arXiv subjects

Victor Galitski

Publications and source records attributed to Victor Galitski.

At least 127 records · Page 7Linked to original sources

arXiv2012

Magnetoresistance of an Anderson insulator of bosons

We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunnelling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ^{-1}(B)-ξ^{-1}(0)\sim B^{4/5}. The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the non-trivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.

cond-mat.dis-nn↗

arXiv2012

Exotic quantum spin models in spin-orbit-coupled Mott insulators

We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method" and derive the low-energy spin Hamiltonian for fermions and bosons. The spin Hamiltonian is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interactions and it has a rich classical phase diagram with collinear, spiral and vortex phases.

cond-mat.quant-gas↗

arXiv2012

Two-component Coulomb Glass in Disordered Superconducting Films

Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range inter-electron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.

cond-mat.dis-nn↗

arXiv2012

Microscopic theory for a ferromagnetic-nanowire/superconductor heterostructure: Transport, fluctuations and topological superconductivity

Motivated by the recent experiment of Wang et al. [Nature Physics 6, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic Cobalt nanowires proximity-coupled to superconducting electrodes, we study proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit-coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interface, derive a set of self-consistent boundary conditions, and find an expression for the p-wave minigap in terms of the microscopic parameters of the contact. Second, we study temperature-dependence of the resistance near the superconducting transition and find that it should generally feature a fluctuation-induced peak. The upturn in resistance is related to the suppression of the single-particle density of states due to the formation of fluctuating pairs, whose tunneling is suppressed. In conclusion, we discuss this and related setups involving ferromagnetic nanowires in the context of one-dimensional topological superconductors. It is argued that to realize unpaired end Majorana modes, one does not necessarily need a half-metallic state, but a partial spin polarization may suffice. Finally, we propose yet another related class of material systems -- ferromagnetic semiconductor wires coupled to ferromagnetic superconductors -- where direct realization of Kitaev-Majorana model should be especially straightforward.

cond-mat.supr-con↗

arXiv2012

Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance

A recent theoretical work [Nature Phys., 7, 490 (2011)] has demonstrated that external non-equilibrium perturbations may be used to convert a two-dimensional semiconductor, initially in a topologically trivial state, into a Floquet topological insulator. Here, we develop a non-trivial extension of these ideas to three-dimensional systems. In this case, we show that a two-photon resonance may provide the necessary twist needed to transform an initially unremarkable band structure into a topological Floquet spectrum. We provide both an intuitive, geometrical, picture of this phenomenon and also support it by an exact solution of a realistic lattice model that upon irradiation features single topological Dirac modes at the two-dimensional boundary of the system. It is shown that the surface spectrum can be controlled by choosing the polarization and frequency of the driving electromagnetic field. Specific experimental realizations of a three-dimensional Floquet topological insulator are proposed.

cond-mat.mes-hall↗

arXiv2011

Topological Phase Transitions for Interacting Finite Systems

In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of this result, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.

cond-mat.str-el↗

arXiv2011

Low-density molecular gas of tightly-bound Rashba-Dresselhaus fermions

We study interacting Rashba-Dresselhaus fermions in two spatial dimensions. First, we present a new exact solution to the two-particle pairing problem of spin-orbit-coupled fermions for arbitrary Rashba and Dresselhaus spin-orbit interactions. An exact molecular wave function and the Green function are explicitly derived along with the binding energy and the spectrum of the molecular state. In the second part, we consider a thermal Boltzmann gas of fermionic molecules and compute the time-of-flight velocity and spin distributions for a single fermion in the gas. We show that the pairing signatures can be observed already in the first-moment expectation values, such as time-of-flight density and spin profiles.

cond-mat.quant-gas↗

arXiv2011

A theory of Topological Kondo Insulators

We examine how the properties of the Kondo insulators change when the symmetry of the underlying crystal field multiplets is taken into account. We employ the Anderson lattice model and consider its low-energy physics. We show that in a large class of crystal field configurations, Kondo insulators can develop a topological non-trivial ground-state. Such topological Kondo insulators are adiabatically connected to non-interacting insulators with unphysically large spin-orbit coupling, and as such may be regarded as interaction-driven topological insulators. We analyze the entanglement entropy of the Anderson lattice model of Kondo insulators by evaluating its entanglement spectrum. Our results for the entanglement spectrum are consistent with the surface state calculations. Lastly, we discuss the construction of the maximally localized Wannier wave functions for generic Kondo insulators.

cond-mat.str-el↗

arXiv2011

Vortices in spin-orbit-coupled Bose-Einstein condensates

Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures, but gives rise instead to non-equilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (1) to rotate both the lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly non-universal and depend strongly on a specific laser scheme and system parameters.

cond-mat.quant-gas↗

arXiv2011

Kaleidoscope of exotic quantum phases in a frustrated XY model

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought for Bose metal with a clearly identifiable Bose surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.

cond-mat.str-el↗

arXiv2011

Gutzwiller-projected wave functions for the pseudogap state of underdoped high-temperature superconductors

Recent experiments strongly suggest that a Fermi surface reconstruction and multiple Fermi pockets are important common features of the underdoped high-temperature cuprate superconductors. A related theoretical work [Phys. Rev. B 79, 134512 (2009)] has demonstrated that a number of hallmark phenomena observed in the underdoped cuprates appear naturally in the scenario of a paired electron pocket co-existing with unpaired hole pockets. We propose Gutzwiller-projected wave-functions to describe this two-fluid state as well as two competing states in its vicinity. It is argued that a pseudogap state constructed from these wave-functions may be selected by energetics at finite temperatures due to spin fluctuations.

cond-mat.supr-con↗

arXiv2011

Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors

Qubits in topological quantum computation are built from non-Abelian anyons. Adiabatic braiding of anyons is exploited as topologically protected logical gate operations. Thus, the adiabaticity upon which the notion of quantum statistics is defined, plays a fundamental role in defining the non-Abelian anyons. We study the non-adiabatic effects in braidings of Ising-type anyons, namely Majorana fermions in topological superconductors, using the formalism of time-dependent Bogoliubov-de Gennes equations. Using this formalism, we consider non-adiabatic corrections to non-Abelian statistics from: (1) tunneling splitting of anyons imposing an additional dynamical phase to the transformation of ground states; (2) transitions to excited states that are potentially destructive to non-Abelian statistics since the non-local fermion occupation can be spoiled by such processes. However, if the bound states are localized and being braided together with the anyons, non-Abelian statistics can be recovered once the definition of Majorana operators is appropriately generalized taking into account the fermion parity in these states. On the other hand, if the excited states are extended over the whole system and form a continuum, the notion of local fermion parity no longer holds. We then quantitatively characterize the errors introduced in this situation.

cond-mat.supr-con↗

arXiv2011

Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach

We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the paper utilizes a geometric Hilbert-space-invariant formulation of unitary time-evolution, where a quantum Hamiltonian is viewed as a trajectory in an abstract Lie algebra, while the sought-after evolution operator is a trajectory in a dynamic group, generated by the algebra via exponentiation. The evolution operator is uniquely determined by the time-dependent dual generators that satisfy a system of differential equations, dubbed here dual Schrodinger-Bloch equations, which represent a viable alternative to the conventional Schrodinger formulation. These dual Schrodinger-Bloch equations are derived and analyzed on a number of specific examples. It is shown that deterministic dynamics of a closed classical dynamical system occurs as action of a symmetry group on a classical manifold and is driven by the same dual generators as in the corresponding quantum problem. This represents quantum-to-classical correspondence. In the second part of the paper, we further extend the Lie algebraic approach to a wide class of interacting many-particle lattice models. A generalized Hubbard-Stratonovich transform is proposed and it is used to show that the thermodynamic partition function of a generic many-body quantum lattice model can be expressed in terms of traces of single-particle evolution operators governed by the dynamic Hubbard-Stratonovich fields. Finally, we derive Hubbard-Stratonovich dynamical systems for the Bose-Hubbard model and a quantum spin model and use the Lie-algebraic approach to obtain new non-perturbative dual descriptions of these theories.

cond-mat.stat-mech↗

arXiv2010

Breakdown of the coherent state path integral: two simple examples

We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.

quant-ph↗

arXiv2010

Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian

Correlation functions of primary fields in the Wess-Zumino-Novikov-Witten (WZNW) model are known to satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of the exactly-solvable Gaudin magnet. We modify the KZ equations by replacing these Gaudin operators with constants of motion of the closely-related Richardson pairing Hamiltonian and reconstruct a deformed WZNW model, whose correlators satisfy these equations. This modified theory, dubbed here the boundary WZNW model, contains a term that breaks translational symmetry and therefore represents a generalized boundary operator. The corresponding correlators of the boundary WZNW model are calculated and are shown to acquire exponential prefactors, in contrast to the bulk WZNW theories. The solution also establishes a connection between correlation functions of the WZNW model and the spectrum of the reduced pairing Hamiltonian.

cond-mat.str-el↗

arXiv2010

Interaction effects and quantum phase transitions in topological insulators

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at $T = 0$ as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

cond-mat.str-el↗

arXiv2010

Floquet Topological Insulator in Semiconductor Quantum Wells

Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride - cadmium telluride quantum wells. We show that a topological state can be induced in such a device, initially in the trivial phase, by irradiation with microwave frequencies, without closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. The velocity of the edge states can be tuned by adjusting the intensity of the microwave radiation. We discuss the necessary experimental parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equilibrium topological state, Floquet topological insulator, introduced in this paper.

cond-mat.mtrl-sci↗

arXiv2010

Tunneling of anyonic Majorana excitations in topological superconductors

We consider topological superconductors and topological insulator/superconductor structures in the presence of multiple static vortices that host Majorana modes and focus on the Majorana tunneling processes between vortices. It is shown that these tunnelings generally lift the degeneracy of the many-body ground state in a non-universal way, sensitive to microscopic details at the smallest length-scales determined by the underlying physical problem. We also discuss an explicit realization of the Jackiw-Rossi zero-mode in a topological insulator/superconductor structure with zero chemical potential. In this case, the exact degeneracy of the many-anyon ground state is protected by an additional chiral symmetry and can be linked to the rigorous index theorem. However, the existence of a non-zero chemical potential, as expected in realistic solid state structures, breaks chiral symmetry and removes protection, which leads to the degeneracy being lifted. Finally, we discuss the implications of our results for the collective states of many-anyon systems. We argue that quantum dynamics of vortices in realistic systems is generally important and may give rise to effective time-dependent gauge factors that enter interaction terms between Majorana modes in many-anyon systems.

cond-mat.supr-con↗