Edge modes in band topological insulators

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the Brillouin zone (BZ). Topologically non-trivial gluing functions, corresponding to non-trivial bundles, then yield edge modes exhibiting spectral flow. We illustrate our results for the case of chiral edge states in two dimensional Chern insulators, as well as helical edges in quantum spin Hall states.Comment: 4 pages, 2 figures; v4 minor change

Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence

We present a new experimental set-up that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We carry out the first experimental results in the transitional regime for this flow. Using flow visualization we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures are nearly stationary. We distinguish two regions of the turbulent spot: the active, turbulent core, which is characterized by waviness of the streaks similar to traveling waves, and the surrounding region, which includes in addition the weak undisturbed streaks and oblique waves at the laminar-turbulent interface. We also study the dependence of the size of these two regions on Reynolds number. Finally, we show that the traveling waves move in the downstream (Poiseuille).Comment: 17 pages, 15 figure

Entanglement spectrum of topological insulators and superconductors

We study two a priori unrelated constructions: the spectrum of edge modes in a band topological insulator or superconductor with a physical edge, and the ground state entanglement spectrum in an extended system where an edge is simulated by an entanglement bipartition. We prove an exact relation between the ground state entanglement spectrum of such a system and the spectrum edge modes of the corresponding spectrally flattened Hamiltonian. In particular, we show that degeneracies of the entanglement spectrum correspond to gapless edge modes.Comment: 4 pages, 1 figure. v

Spontaneous symmetry breaking in a generalized orbital compass model

We introduce a generalized two-dimensional orbital compass model, which interpolates continuously from the classical Ising model to the orbital compass model with frustrated quantum interactions, and investigate it using the multiscale entanglement renormalization ansatz (MERA). The results demonstrate that increasing frustration of exchange interactions triggers a second order quantum phase transition to a degenerate symmetry broken state which minimizes one of the interactions in the orbital compass model. Using boson expansion within the spin-wave theory we unravel the physical mechanism of the symmetry breaking transition as promoted by weak quantum fluctuations and explain why this transition occurs only surprisingly close to the maximally frustrated interactions of the orbital compass model. The spin waves remain gapful at the critical point, and both the boson expansion and MERA do not find any algebraically decaying spin-spin correlations in the critical ground state.Comment: 9 pages, 6 figures, improved presentation, version to appear in Phys. Rev.

Superconducting Hair on Charged Black String Background

Behaviour of Dirac fermions in the background of a charged black string penetrated by an Abelian Higgs vortex is elaborated. One finds the evidence that the system under consideration can support fermion fields acting like a superconducting cosmic string in the sence that a nontrivial Dirac fermion field can be carried by the system in question. The case of nonextremal and extremal black string vortex systems were considered. The influence of electric and Higgs charge, the winding number and the fermion mass on the fermion localization near the black string event horizon was studied. It turned out that the extreme charged black string expelled fermion fields more violently comparing to the nonextremal one.Comment: RevTex, 16 pages, 12 figures, to be published in Phys.REvD1

Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order

We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit coupled nanowires coated with superconducting film and for LaAlO3/SrTiO3 interfaces.Comment: 14 pages. Figures added and a discussion of the effects of quantum phase slips. References Added. Fourth author adde