arXiv subjects

Victor Galitski

Publications and source records attributed to Victor Galitski.

At least 109 records · Page 6Linked to original sources

arXiv2014

Stoner ferromagnetism in a thermal pseudospin-1/2 Bose gas

We compute the finite-temperature phase diagram of a pseudospin-$1/2$ Bose gas with contact interactions, using two complementary methods: the random phase approximation (RPA) and self-consistent Hartree-Fock theory. We show that the inter-spin interactions, which break the (pseudo) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis/easy-plane ferromagnet for sufficiently strong repulsive/attractive inter-species interactions respectively. The normal easy-axis ferromagnet is the bosonic analog of Stoner ferromagnetism known in electronic systems. For the case of inter-spin attraction, we also discuss the possibility of a \textit{bosonic} analog of the Cooper paired phase. This state is shown to significantly lose in energy to the transverse ferromagnet in three dimensions, but is more energetically competitive in lower dimensions. Extending our calculations to a spin-orbit-coupled Bose gas with equal Rashba and Dresselhaus-type couplings (as recently realized in experiment), we investigate the possibility of stripe ordering in the normal phase. Within our approximations however, we do not find an instability towards stripe formation, suggesting that the stripe order melts below the condensation temperature, which is consistent with the experimental observations of Ji \textit{et al.} [Ji \textit{et al.}, Nature Physics \textbf{10}, 314 (2014)].

cond-mat.quant-gas↗

arXiv2014

Surface Theory of a Family of Topological Kondo Insulators

A low-energy theory for the helical metallic states, residing on the surface of cubic topological Kondo insulators, is derived. Despite our analysis being primarily focused on a prototype topological Kondo insulator, Samarium hexaboride (SmB$_6$), the surface theory derived here can also capture key properties of other heavy fermion topological compounds with a similar underlying crystal structure. Starting from an effective mean-field eight-band model in the bulk, we arrive at a low-energy description of the surface states, pursuing both analytical and numerical approaches. In particular, we show that helical Dirac excitations occur near the $\barΓ$ point and the two $\bar{X}$-points of the surface Brillouin zone and generally the energies of the Dirac points display {\it offset} relative to each other. We calculate the dependence of several observables (such as bulk insulating gap, energies of the surface Dirac fermions, their relative position to the bulk gap, etc.) on various parameters in the theory. We also investigate the effect of a spatial modulation of the chemical potential on the surface spectrum and show that this band bending generally results in "dragging down" of the Dirac points deep into the valence band and strong enhancement of Fermi velocity of surface electrons. Comparisons with recent ARPES and quantum oscillation experiments are drawn.

cond-mat.mes-hall↗

arXiv2014

A Strongly-Interacting Dirac Liquid on the Surface of a Topological Kondo Insulator

A topological Kondo insulator (TKI) is a strongly-correlated material, where hybridization between the conduction electrons and localized f-electrons gives rise to a crossover from a metallic behavior at high temperatures to a topologically non-trivial insulating state at low temperatures. The existing description of the TKIs is based on a slave-boson mean-field theory, which neglects dynamic fluctuation phenomena. Here, we go beyond the mean-field theory and investigate the role of Kondo fluctuations on the topological surface states. We derive an effective theory of the Dirac surface states coupled to fluctuations and show that the latter mediate strong repulsive interactions between surface excitations. We show that these effects renormalize the plasmon spectrum on the surface. We also argue that Kondo-mediated interactions may drive a magnetic instability of the surface spectrum.

cond-mat.mes-hall↗

arXiv2014

Long range $p$-wave proximity effect into a disordered metal

We use quasiclassical methods of superconductivity to study the superconducting proximity effect from a topological $p$-wave superconductor into a disordered one-dimensional metallic wire. We demonstrate that the corresponding Eilenberger equations with disorder reduce to a closed non-linear equation for the superconducting component of the matrix Green's function. Remarkably, this equation is formally equivalent to a classical mechanical system (i.e., Newton's equations), with the Green function corresponding to a coordinate of a fictitious particle and the coordinate along the wire corresponding to time. This mapping allows to obtain exact solutions in the disordered nanowire in terms of elliptic functions. A surprising result that comes out of this solution is that the $p$-wave superconductivity proximity-induced into the disordered metal remains long-range, decaying as slowly as the conventional $s$-wave superconductivity. It is also shown that impurity scattering leads to the appearance of a zero-energy peak.

cond-mat.supr-con↗

arXiv2014

Nonequilibrium probe of paired electron pockets in the underdoped cuprates

We propose an experimental method that can be used generally to test whether the cuprate pseudogap involves precursor pairing that acts to gap out the Fermi surface. The proposal involves angular-resolved photoemission spectroscopy (ARPES) performed in the presence of a transport current driven through the sample. We illustrate this proposal with a specific model of the pseudogap that contains a phase-incoherent paired electron and unpaired hole Fermi surfaces. We show that even a weak current tilts the paired band and reveals parts of the previously gapped electron Fermi surface in ARPES if the binding energy is smaller but close to the pseudogap. Stronger currents can also reveal the Fermi surface through direct suppression of pairing. The proposed experiment is sufficiently general such that it can be used to reveal putative Fermi surfaces that have been reconstructed from other types of periodic order and are gapped out due to pairing. The observation of the predicted phenomena should help resolve the central question about the existence of pairs in the enigmatic pseudogap regime.

cond-mat.supr-con↗

arXiv2014

Spiral antiferromagnets beyond the spin-wave approximation: frustrated $XY$ and Heisenberg models in the honeycomb lattice

We examine the stability of classical states with a generic incommensurate spiral order against quantum fluctuations. Specifically, we focus on the frustrated spin-1/2 $XY$ and Heisenberg models on the honeycomb lattice with nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Our variational approach is based on the Jastrow wave functions, which include quantum correlations on top of classical spin waves. We perform a systematic optimization of wave vectors and Jastrow pseudo-potentials within this class of variational states and find that quantum fluctuations favor collinear states over generic coplanar spirals. The Néel state with ${\bf Q}=(0,0)$ extends its stability well beyond the classical value $J_2/J_1=1/6$. Most importantly, the collinear states with ${\bf Q}=(0,2π/\sqrt{3})$ (and the two symmetry-related states) are found to be stable in a large regime with intermediate frustration, while at the classical level they are limited to the point $J_2/J_1=0.5$. For large frustration, the $120^\circ$ state is stabilized for finite values of $J_2/J_1$ in both models.

cond-mat.str-el↗

arXiv2014

Quasiclassical Eilenberger theory of the topological proximity effect in a superconducting nanowire

We use the quasiclassical Eilenberger theory to study the topological superconducting proximity effects between a segment of a nanowire with a p-wave order parameter and a metallic segment. This model faithfully represents key qualitative features of an experimental setup, where only a part of a nanowire is in immediate contact with a bulk superconductor, inducing topological superconductivity. It is shown that the Eilenberger equations represent a viable alternative to the Bogoliubov-de Gennes theory of the topological superconducting heterostructures and provide a much simpler quantitative description of some observables. For our setup, we obtain exact analytical solutions for the quasiclassical Green's functions and the density of states as a function of position and energy. The correlations induced by the boundary involve terms associated with both p-wave and odd-frequency pairing, which are intertwined and contribute to observables on an equal footing. We recover the signatures of the standard Majorana mode near the end of the superconducting segment, but find no such localized mode induced in the metallic segment. Instead, the zero-bias feature is spread out across the entire metallic part in accordance with the previous works. In shorter wires, the Majorana mode and delocalized peak split up away from zero energy. For long metallic segments, non-topological Andreev bound states appear and eventually merge together, giving rise to a gapless superconductor.

cond-mat.supr-con↗

arXiv2014

Nature of the phases in the frustrated XY model on the honeycomb lattice

We study the phase diagram of the frustrated XY model on the honeycomb lattice by using accurate correlated wave functions and variational Monte Carlo simulations. Our results suggest that a spin-liquid state is energetically favorable in the region of intermediate frustration, intervening between two magnetically ordered phases. The latter ones are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the model. The construction of the spin-liquid state is based on a decomposition of the underlying bosonic particles in terms of spin-1/2 fermions (partons), with a Gutzwiller projection enforcing no single occupancy, as well as a long-range Jastrow factor.

cond-mat.str-el↗

arXiv2013

Non-analytic behavior of the Casimir force across a Lifshitz transition in a spin-orbit coupled material

We propose the Casimir effect as a general method to observe Lifshitz transitions in electron systems. The concept is demonstrated with a planar spin-orbit coupled semiconductor in a magnetic field. We calculate the Casimir force between two such semiconductors and between the semiconductor and a metal as a function of the Zeeman splitting in the semiconductor. The Zeeman field causes a Fermi pocket in the semiconductor to form or collapse by tuning the system through a topological Lifshitz transition. We find that the Casimir force experiences a kink at the transition point and noticeably different behaviors on either side of the transition. The simplest experimental realization of the proposed effect would involve a metal-coated sphere suspended from a micro-cantilever above a thin layer of InSb (or another semiconductor with large $g$-factor). Numerical estimates are provided and indicate that the effect is well within experimental reach.

cond-mat.mes-hall↗

arXiv2013

Spin-orbit coupling in quantum gases

Spin-orbit coupling links a particle's velocity to its quantum mechanical spin, and is essential in numerous condensed matter phenomena, including topological insulators and Majorana fermions. In solid-state materials, spin-orbit coupling originates from the movement of electrons in a crystal's intrinsic electric field, which is uniquely prescribed. In contrast, for ultracold atomic systems, the engineered "material parameters" are tuneable: a variety of synthetic spin-orbit couplings can be engineered on demand using laser fields. Here we outline the current experimental and theoretical status of spin-orbit coupling in ultracold atomic systems, discussing unique features that enable physics impossible in any other known setting.

cond-mat.quant-gas↗

arXiv2013

Driven Electronic States at the Surface of a Topological Insulator

Motivated by recent photoemission experiments on the surface of topological insulators we compute the spectrum of driven topological surface excitations in the presence of an external light source. We completely characterize the spectral function of these non-equilibrium electron excitations for both linear and circular polarizations of the incident light. We find that in the latter case, the circularly polarized light gaps out the surface states, whereas linear polarization gives rise to an anisotropic metal with multiple Dirac cones. We compare the sizes of the gaps with recent pump-probe photoemission measurements and find good agreement. We also identify theoretically several new features in the time-dependent spectral function, such as shadow Dirac cones.

cond-mat.str-el↗

arXiv2013

Interaction-Tuned Dynamical Transitions in a Rashba Spin-Orbit Coupled Fermi Gas

We consider the time evolution of the magnetization in a Rashba spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting non-linear system of equations gives rise to three distinct dynamical regimes with qualitatively different asymptotic behaviors of the magnetization at long times. The distinct regimes and the transitions between them are controlled by the interaction strength: for weakly interacting fermions, the magnetization decays to zero. For intermediate interactions, it displays undamped oscillations about zero and for strong interactions, a partially magnetized state is dynamically stabilized. The dynamics we find is a spin analog of interaction induced self-trapping in double-well Bose Einstein condensates. The predicted phenomena can be realized in trapped Fermi gases with synthetic spin-orbit interactions.

cond-mat.quant-gas↗

arXiv2013

Kramers-Wannier Duality of Statistical Mechanics Applied to the Boolean Satisfiability Problem of Computer Science

We present a novel application of the Kramers-Wannier duality on one of the most important problems of computer science, the Boolean satisfiability problem (SAT). More specifically, we focus on sharp-SAT or equivalently #SAT - the problem of counting the number of solutions to a Boolean satisfaction formula. #SAT can be cast into a statistical-mechanical language, where it reduces to calculating the partition function of an Ising spin Hamiltonian with multi-spin interactions. We show that Kramers-Wannier duality can be generalized to apply to such multi-connected spin networks. We present an exact dual partner to #SAT and explicitly verify their equivalence with a few simple examples. It is shown that the NP-completeness of the original problem maps on the complexity of the dual problem of enumerating the number of non-negative solutions to a Diophantine system of equations. We discuss the implications of this duality and the prospects of similar dualities applied to computer science problems.

cond-mat.stat-mech↗

arXiv2013

A new exotic state in an old material: A tale of Samarium Hexaboride

We review current theoretical and experimental efforts to identify a novel class of intermetallic 4f and 5f orbital materials in which strong interactions between itinerant and predominately localized degrees of freedom gives rise to a bulk insulating state at low temperatures, while the surface remains metallic. This effect arises due to inversion of even parity conduction bands and odd parity very narrow f-electron bands. The number of band inversions is mainly determined by the crystal symmetry of a material and the corresponding degeneracy of the hybridized f-electron bands. For odd number of band inversions the metallic surface states are chiral and therefore remain robust against disorder and time-reversal invariant perturbations. We discuss a number of unresolved theoretical issues specific to topological Kondo insulators and outline experimental challenges in probing the chiral surface states in these materials.

cond-mat.str-el↗

arXiv2013

Probing the structure of entanglement with entanglement moments

We introduce and define a set of functions on pure bipartite states called entanglement moments. Usual entanglement measures tell you if two systems are entangled, while entanglement moments tell you both if and how two systems are entangled. They are defined with respect to a measurement basis in one system (e.g., a measuring device), and output numbers describing how a system (e.g., a qubit) is entangled with that measurement basis. The moments utilize different distance measures on the Hilbert space of the measured system, and can be generalized to any N-dimensional Hilbert space. As an application, they can distinguish between projective and non-projective measurements. As a particular example, we take the Rabi model's eigenstates and calculate the entanglement moments as well as the full distribution of entanglement.

quant-ph↗

arXiv2013

Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors

The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet. We assume that inversion symmetry breaking at the tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and allows equal-spin triplet superconductivity to exist in the ferromagnet. Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier, and taking account of the transport anisotropy in the HTSC. By making use of the self-consistent boundary conditions and solutions for the barrier and HTSC regions, an effective equation of motion for the ferromagnet is obtained where Andreev scattering at the barrier is incorporated as a boundary condition for the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of the HTSC, triplet p-wave superconductivity is induced. For the layer deposited on a (110) facet, the induced gap does not have the p-wave orbital character, but has an even orbital symmetry and an odd dependence on energy. For the layer on the (001) facet, an exotic f-wave superconductivity is induced. We also consider the induced triplet gap in a one-dimensional half-metallic nanowire deposited on a (001) facet of a HTSC. We find that for a wire axis along the a-axis, a robust triplet p-wave gap is induced. For a wire oriented 45 degrees away from the a-axis the induced triplet p-wave gap vanishes. For the appropriately oriented wire, the induced p-wave gap should give rise to Majorana fermions at the ends of the half-metallic wire. Based on our result, topological superconductivity in a semi-conductor nanowire may also be possible given that it is oriented along the a-axis of the HTSC.

cond-mat.supr-con↗

arXiv2012

SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms

Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as "SU(3) spin-orbit-coupling," where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically non-trivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an exact equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states -- the hallmark feature of such an SU(3) topological insulator.

cond-mat.quant-gas↗

arXiv2012

Quantum phases of hard-core bosons in a frustrated honeycomb lattice

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose-Hubbard-Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.

cond-mat.str-el↗