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Shinsei Ryu

Bio: Shinsei Ryu is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Topological order & Symmetry protected topological order. The author has an hindex of 36, co-authored 91 publications receiving 6523 citations. Previous affiliations of Shinsei Ryu include University of California, Berkeley.

Papers published on a yearly basis

Papers
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Journal ArticleDOI
TL;DR: In this article, a review of the classification schemes of both fully gapped and gapless topological materials is presented, and a pedagogical introduction to the field of topological band theory is given.
Abstract: In recent years an increasing amount of attention has been devoted to quantum materials with topological characteristics that are robust against disorder and other perturbations. In this context it was discovered that topological materials can be classified with respect to their dimension and symmetry properties. This review provides an overview of the classification schemes of both fully gapped and gapless topological materials and gives a pedagogical introduction into the field of topological band theory.

2,123 citations

Journal ArticleDOI
TL;DR: In this paper, the authors constructed representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians.
Abstract: 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 or a 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 -topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The -topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent -topological insulators in the same class, from which they inherit their topological properties. The eightfold 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 eightfold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). Furthermore, we derive for general spatial dimensions a relation between the topological invariant that characterizes topological insulators and superconductors with chiral symmetry (i.e., the winding number) and the Chern–Simons invariant. For lower-dimensional cases, this formula relates the winding number to the electric polarization (d=1 spatial dimensions) or to the magnetoelectric polarizability (d=3 spatial dimensions). Finally, we also discuss topological field theories describing the spacetime theory of linear responses in topological insulators (superconductors) and study how the presence of inversion symmetry modifies the classification of topological insulators (superconductors).

1,648 citations

Journal ArticleDOI
TL;DR: In this paper, a topological classification of insulators and superconductors in the presence of both (nonspatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions is discussed.
Abstract: We discuss a topological classification of insulators and superconductors in the presence of both (nonspatial) 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 nontrivial topological insulators and superconductors support gapless modes localized at the boundary.

290 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that for topological superconductors with time-reversal symmetry, which lack spin rotation symmetry (e.g., due to spin-orbit interactions), the thermal response is the only probe that can detect the topological character through transport.
Abstract: 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 analog of such a magnetoelectric effect in the thermal (or gravitational) and magnetic dipole responses in all symmetry classes that admit topologically nontrivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry, which lack $\text{SU}(2)$ 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 that can detect the nontrivial 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 ``tenfold'' 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, 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.

257 citations

Proceedings ArticleDOI
18 May 2009
TL;DR: In this article, an exhaustive classification scheme of topological insulators and superconductors is presented, based on the appearance of gapless degrees of freedom at the interface/boundary between topologically trivial and a topologically non-trivial state.
Abstract: 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 Z2 quantity. One of the five topological insulators is the “quantum spin Hall” (or: Z2 topological) insulator in d = 2, and its generalization in d = 3 dimensions. For each dimension d, the five topological insulators correspond to a certain ...

233 citations


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Journal ArticleDOI
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

11,092 citations

Journal ArticleDOI
TL;DR: Weyl and Dirac semimetals as discussed by the authors are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry, and they have generated much recent interest.
Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

3,407 citations

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TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Abstract: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

3,052 citations

Journal ArticleDOI
TL;DR: In this paper, a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures is provided.
Abstract: We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.

2,930 citations

Journal ArticleDOI
TL;DR: In this article, a review of recent advances in the condensed matter search for Majorana fermions is presented, which has led many in the field to believe that this quest may soon bear fruit.
Abstract: The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

2,156 citations