice versa. We thus establish a link between the stability of non-BPS D-branes and the topological stability of topological insulators.

cond-mat.mes-hall↗

arXiv2012

Holographic Geometry of Entanglement Renormalization in Quantum Field Theories

We study a conjectured connection between the AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction, which is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.

hep-th↗

arXiv2012

Interacting topological phases and modular invariance

We discuss a (2+1) dimensional topological superconductor with $N_f$ left- and right-moving Majorana edge modes and a $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry. In the absence of interactions, these phases are distinguished by an integral topological invariant $N_f$. With interactions, the edge state in the case $N_f=8$ is unstable against interactions, and a $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant mass gap can be generated dynamically. We show that this phenomenon is closely related to the modular invariance of type II superstring theory. More generally, we show that the global gravitational anomaly of the non-chiral Majorana edge states is the physical manifestation of the bulk topological superconductors classified by $\mathbb{Z}_8$.

cond-mat.str-el↗

arXiv2012

Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analogue of such a magnetoelectric effect in the thermal (or gravitational) and the magnetic dipole responses in all symmetry classes which admit topologically non-trivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry which lack SU(2) spin rotation symmetry (e.g. due to spin-orbit interactions), such as the B phase of $^3$He, the thermal response is the only probe which can detect the non-trivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal- (or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover we find, for a significant part of the 'ten-fold' list of topological insulators found in previous work in the absence of interactions, that in general dimensions the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting or not, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DIII, CI, and AIII in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.

cond-mat.str-el↗

arXiv2012

Global phase diagram of two-dimensional Dirac fermions in random potentials

Anderson localization is studied for two flavors of massless Dirac fermions in 2D space perturbed by static disorder that is invariant under a chiral symmetry (chS) and a time-reversal symmetry (TRS) operation which, when squared, is equal either to plus or minus the identity. The former TRS (symmetry class BDI) can for example be realized when the Dirac fermions emerge from spinless fermions hopping on a 2D lattice with a linear energy dispersion such as the honeycomb lattice (graphene) or the square lattice with $π$-flux per plaquette. The latter TRS is realized by the surface states of 3D $\mathbb{Z}_{2}$-topological band insulators in symmetry class CII. In the phase diagram parametrized by the disorder strengths, there is an infrared stable line of critical points for both symmetry classes BDI and CII. Here we discuss a "global phase diagram" in which disordered Dirac fermion systems in all three chiral symmetry classes, AIII, CII, and BDI, occur in 4 quadrants, sharing one corner which represents the clean Dirac fermion limit. This phase diagram also includes symmetry classes AII [e.g., appearing at the surface of a disordered 3D $\mathbb{Z}_2$-topological band insulator in the spin-orbit (symplectic) symmetry class] and D (e.g., the random bond Ising model in two dimensions) as boundaries separating regions of the phase diagram belonging to the three chS classes AIII, BDI, and CII. Moreover, we argue that physics of Anderson localization in the CII phase can be presented in terms of a non-linear-sigma model (NLsM) with a $\mathbb{Z}_{2}$-topological term. We thereby complete the derivation of topological or Wess-Zumino-Novikov-Witten terms in the NLsM description of disordered fermionic models in all 10 symmetry classes relevant to Anderson localization in two spatial dimensions.

cond-mat.mes-hall↗

arXiv2012

Masses and Majorana fermions in graphene

We review the classification of all the 36 possible gap-opening instabilities in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac Hamiltonian when the spin, valley, and superconducting channels are included. We then show that in graphene it is possible to realize an odd number of Majorana fermions attached to vortices in superconducting order parameters if a proper hierarchy of mass scales is in place.

cond-mat.mes-hall↗

arXiv2012

Noncommutative geometry for three-dimensional topological insulators

We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.

cond-mat.str-el↗

arXiv2012

Non-Abelian SU(2) gauge fields through density-wave order and strain in graphene

Spatially varying strain patterns can qualitatively alter the electronic properties of graphene, acting as effective valley-dependent magnetic fields and giving rise to pseudo-Landau-level (PLL) quantization. Here, we show that the strain-induced magnetic field is one component of an SU(2) non-Abelian gauge field within the low-energy theory of graphene, and identify the other two components as period-3 charge-density waves. We show that these density-waves, if spatially varied, give rise to PLL quantization. We also argue that strain-induced magnetic fields can induce density-wave order in graphene, thus dynamically gapping out the lowest PLL; moreover, the ordering should generically be accompanied by dislocations. We discuss experimental signatures of these effects.

cond-mat.mes-hall↗

arXiv2012

Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the π-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.

cond-mat.str-el↗

arXiv2012

Topological Hubbard model and its high-temperature quantum Hall effect

The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.

cond-mat.str-el↗

arXiv2012

Competing orders in the Dirac-like electronic structure and the non-linear sigma model with the topological terms

The Dirac-like electronic structure can host a large number of competing orders in the form of mass terms. In particular, two different order parameters can be said to be dual to each other, when a static defect in one of them traps a quantum number (or "charge") of the other. We discuss that such complementary nature of the pair of the order parameters shows up in their correlation functions and dynamical properties when a quantum phase transition is driven by fluctuations of the one of the order parameters. Approaching the transition from the disordered (paramagnetic) side, the order parameter correlation function at the critical point is reduced, while such fluctuations enhance the correlation of the dual order parameter. Such complementary behaviors in the correlation function can be used to diagnose the nature of quantum fluctuations that is the driving force of the quantum phase transition.

cond-mat.str-el↗

arXiv2011

Cross-Correlated Responses of Topological Superconductors and Superfluids

We study nontrivial responses of topological superconductors and superfluids to the temperature gradient and rotation of the system. In two-dimensional gapped systems, the Strěda formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the orbital angular momentum and thermal polarization (entropy polarization). These results can be naturally related to the gravitoelectromagnetism description of three-dimensional topological superconductors and superfluids, analogous to the topological magnetoelectric effect in ${\mathbb{Z}}_2$ topological insulators.

cond-mat.supr-con↗

arXiv2011

Time-reversal symmetric hierarchy of fractional incompressible liquids

We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described by the bulk theory.

cond-mat.str-el↗

arXiv2011

Fractional topological liquids with time-reversal symmetry and their lattice realization

We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes and the spin Hall conductance needs not be quantized. We then analyze the stability of edge states in these two-dimensional topological fluids against localization by disorder. We find a Z_2 stability criterion for whether or not there exists a Kramers pair of edge modes that is robust against disorder. We also introduce an interacting electronic two-dimensional lattice model based on partially filled flattened bands of a Z_2 topological band insulator, which we study using numerical exact diagonalization. We show evidence for instances of the fractional topological liquid phase as well as for a time-reversal symmetry broken phase with a quantized (charge) Hall conductance in the phase diagram for this model.

cond-mat.str-el↗