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arXiv2008

Quantized vortices in atomic Bose-Einstein condensates

In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.

cond-mat.other↗
arXiv2008

Theory of Electromotive Force Induced by Domain Wall Motion

We formulate a theory on the dynamics of conduction electrons in the presence of moving magnetic textures in ferromagnetic materials. We show that the variation of local magnetization in both space and time gives rise to topological fields, which induce electromotive forces on the electrons. Universal results are obtained for the emf induced by both transverse and vortex domain walls traveling in a magnetic film strip, and their measurement may provide clear characterization on the motion of such walls.

cond-mat.mtrl-sci↗
arXiv2009

Revealing anyonic features in a toric code quantum simulation

Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons on the toric code model. By encoding the model in the multi-partite entangled state of polarized photons, we are able to demonstrate various manipulations of anyonic states and, in particular, their characteristic fractional statistics.

quant-ph↗
arXiv2007

From spin and orbital SU(4) to spin SU(2) Kondo effect in double quantum dot

We consider spin and orbital Kondo effect in a parallel arrangement of two strongly electrostatically coupled quantum dots. Increasing the exchange of electrons between the dots through the attached leads induces a smooth crossover between SU(4) spin- and orbital Kondo effect and SU(2) spin Kondo effect. Being the same for the SU(4) and SU(2) symmetry points, the Kondo temperature drops slightly in the intermediate regime. Experimentally, two kinds of Kondo effect can be discriminated by the sensitivity to the suppression of the spin Kondo effect by Zeeman field. The dependence of the Kondo temperature and of the differential conductance on the strength of electronic exchange through the leads and Zeeman field is analyzed in detail.

cond-mat.mes-hall↗
arXiv2008

Double quantum dot as a probe of nonequilibrium charge fluctuations at the quantum point contact

Absorption of energy quanta generated by quantum point contact results in the inelastic current through the double quantum dot placed nearby. In contrast to a single quantum dot, the inelastic current through the double quantum dot is sensitive to the energy dependence of the quantum point contact transmission, which can explain the experimentally observed features. We calculate the inelastic current as a function of microscopic parameters of the circuit.

cond-mat.mes-hall↗
arXiv2008

Dynamics of Localized Waves

We have measured pulsed microwave transmission through quasi-1D samples with lengths up to three localization lengths. For times approaching four times the diffusion time τ_D, transmission is diffusive in accord with the self-consistent theory of localization for the renormalized diffusion coefficient in space and frequency, D(z,Ω). For longer times, the transmission decay rate first agrees with and later falls increasingly below the self-consistent theory. Beyond the Heisenberg time, the decay rate approaches the predictions of a dynamic single parameter scaling model which reflects the decay of long-lived localized modes and converges to the results of 1D simulations.

cond-mat.dis-nn↗
arXiv2008

Critical points of 2d disordered Dirac fermions: the Quantum Hall Transitions revisited

We propose a resolution of the renormalization group flow for the disordered Dirac fermion theories describing the quantum Hall transition (QHT) and spin Quantum Hall transition (SQHT), which previously revealed no perturbative fixed points at 1-loop and higher. The approach involves carrying out the flow in 2 stages, the first stage utilizing a new form of super spin-charge separation to flow to gl(1|1)_N and osp(2|2)_{-2N} supercurrent algebra theories, where N is the number of copies. This leads to the unconventional feature that at the critical point the exponents depend on the original number of copies N. In the second stage, additional forms of disorder are incorporated as dimension zero logarithmic operators, and the resulting actions have explicit forms in terms of two scalar fields and a symplectic fermion. Under some assumptions, the multi-fractal exponents are computed with the result q(1-q)/4 and q(1-q)/8 for the QHT and SQHT respectively, and are within a few percent of numerical estimates.

cond-mat.mes-hall↗
arXiv2007

Alternative approach to the description of metallic clusters

A detailed simple model is applied to study a metallic cluster. It is assumed that the ions and delocalized electrons are distributed randomly throughout the cluster. The delocalized electrons are assumed to be degenerate. A spherical ball models the shape of a cluster. The energy of the microscopic electrostatic field around the ions is taken into account and calculated. It is shown in the framework of the model that the cluster is stable. Equilibrium radius of a ball and the energy of the equilibrium cluster are calculated. Bulk modulus of a cluster is calculated also.

cond-mat.mtrl-sci↗
arXiv2007

Thermoelectrical manipulation of nano-magnets

We propose a device that can operate as a magneto-resistive switch or oscillator. The device is based on a spin-thermo-electronic control of the exchange coupling of two strong ferromagnets through a weakly ferromagnetic spacer. We show that the local Joule heating due to a high concentration of current in a magnetic point contact or a nanopillar can be used to reversibly drive the weak ferromagnet through its Curie point and thereby exchange-decouple the strongly ferromagnetic layers, which have an antiparallel ground state. Such a spin-thermionic parallel-to-antiparallel switching causes magnetoresistance oscillations where the frequency can be controlled by proper biasing from essentially DC to GHz.

cond-mat.mes-hall↗
arXiv2007

Anderson localization in quantum chaos: scaling and universality

The one parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one parameter scaling theory to: a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in what situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Schmit-Giannoni conjecture, b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1$d$ kicked rotors with non analytical potentials and a 3$d$ kicked rotor with a smooth potential.

cond-mat.dis-nn↗
arXiv2008

Leaky Quantum Graphs: A Review

The aim of this review is to provide an overview of a recent work concerning ``leaky'' quantum graphs described by Hamiltonians given formally by the expression $-Δ-αδ(x-Γ)$ with a singular attractive interaction supported by a graph-like set in $\mathbb{R}^ν,\: ν=2,3$. We will explain how such singular Schrödinger operators can be properly defined for different codimensions of $Γ$. Furthermore, we are going to discuss their properties, in particular, the way in which the geometry of $Γ$ influences their spectra and the scattering, strong-coupling asymptotic behavior, and a discrete counterpart to leaky-graph Hamiltonians using point interactions. The subject cannot be regarded as closed at present, and we will add a list of open problems hoping that the reader will take some of them as a challenge.

math-ph↗
arXiv2008

Quenching of quantum Hall effect and the role of undoped planes in multilayered epitaxial graphene

We propose a mechanism for the quenching of the Shubnikov de Haas oscillations and the quantum Hall effect observed in epitaxial graphene. Experimental data show that the scattering time of the conduction electron is magnetic field dependent and of the order of the cyclotron orbit period, \textit{i.e.} can be much smaller than the zero field scattering time. Our scenario involves the extraordinary graphene $n=0$ Landau level of the uncharged layers that produces a high density of states at the Fermi level. We find that the coupling between this $n=0$ Landau level and the conducting states of the doped plane leads to a scattering mechanism having the right magnitude to explain the experimental data.

cond-mat.mes-hall↗
arXiv2007

Persistent Current for a genus g=2 structure

We report the first calculation of persistent current in two coupled rings which form a character ``8'' genus g=2 structure. We obtain an exact solution for the persistent current and investigated the exact solution numerically. For two large coupled rings with equal fluxes, we find that the persistent current in the two coupled rings is equal to that in a single ring. For opposite fluxes the energy has a chaotic structure. For both cases the periodicity is $h/e$. This results are obtained within an extension of Dirac's second class method to fermionic constraints. This theory can be tested in the ballistic regime.

cond-mat.mes-hall↗
arXiv2007

Non-Abelian gauge field effects and its relevance to spinning particle dynamics in the technology of spintronics

We describe formally the precession of spin vector about the k-space effective magnetic field in condensed matter system with spin orbital effects as constituting a local transformation of the electron wavefunction which necessarily invokes the SU(2) transformation rule to ensure covariance. We showed a "no-precession" condition as pre-requisite for the spin gauge field to exert its influence on spin particle motion. The effects of the spin gauge field on spin particle motion were shown to be consistent in both classical and quantum pictures, which hence should underpin theoretical explanations for important effects in anomalous Hall, spin Hall, spin torque, optical Magnus, geometric quantum computation.

quant-ph↗
arXiv2009

Resonant carrier dynamics in strongly biassed superlattices

We study coherent electron dynamics in a biassed undriven ideal semiconductor superlattice coupled to the continuum, near energy level anticrossings. In particular, we examine the dependence of wavepacket dynamical characteristics on electric field detuning, and investigate mixed regimes involving a superposition of energy level anticrossings showing both Rabi oscillations and resonant tunnelling. In earlier work [Phys. Rev. B 75 165421 (2007)], Rabi and Zener resonances were shown to have a common origin, and a criteria for the occurrence of either was proposed. The present results allow a better understanding of the nature of an interminiband resonance, which can be useful in the areas of microwave radiation generation and matter manipulation on the particle level, as well as demonstrate an alternative approach to examining electron level structure of a finite superlattice.

cond-mat.mtrl-sci↗
arXiv2009

On classification of modular tensor categories

We classify all unitary modular tensor categories (UMTCs) of rank $\leq 4$. There are a total of 70 UMTCs of rank $\leq 4$ (Note that some authors would have counted as 35 MTCs.) In our convention there are two trivial unitary MTCs distinguished by the modular $S$ matrix $S=(\pm1)$. Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. UMTCs encode topological properties of anyonic quantum systems and can be used to build fault-tolerant quantum computers. We conjecture that there are only finitely many equivalence classes of MTCs for any given rank, and a UMTC is universal for anyonic quantum computation if and only if its global quantum dimension $D^2$ is \emph{not} an integer. Discovery of non-abelain anyons in Nature will be a landmark in condensed matter physics. The non-abelian anyons in UMTCs of rank $\leq 4$ are the simplest, and, therefore, are most likely to be found. G. Moore and N. Read proposed that non-abelian statistics could occur in fractional quantum Hall (FQH) liquids. The Read-Rezayi conjecture predicts the existence of anyons related to $SU(2)_k$ in FQH liquids at filling fractions $ν=2+\frac{k}{k+2}$ for $k=1,2,3$. For $ν={5/2}$ and $SU(2)_2$, there is a numerical proof and experimental evidence for this conjecture. The Ising anyons might exist in chiral superconductors (strontium ruthenate). There are theoretical designs for the toric code MTC using Josephson junction array, for the $Fib\times Fib$ MTC using optical lattice, and for the $SU(2)_k$ using cold trapped bosonic atoms.

math.QA↗
arXiv2007

Dynamical Symmetry Breaking of a Relativistic Model in Quasi-(1+1)-Dimensions. I. Formulation

The dynamical symmetry breaking in a quasi-(1+1)-dimensional relativistic model is investigated. The motions of particles in intrachain are described as a relativistic electron-hole gas, while the interchain hopping term is introduced as a 0th-component of vector in (1+1)-dimensions, a kind of chemical potential of the system. The gauge symmetry of the model is chosen as U(1) suitable for a possible situation of a real substance in condensed matter physics. We consider the BCS-type contact interactions for the s-wave fermion-pair condensates, while employ the nonlocal interactions of the generalized BCS framework to generate the $p$-, $d$- and $f$-wave condensations in the system. Especially we examine the dynamical generation of a Dirac mass term and superconductivity in the model. The phenomenon is interpreted as metal-insulator/metal-superconductor phase transitions.

cond-mat.supr-con↗