A new class of models for surface relaxation with exact mean-field solutions

We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will also map our model to a diffusive system of particles on a ring and reinterpret our results in this new setting.Comment: 12 pages, 3 figures,references adde

Midgap spectrum of the fermion-vortex system

I study the midgap spectrum of the fermion-vortex system in two spatial dimensions. The existence of bound states, in addition to the zero modes found by Jackiw and Rossi, is established. For a singly quantized vortex, I present complete analytical solutions in terms of generalized Laguerre polynomials in the opposite limits of vanishing and large vortex core size. There is an infinite number of such bound states, with a spectrum that is, when squared, given by, respectively, the Coulomb potential and the isotropic harmonic oscillator. Possible experimental signatures of this spectrum in condensed-matter realizations of the system are pointed out.Comment: 10 pages, no figure

Fractionalization in a square-lattice model with time-reversal symmetry

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.Comment: 4 pages, 3 figures, RevTex 4. (v2) improved discussion of lattice effects and confinement; clearer figure

Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.Comment: (v2) A typo in Fig. 1 and a slight error in Eq. (4) corrected; all the main results and conclusions remain unchange

Linear Response Theory and Optical Conductivity of Floquet Topological Insulators

Motivated by the quest for experimentally accessible dynamical probes of Floquet topological insulators, we formulate the linear response theory of a periodically driven system. We illustrate the applications of this formalism by giving general expressions for optical conductivity of Floquet systems, including its homodyne and heterodyne components and beyond. We obtain the Floquet optical conductivity of specific driven models, including two-dimensional Dirac material such as the surface of a topological insulator, graphene, and the Haldane model irradiated with circularly or linearly polarized laser, as well as semiconductor quantum well driven by an ac potential. We obtain approximate analytical expressions and perform numerically exact calculations of the Floquet optical conductivity in different scenarios of the occupation of the Floquet bands, in particular, the diagonal Floquet distribution and the distribution obtained after a quench. We comment on experimental signatures and detection of Floquet topological phases using optical probes.Comment: 16 pages, 10 figure

Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit

We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger-Rabi and the Landau-Zener-St\"uckelberg-Majorana models. We reproduce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.Comment: v2: 28 single-column pages, 5 figures; various typos fixed; some notation and connection to other perturbation schemes clarified; new, more descriptive title and abstract. Published versio

Quantum noise detects Floquet topological phases

We study quantum noise in a nonequilibrium, periodically driven, open system attached to static leads. Using a Floquet Green's function formalism we show, both analytically and numerically, that local voltage noise spectra can detect the rich structure of Floquet topological phases unambiguously. Remarkably, both regular and anomalous Floquet topological bound states can be detected, and distinguished, via peak structures of noise spectra at the edge around zero-, half-, and full-drive-frequency. We also show that the topological features of local noise are robust against moderate disorder. Thus, local noise measurements are sensitive detectors of Floquet topological phases.Comment: 4.5 pages + supplemental material; v2: improved presentation and new and updated reference

Exciton condensation and charge fractionalization in a topological insulator film

An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a coherent exciton condensate, similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. Such a `topological' exciton condensate (TEC) exhibits a host of unusual properties; the most interesting among them is the fractional charge +-e/2 carried by a singly quantized vortex in the TEC order parameter.Comment: 4 pages, 1 figure, version to appear in PRL (minor stylistic changes). For related work and info visit http://www.physics.ubc.ca/~franz

Two-dimensional Dirac fermions in a topological insulator: transport in the quantum limit

Pulsed magnetic fields of up to 55T are used to investigate the transport properties of the topological insulator Bi_2Se_3 in the extreme quantum limit. For samples with a bulk carrier density of n = 2.9\times10^16cm^-3, the lowest Landau level of the bulk 3D Fermi surface is reached by a field of 4T. For fields well beyond this limit, Shubnikov-de Haas oscillations arising from quantization of the 2D surface state are observed, with the \nu =1 Landau level attained by a field of 35T. These measurements reveal the presence of additional oscillations which occur at fields corresponding to simple rational fractions of the integer Landau indices.Comment: 5 pages, 4 figure