Bogdan Andrei Bernevig

Pairing Symmetry in a Two-Orbital Exchange Coupling Model of Oxypnictides

We study the pairing symmetry of a two-orbital J1-J2 model for FeAs layers in oxypnictides. We show that the mixture of an intraorbital unconventional s_{x;{2}y;{2}} approximately cos(k_{x})cos(k_{y}) pairing symmetry, which changes sign between the electron and hole Fermi surfaces, and a very small d_{x;{2}-y;{2}} approximately cos(k_{x})-cos(k_{y}) component is favored in a large part of the J1-J2 phase diagram. A pure s_{x;{2}y;{2}} pairing state is favored for J2>J1. The signs of the d_{x;{2}-y;{2}} order parameters in the two different orbitals are opposite. While a small d_{xy} approximately sin(k_{x})sin(k_{y}) interorbital pairing coexists in the above phases, the intraorbital d_{xy} pairing is not favored even for large J2.

Multi-Weyl topological semimetals stabilized by point group symmetry.

We perform a complete classification of two-band k·p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by C(4,6)-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C(6)-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr(2)Se(4) and confirm it is a double-Weyl metal protected by C(4) symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001] axis to the [111] axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group S(6) of that phase. Finally, we discuss experimentally relevant effects including the splitting of multi-Weyl nodes by applying a C(n) breaking strain and the surface Fermi arcs in these new semimetals.

How Bob Laughlin Tamed the Giant Graviton from Taub-NUT Space

In this paper we show how two dimensional electron systems can be modeled by strings interacting with D-branes. The dualities of string theory allow several descriptions of the system. These include descriptions in terms of solitons in the near horizon D6-brane theory, non-commutative gauge theory on a D2-brane, the Matrix Theory of D0-branes and finally as a giant graviton in M-theory. The soliton can be described as a D2-brane with an incompressible fluid of D0-branes and charged string-ends moving on it. Including an NS5-brane in the system allows for the existence of an edge with the characteristic massless chiral edge states of the Quantum Hall system.

Eight-dimensional quantum Hall effect and octonions

We construct a generalization of the quantum Hall effect where particles move in an eight-dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the octonions. Two fundamentally different liquids with distinct configuration spaces can be constructed, depending on whether the particles carry spinor or vector SO(8) quantum numbers. One of the liquids lives on a 20-dimensional manifold with an internal component of SO(7) holonomy, whereas the second liquid lives on a 14-dimensional manifold with an internal component of G2 holonomy.

Localization and the Kosterlitz-Thouless Transition in Disordered Graphene

We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is expected to be equivalent to a disordered two-dimensional Dirac fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder (therefore inevitable intervalley scattering) and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.

Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U

Geometry of the three-qubit state, entanglement and division algebras

We present a generalization to three qubits of the standard Bloch sphere representation for a single qubit and of the seven-dimensional sphere representation for two qubits presented in Mosseri et al (Mosseri R and Dandoloff R 2001 J. Phys. A: Math. Gen. 34 10243). The Hilbert space of the three-qubit system is the 15-dimensional sphere S15, which allows for a natural (last) Hopf fibration with S8 as base and S7 as fibre. A striking feature is, as in the case of one and two qubits, that the map is entanglement sensitive, and the two distinct ways of un-entangling three qubits are naturally related to the Hopf map. We define a quantity that measures the degree of entanglement of the three-qubit state. Conjectures on the possibility of generalizing the construction for higher qubit states are also discussed.

Quantum blockade and loop currents in graphene with topological defects

We investigate the effect of topological defects on the transport properties of a narrow ballistic ribbon of graphene with zigzag edges. Our results show that the longitudinal conductance vanishes at several discrete Fermi energies where the system develops loop orbital electric currents with certain chirality. The chirality depends on the direction of the applied bias voltage and the sign of the local curvature created by the topological defects. This quantum localization phenomenon provides a way to generate a magnetic moment by an external electric field, which can prove useful in nanotronics.

Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb

Topological insulators (TIs) host novel states of quantum matter, distinguished from trivial insulators by the presence of nontrivial conducting boundary states connecting the valence and conduction bulk bands. Up to date, all the TIs discovered experimentally rely on the presence of either time reversal or symmorphic mirror symmetry to protect massless Dirac-like boundary states. Very recently, it has been theoretically proposed that several materials are a new type of TIs protected by nonsymmorphic symmetry, where glide-mirror can protect novel exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of such new nonsymmorphic TI (NSTI) is still missing. Using angle-resolved photoemission spectroscopy, we reveal that such hourglass topology exists on the (010) surface of crystalline KHgSb while the (001) surface has no boundary state, which is fully consistent with first-principles calculations. We thus experimentally demonstrate that KHgSb is a NSTI hosting hourglass fermions. By expanding the classification of topological insulators, this discovery opens a new direction in the research of nonsymmorphic topological properties of materials.Photoemission established KHgSb as a nonsymmorphic topological insulator, which hosts hourglass-shaped surface states. Topological insulators (TIs) host novel states of quantum matter characterized by nontrivial conducting boundary states connecting valence and conduction bulk bands. All TIs discovered experimentally so far rely on either time-reversal or mirror crystal symmorphic symmetry to protect massless Dirac-like boundary states. Several materials were recently proposed to be TIs with nonsymmorphic symmetry, where a glide mirror protects exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of this new fermion is missing. Using angle-resolved photoemission spectroscopy, we provide experimental evidence of hourglass fermions on the (010) surface of crystalline KHgSb, whereas the (001) surface has no boundary state, in agreement with first-principles calculations. Our study will stimulate further research activities of topological properties of nonsymmorphic materials.

Magnetic instability in strongly correlated superconductors.

Recently, a new phenomenological Hamiltonian has been proposed to describe the superconducting cuprates. This so-called Gossamer Hamiltonian is an apt model for a superconductor with strong on-site Coulomb repulsion between the electrons. It is shown that at half-filling the Gossamer superconductor with strong repulsion is unstable toward an antiferromagnetic insulator. The superconducting state undergoes a quantum phase transition to an antiferromagnetic insulator as one increases the on-site Coulomb repulsion. Near the transition the Gossamer superconductor becomes spectroscopically indistinguishable from the insulator.