arXiv subjects

L. Radzihovsky

Publications and source records attributed to L. Radzihovsky.

At least 19 recordsLinked to original sources

arXiv2017

High-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors and Related Systems

It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localisation that have manifestations in the disorder-averaged density of states, conductivity and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors and all sufficiently high-dimensional systems. Moreover, such systems exhibit unconventional behaviour of Lifshitz tails, energy-level statistics and ballistic-transport properties. Here we review recent progress and the status of results on non-Anderson disorder-driven transitions and related phenomena.

cond-mat.mes-hall↗

arXiv2016

Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems

Systems with the power-law quasiparticle dispersion $ε_{\bf k}\propto k^α$ exhibit non-Anderson disorder-driven transitions in dimensions $d>2α$, as exemplified by Weyl semimetals, 1D and 2D arrays of ultracold ions with long-range interactions, quantum kicked rotors and semiconductor models in high dimensions. We study the wavefunction structure in such systems and demonstrate that at these transitions they exhibit fractal behaviour with an infinite set of multifractal exponents. The multifractality persists even when the wavefunction localisation is forbidden by symmetry or topology and occurs as a result of elastic scattering between all momentum states in the band on length scales shorter than the mean free path. We calculate explicitly the multifractal spectra in semiconductors and Weyl semimetals using one-loop and two-loop renormalisation-group approaches slightly above the marginal dimension $d=2α$.

cond-mat.mes-hall↗

arXiv2016

Critical exponents at the unconventional disorder-driven transition in a Weyl semimetal

Disordered non-interacting systems in sufficiently high dimensions have been predicted to display a non-Anderson disorder-driven transition that manifests itself in the critical behaviour of the density of states and other physical observables. Recently the critical properties of this transition have been extensively studied for the specific case of Weyl semimetals by means of numerical and renormalisation-group approaches. Despite this, the values of the critical exponents at such a transition in a Weyl semimetal are currently under debate. We present an independent calculation of the critical exponents using a two-loop renormalisation-group approach for Weyl fermions in $2-\varepsilon$ dimensions and resolve controversies currently existing in the literature.

cond-mat.mes-hall↗

arXiv2015

Disorder-driven transition in a chain with power-law hopping

We study a 1D system with a power-law quasiparticle dispersion $\propto |k|^α\sign k$ in the presence of a short-range-correlated random potential and demonstrate that for $α<1/2$ it exhibits a disorder-driven quantum phase transition with the critical properties similar to those of the localisation transition near the edge of the band of a semiconductor in high dimensions, studied in Refs. 1 and 2. Despite the absence of localisation in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of $α$. The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localisation effects and has the potential for experimental realisations in chains of ultracold atoms in optical traps.

cond-mat.mes-hall↗

arXiv2015

Critical transport in weakly disordered semiconductors and semimetals

Motivated by Weyl semimetals and weakly doped semiconductors, we study transport in a weakly disordered semiconductor with a power-law quasiparticle dispersion $ξ_{\bf k}\propto k^α$. We show, that in $2α$ dimensions short-correlated disorder experiences logarithmic renormalisation from all energies in the band. We study the case of a general dimension $d$ using a renormalisation group, controlled by an $\varepsilon=2α-d$-expansion. Above the critical dimensions, conduction exhibits a localisation-delocalisation phase transition or a sharp crossover (depending on the symmetries of the Hamiltonian) as a function of disorder strength. We utilise this analysis to compute the low-temperature conductivity in Weyl semimetals and weakly doped semiconductors near and below the critical disorder point.

cond-mat.mes-hall↗

arXiv2015

Unconventional localisation transition in high dimensions

We study non-interacting systems with a power-law quasiparticle dispersion $ξ_{\bf k}\propto k^α$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2α$ there exists a critical disorder strength (set by the band width), at which the system exhibits a disorder-driven quantum phase transition at the bottom of the band, that lies in a universality class distinct from the Anderson transition. In contrast to the conventional wisdom, it manifests itself in, e.g., the disorder-averaged density of states. For systems in symmetry classes that permit localisation, the striking signature of this transition is a non-analytic behaviour of the mobility edge, that is pinned to the bottom of the band for subcritical disorder and grows for disorder exceeding a critical strength. Focussing on the density of states, we calculate the critical behaviour (exponents and scaling functions) at this novel transition, using a renormalisation group, controlled by an $\varepsilon=2α-d$ expansion. We also apply our analysis to Dirac materials, e.g., Weyl semimetal, where this transition takes place in physically interesting three dimensions.

cond-mat.mes-hall↗

arXiv2013

Magnetic orders, excitations, and phase transitions in Fe_1+yTe

We study the magnetic properties of Fe_1+y Te, a parent compound of the iron-based high-temperature superconductors. Motivated by recent neutron scattering experiments, we show that a spin-1 exchange model, supplemented by a single-ion spin anisotropy, accounts well for the experimentally observed low temperature magnetic phase diagram, that exhibits a commensurate bicollinear order at low Fe dopings (y < 0.12) and an incommensurate spin-spiral order at high Fe dopings (y > 0.12). We suggest that the commensurate-incommensurate transition at y = 0.12 is due to the competition between the exchange interaction and the local spin anisotropy. At low Fe dopings, the single-ion spin anisotropy is strong and pins the spins along the easy axis, which, together with the spatially anisotropic exchanges, induces a unusual bicollinear commensurate magnetic order. The low-energy spin-wave excitation is gapped due to the explict breaking of spin-rotational symmetry by the local spin anisotropy. At high Fe dopings, the single-ion anisotropy is weak, and the exchange favors an incommensurate coplanar state. The incommensurate magnetic wavevector averages out the spin anisotropy so that a gapless low-energy spin-wave excitation is obtained. We also analyze the low-energy hydrodynamic model and use it to describe the magneto-structural transition and the static and dynamical spin structure factors across the magnetic ordering transitions.

cond-mat.str-el↗

arXiv2012

Reentrant BCS-BEC crossover and a superfluid-insulator transition in optical lattices

We study thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the non-monotonic dependence of the chemical potential on detuning and the concomitant Cooper-pair/molecular size, larger in the BCS and smaller in the BEC regimes. For a single filled band we find a quantum phase transition from a band insulator to a BCS-BEC superfluid, and map out the corresponding phase diagram.

cond-mat.quant-gas↗

arXiv2012

Competition between commensurate and incommensurate magnetic ordering in Fe(1+y)Te

The Fe1+y Te1-x Sex compounds belong to the family of iron-based high temperature superconductors, in which superconductivity often appears upon doping antiferromagnetic parent compounds. Unlike other Fe-based superconductors (in which the antiferromagnetic order is at the Fermi surface nesting wavevector [1/2,1/2,1]), the Fe1+y Te1-x Sex parent compound Fe1+y Te orders at a different wavevector, [1/2, 0, 1/2]. Furthermore, the ordering wavevector depends on y, the occupation of interstitial sites with excess iron; the origin of this behavior is controversial. Using inelastic neutron scattering on Fe1.08 Te, we find incommensurate magnetic fluctuations above the Neel temperature, even though the ordered state is bicollinear and commensurate with gapped spin waves. This behavior can be understood in terms of a competition between commensurate and incommensurate order, which we explain as a lock-in transition caused by the magnetic anisotropy.

cond-mat.supr-con↗

arXiv2007

Large-N expansion for unitary superfluid Fermi gases

We analyze strongly interacting Fermi gases in the unitary regime by considering the generalization to an arbitrary number N of spin-1/2 fermion flavors with Sp(2N) symmetry. For N=\infty this problem is exactly solved by the BCS-BEC mean-field theory, with corrections small in the parameter 1/N. The large-N expansion provides a systematic way to determine corrections to mean-field predictions, allowing the calculation of a variety of thermodynamic quantities at (and in the proximity to) unitarity, including the energy, the pairing gap, and upper-critical polarization (in the case of a polarized gas) for the normal to superfluid instability. For the physical case of N=1, among other quantities, we predict in the unitarity regime, the energy of the gas to be ξ=0.28 times that for the non-interacting gas and the pairing gap to be 0.52 times the Fermi energy.

cond-mat.other↗

arXiv2006

Resonantly-paired fermionic superfluids

We present a theory of a degenerate atomic Fermi gas, interacting through a narrow Feshbach resonance, whose position and therefore strength can be tuned experimentally, as demonstrated recently in ultracold trapped atomic gases. The distinguishing feature of the theory is that its accuracy is controlled by a dimensionless parameter proportional to the ratio of the width of the resonance to Fermi energy. The theory is therefore quantitatively accurate for a narrow Feshbach resonance. In the case of a narrow s-wave resonance, our analysis leads to a quantitative description of the crossover between a weakly-paired BCS superconductor of overlapping Cooper pairs and a strongly-paired molecular Bose-Einstein condensate of diatomic molecules. In the case of pairing via a p-wave resonance, that we show is always narrow for a sufficiently low density, we predict a detuning-temperature phase diagram, that in the course of a BCS-BEC crossover can exhibit a host of thermodynamically-distinct phases separated by quantum and classical phase transitions. For an intermediate strength of the dipolar anisotropy, the system exhibits a p_x + i p_y paired superfluidity that undergoes a topological phase transition between a weakly-coupled gapless ground state at large positive detuning and a strongly-paired fully-gapped molecular superfluid for a negative detuning. In two dimensions the former state is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian vortex excitations familiar from fractional quantum Hall systems.

cond-mat.supr-con↗

arXiv2006

Zero modes of two-dimensional chiral p-wave superconductors

We discuss fermionic zero modes in the two-dimensional chiral p-wave superconductors. We show quite generally, that without fine-tuning, in a macroscopic sample there is only one or zero of such Majorana-fermion modes depending only on whether the total vorticity of the order parameter is odd or even, respectively. As a special case of this, we find explicitly the one zero mode localized on a single odd-vorticity vortex, and show that, in contrast, zero modes are absent for an even-vorticity vortex. One zero mode per odd vortex persists, within an exponential accuracy, for a collection of well-separated vortices, shifting to finite E or -E energies as two odd vortices approach. These results should be useful for the demonstration of the non-Abelian statistics that such zero-mode vortices are expected to exhibit, and for their possible application in quantum computation.

cond-mat.supr-con↗

arXiv2005

Quantum phase transitions across p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a BEC-BCS crossover the system can undergo a magnetic field-tuned quantum phase transition from a p_x-wave to a p_x+i p_y-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological p_x+ i p_y to p_x+ i p_y transition at zero chemical potential μ. In two-dimensions, for μ>0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

cond-mat.supr-con↗

arXiv2005

Elasticity, fluctuations and vortex pinning in ferromagnetic superconductors: A "columnar elastic glass"

We study the elasticity, fluctuations and pinning of a putative spontaneous vortex solid in ferromagnetic superconductors. Using a rigorous thermodynamic argument, we show that in the idealized case of vanishing crystalline pinning anisotropy the long-wavelength tilt modulus of such a vortex solid vanishes identically, as guaranteed by the underlying rotational invariance. The vanishing of the tilt modulus means that, to lowest order, the associated tension elasticity is replaced by the softer, curvature elasticity. The effect of this is to make the spontaneous vortex solid qualitatively more susceptible to the disordering effects of thermal fluctuations and random pinning. We study these effects, taking into account the nonlinear elasticity, that, in three dimensions, is important at sufficiently long length scales, and showing that a ``columnar elastic glass'' phase of vortices results. This phase is controlled by a previously unstudied zero-temperature fixed point and it is characterized by elastic moduli that have universal strong wave-vector dependence out to arbitrarily long length scales, leading to non-Hookean elasticity. We argue that, although translationally disordered for weak disorder, the columnar elastic glass is stable against the proliferation of dislocations and is therefore a topologically ordered {\em elastic} glass. As a result, the phenomenology of the spontaneous vortex state of isotropic magnetic superconductors differs qualitatively from a conventional, external-field-induced mixed state. For example, for weak external fields $H$, the magnetic induction scales {\em universally} like $B(H)\sim B(0)+ c H^α$, with $α\approx 0.72$.

cond-mat.supr-con↗

arXiv2004

Transition to zero resistance in a two dimensional electron gas driven with microwaves

High-mobility 2D electron systems in a perpendicular magnetic field exhibit zero resistance states (ZRS) when driven with microwave radiation. We study the nonequilibrium phase transition into this ZRS using phenomenological equations of motion to describe the current and density fluctuations. We focus on two models for the transition into a time-independent steady state. Model-I assumes rotational invariance, density conservation, and symmetry under shifting the density globally by a constant. This model is argued to describe physics on small length scales where the density does not vary appreciably from its mean. The ordered state that arises in this case breaks rotational invariance and consists of a uniform current and transverse Hall field. We discuss some properties of this state, such as stability to fluctuations and the appearance of a Goldstone mode associated with the continuous symmetry breaking. Using dynamical renormalization group techniques, we find that with short-range interactions this model can admit a continuous transition described by mean-field theory, whereas with long-range interactions the transition is driven first-order. Model-II, which assumes only rotational invariance and density conservation and is argued to be appropriate on longer length scales, is shown to predict a first-order transition with either short- or long-range interactions. We discuss implications for experiments, including scaling relations and a possible way to detect the Goldstone mode in the case of a continuous transition into the ZRS, as well as possible signatures of a first-order transition in larger samples. We also point out the connection of our work to the well-studied phenomenon of `flocking'.

cond-mat.mes-hall↗

arXiv2004

Nonequilibrium dynamics and thermodynamics of a degenerate Fermi gas across a Feshbach resonance

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the system's parameters, such as for example a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting soliton-like collisionless dynamics can be calculated analytically. In equilibrium the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.

cond-mat.supr-con↗

arXiv2003

Critical Currents of Ideal Quantum Hall Superfluids

Filling factor $ν=1$ bilayer electron systems in the quantum Hall regime have an excitonic-condensate superfluid ground state when the layer separation $d$ is less than a critical value $d_c$. On a quantum Hall plateau current injected and removed through one of the two layers drives a dissipationless edge current that carries parallel currents, and a dissipationless bulk supercurrent that carries opposing currents in the two layers. In this paper we discuss the theory of finite supercurrent bilayer states, both in the presence and in the absence of symmetry breaking inter-layer hybridization. Solutions to the microscopic mean-field equations exist at all condensate phase winding rates for zero and sufficiently weak hybridization strengths. We find, however, that collective instabilities occur when the supercurrent exceeds a critical value determined primarily by a competition between direct and exchange inter-layer Coulomb interactions. The critical current is estimated using a local stability criterion and varies as $(d_c-d)^{1/2}$ when $d$ approaches $d_c$ from below. For large inter-layer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.

cond-mat.mes-hall↗

arXiv2003

Liquid Crystal-Solid Interface Structure at the Antiferroelectric-Ferroelectric Phase Transition

Total Internal Reflection (TIR) is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented.

cond-mat.soft↗