Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dir
ac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material. We study the effect numerically and demonstrate its robustness against moderate disorder and small deviations in optical parameters.
We propose a $mathbb{U}(1) times mathbb{Z}_2$ effective gauge theory for vortices in a $p_x+ip_y$ superfluid in two dimensions. The combined gauge transformation binds $mathbb{U}(1)$ and $mathbb{Z}_2$ defects so that the total transformation remains
single-valued and manifestly preserves the the particle-hole symmetry of the action. The $mathbb{Z}_2$ gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the $mathbb{U}(1)$ gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. More importantly, it predicts a universal Abelian phase, $exp(ipi/8)$, upon the exchange of two vortices. This phase is modified by non-universal corrections due to the partial Chern-Simon term, which are nevertheless screened in a charged superfluid at distances that are larger than the penetration depth.
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e
. metallic bulk transport with conductivity of order $e^2/h$, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.
We describe and analyze in detail our recent theoretical proposal for the realization and manipulation of anyons in a weakly interacting system consisting of a two-dimensional electron gas in the integer quantum Hall regime adjacent to a type-II supe
rconducting film with an artificial array of pinning sites. The anyon is realized in response to a defect in the pinned vortex lattice and carries a charge pm e/2 and a statistical angle pi/4. We establish this result, both analytically and numerically, in three complementary approaches: (i) a continuum model of two-dimensional electrons in the vortex lattice of the superconducting film; (ii) a minimal tight-binding lattice model that captures the essential features of the system; and (iii) an effective theory of the superconducting vortex lattice superposed on the integer quantum Hall state. We propose a novel method to measure the fractional charge directly in a bulk transport experiment and an all-electric setup for an ``anyon shuttle implementing the braiding operations. We briefly discuss conditions for fabricating the system in the lab and its potential applications in quantum information processing with non-Abelian anyons.
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.
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 s
olutions 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.
