Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.Comment: 11 pages, 6 figure

Irreducible Representations of Diperiodic Groups

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a generalized translational group and an axial point group. The results are presented in the form of the tables, containing the matrices of the irreducible representations of the generators of the groups. General properties and some physical applications (degeneracy and topology of the energy bands, selection rules, etc.) are discussed.Comment: 30 pages, 5 figures, 28 tables, 18 refs, LaTex2.0

Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point

We study the adiabatic dynamics of Majorana fermions across a quantum phase transition. We show that the Kibble-Zurek scaling, which describes the density of bulk defects produced during the critical point crossing, is not valid for edge Majorana fermions. Therefore, the dynamics governing an edge state quench is nonuniversal and depends on the topological features of the system. Besides, we show that the localization of Majorana fermions is a necessary ingredient to guaranty robustness against defect production.Comment: Submitted to the Special Issue on "Dynamics and Thermalization in Isolated Quantum Many-Body Systems" in New Journal of Physics. Editors:M. Cazalilla, M. Rigol. New references and some typos correcte

The Cosmological Constant and Horava-Lifshitz Gravity

Horava-Lifshitz theory of gravity with detailed balance is plagued by the presence of a negative bare (or geometrical) cosmological constant which makes its cosmology clash with observations. We argue that adding the effects of the large vacuum energy of quantum matter fields, this bare cosmological constant can be approximately compensated to account for the small observed (total) cosmological constant. Even though we cannot address the fine-tuning problem in this way, we are able to establish a relation between the smallness of observed cosmological constant and the length scale at which dimension 4 corrections to the Einstein gravity become significant for cosmology. This scale turns out to be approximately 5 times the Planck length for an (almost) vanishing observed cosmological constant and we therefore argue that its smallness guarantees that Lorentz invariance is broken only at very small scales. We are also able to provide a first rough estimation for the infrared values of the parameters of the theory $\mu$ and $Lambda_w$.Comment: 9 pages, Late

Some remarks on a nongeometrical interpretation of gravity and the flatness problem

In a nongeometrical interpretation of gravity, the metric $g_{\mu\nu}(x)=\eta_{\mu\nu}+\Phi_{\mu\nu}(x)$ is interpreted as an {\em effective} metric, whereas $\Phi_{\mu\nu}(x)$ is interpreted as a fundamental gravitational field, propagated in spacetime which is actually flat. Some advantages and disadvantages of such an interpretation are discussed. The main advantage is a natural resolution of the flatness problem.Comment: 6 pages, late

Quantum transport through mesoscopic disordered interfaces, junctions, and multilayers

The study explores perpendicular transport through macroscopically inhomogeneous three-dimensional disordered conductors using mesoscopic methods (real-space Green function technique in a two-probe measuring geometry). The nanoscale samples (containing $\sim1000$ atoms) are modeled by a tight-binding Hamiltonian on a simple cubic lattice where disorder is introduced in the on-site potential energy. I compute the transport properties of: disordered metallic junctions formed by concatenating two homogenous samples with different kinds of microscopic disorder, a single strongly disordered interface, and multilayers composed of such interfaces and homogeneous layers characterized by different strength of the same type of microscopic disorder. This allows us to: contrast resistor model (semiclassical) approach with fully quantum description of dirty mesoscopic multilayers; study the transmission properties of dirty interfaces (where Schep-Bauer distribution of transmission eigenvalues is confirmed for single interface, as well as for the stack of such interfaces that is thinner than the localization length); and elucidate the effect of coupling to ideal leads (``measuring apparatus'') on the conductance of both bulk conductors and dirty interfaces When multilayer contains a ballistic layer in between two interfaces, its disorder-averaged conductance oscillates as a function of Fermi energy. I also address some fundamental issues in quantum transport theory--the relationship between Kubo formula in exact state representation and ``mesoscopic Kubo formula'' (which gives the zero-temperature conductance of a finite-size sample attached to two semi-infinite ideal leads) is thoroughly reexamined by comparing their answers for both the junctions and homogeneous samples.Comment: 18 pages, 17 embedded EPS figure

Asymptotic symmetry and conservation laws in 2d Poincar\'e gauge theory of gravity

The structure of the asymptotic symmetry in the Poincar\'e gauge theory of gravity in 2d is clarified by using the Hamiltonian formalism. The improved form of the generator of the asymptotic symmetry is found for very general asymptotic behaviour of phase space variables, and the related conserved quantities are explicitly constructed.Comment: 22 pages, Plain Te