arXiv subjects

Ganpathy Murthy

Publications and source records attributed to Ganpathy Murthy.

At least 55 records · Page 3Linked to original sources

arXiv2010

Compact $z=2$ Electrodynamics in 2+1 dimensions: Confinement with gapless modes

We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms a non-relativistic Sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as $L^3$.

hep-th↗

arXiv2010

Bilayer Quantum Hall Ferromagnet in a Periodic Potential

The bilayer quantum Hall system at a total filling of $ν_T=1$ has long resisted explanation in terms of a true counterflow superfluid, though many experimental features can be seen to be "almost" that of a superfluid. It is widely believed that quenched disorder is the root cause of this puzzle. Here we model the nonperturbative effects of disorder by investigating the $ν=1$ bilayer in a strong periodic potential. Our model assumes that fermions are gapped and real spins are fully polarized, and concentrates on the pseudospin variable (the layer index), with the external potential coupling to the topological (Pontryagin) density of the pseudospin. We find that as the potential strength increases, there are ground state transitions in which the topological content of the pseudospin configuration changes. These transitions are generically weakly first-order, with a new quadratically dispersing mode (in addition to the linearly dispersing Goldstone mode) sometimes becoming nearly gapless near the transition. We show that this leads to strong suppressions of both the Kosterlitz-Thouless transition temperature and the interlayer tunneling strength, which we treat perturbatively. We discuss how these results might extend to the case of true disorder.

cond-mat.str-el↗

arXiv2009

$CP^{N-1}$ Models at a Lifshitz Point

We consider $CP^{N-1}$ models in $d+1$ dimensions around Lifshitz fixed points with dynamical critical exponent $z$, in the large-N expansion. It is shown that these models are asymptotically free and dynamically generate a mass for the $CP^{N-1}$ fields for all $d=z$. We demonstrate that, for $z=d=2$, the initially nondynamical gauge field acquires kinetic terms in a way similar to usual $CP^{N-1}$ models in 1+1 dimensions. Lorentz invariance emerges generically in the low-energy electrodynamics, with a nontrivial dielectric constant given by the inverse mass gap and a magnetic permeability which has a logarithmic dependence on scale. At a special multicritical point, the low-energy electrodynamics also has $z=2$, and an essentially singular dependence of the effective action on $B=ε_{ij}\partial_iA_j$.

hep-th↗

arXiv2009

Quantum criticality near the Stoner transition in a two-dot with spin-orbit coupling

We study a system of two tunnel-coupled quantum dots, with the first dot containing interacting electrons (described by the Universal Hamiltonian) not subject to spin-orbit coupling, whereas the second contains non-interacting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum critical regime. The large-$N$ approximation allows us to calculate physical quantitites reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi liquid regime and the quantum critical regime.

cond-mat.mes-hall↗

arXiv2009

Hamiltonian Theory of Disorder at 1/3

The Hamiltonian Theory of the fractional quantum Hall (FQH) regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this paper we include disorder in our treatment, and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

cond-mat.str-el↗

arXiv2008

Quantum Hall to Insulator Transition in the Bilayer Quantum Hall Ferromagnet

We describe a new phase transition of the bilayer quantum Hall ferromagnet at filling fraction $ν= 1$. In the presence of static disorder (modeled by a periodic potential), bosonic $S=1/2$ spinons can undergo a superfluid-insulator transition while preserving the ferromagnetic order. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Physical consequences for charge and counterflow conductivity, and for interlayer tunneling conductance in the presence of quenched disorder are discussed.

cond-mat.mes-hall↗

arXiv2008

Diamagnetic persistent currents for electrons in ballistic billiards subject to a point flux

We study the persistent current of noninteracting electrons subject to a pointlike magnetic flux in the simply connected chaotic Robnik-Berry quantum billiard, and also in an annular analog thereof. For the simply connected billiard we find a large diamagnetic contribution to the persistent current at small flux, which is independent of the flux and is proportional to the number of electrons (or equivalently the density since we keep the area fixed). The size of this diamagnetic contribution is much larger than mesoscopic fluctuations in the persistent current in the simply connected billiard, and can ultimately be traced to the response of the angular momentum $l=0$ levels (neglected in semiclassical expansions) on the unit disk to a pointlike flux at its center. The same behavior is observed for the annular billiard when the inner radius is much smaller than the outer one, while the usual fluctuating persistent current and Anderson-like localization due to boundary scattering are seen when the annulus tends to a one-dimensional ring. We explore the conditions for the observability of this phenomenon.

cond-mat.mes-hall↗

arXiv2007

A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots

Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well-understood. When a specific type of spin-orbit coupling known to be dominant in two dimensional semiconductor quantum dots is introduced, we show that a new interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.

cond-mat.mes-hall↗

arXiv2007

Hamiltonian theory of the half-filled Landau level with disorder: Application to recent NMR data

The Hamiltonian Theory of the fractional quantum Hall effect is an operator description that subsumes many properties of Composite Fermions, applies to gapped and gapless cases, and has been found to provide results in quantitative accord with data on gaps, relaxation rates and polarizations at temperatures of $300mK$ and above. The only free parameter is $λ$, which is related to the sample thickness and appears in the Zhang-Das Sarma potential $v(q) = {2πe^2\over κq} e^{-qlλ}$ where $l$ and $κ$ are the magnetic length and dielectric constant. Here we examine the recent data of Tracy and Eisenstein on the nuclear magnetic resonance relaxation rate at filling factor $ν=\half$ deduced from resistivity measurements at temperatures as low as $45mK$. We find that their results can be satisfactorily described by this theory, if in addition to a $v(q)$ with $λ\simeq 2$, a constant disorder width $Γ\simeq 100 mK$ is incorporated.

cond-mat.mes-hall↗

arXiv2007

Interactions, superconducting $T_c$, and fluctuation magnetization for two coupled dots in the crossover between the Gaussian Orthogonal and Unitary ensembles

We study a system of two quantum dots connected by a hopping bridge. Both the dots and connecting region are assumed to be in universal crossover regimes between Gaussian Orthogonal and Unitary ensembles. Using a diagrammatic approach appropriate for energy separations much larger than the level spacing we obtain the ensemble-averaged one- and two-particle Green's functions. It turns out that the diffuson and cooperon parts of the two-particle Green's function can be described by separate scaling functions. We then use this information to investigate a model interacting system in which one dot has an attractive s-wave reduced Bardeen-Cooper-Schrieffer interaction, while the other is noninteracting but subject to an orbital magnetic field. We find that the critical temperature is {\it nonmonotonic} in the flux through the second dot in a certain regime of interdot coupling. Likewise, the fluctuation magnetization above the critical temperature is also nonmonotonic in this regime, can be either diamagnetic or paramagnetic, and can be deduced from the cooperon scaling function.

cond-mat.mes-hall↗

arXiv2006

Large spin-orbit effects in small quantum dots

We consider small ballistic quantum dots weakly coupled to the leads in the chaotic regime and look for significant spin-orbit effects. We find that these effects can become quite prominent in the vicinity of degeneracies of many-body energies. We illustrate the idea by considering a case where the intrinsic exchange term -JS^2 brings singlet and triplet many-body states near each other, while an externally tunable Zeeman term then closes the gap between the singlet and the one of the triplet states (with spin projection parallel the external field). Near this degeneracy, the spin-orbit coupling leads to a striking temperature dependence of the conductance, with observable effects of order unity at temperatures lower than the strength of the spin-orbit coupling. Under favorable circumstances, spelled out in the paper, these order unity effects in the conductance persist to temperatures much higher than the spin-orbit coupling strength. Our conclusions are unaffected by the presence of non-universal perturbations. We suggest a class of experiments to explore this regime.

cond-mat.mes-hall↗

arXiv2005

Coherence Network in the Quantum Hall Bilayer

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an ``imperfect'' two-dimensional superfluidity, in which there is nearly dissipationless transport at non-vanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a {\it coherence network} induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.

cond-mat.mes-hall↗

arXiv2005

A nearly closed ballistic billiard with random boundary transmission

A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary, and optical cavities with random surface refractive index. The specific example we study is a circular (integrable) billiard with no internal impurities weakly coupled to the exterior by a large number of leads with one channel open in each lead. We construct a supersymmetric nonlinear $σ$-model by averaging over the random coupling strengths between bound states and channels. The resulting theory can be used to evaluate the statistical properties of any physically measurable quantity in a billiard. As an illustration, we present results for the local density of states.

cond-mat.mes-hall↗

arXiv2005

Ballistic dynamics of a convex smooth-wall billiard with finite escape rate along the boundary

We focus on the problem of an impurity-free billiard with a random position-dependent boundary coupling to the environment. The response functions of such an open system can be obtained non-perturbatively from a supersymmetric generating functional. The derivation of this functional is based on averaging over the escape rates and results in a non-linear ballistic $σ$-model, characterized by system-specific parameters. Particular emphasis is placed on the {}``whispering gallery modes'' as the origin of surface diffusion modes in the limit of large dimensionless conductance.

cond-mat.mes-hall↗

arXiv2005

Deconfinement in d=1: A closer look

The notion of deconfinement in two d=1 models, the Schwinger model and the Heisenberg chain, is re-examined. Both have half-asymptotic excitations (where particles and antiparticles must alternate) and also truly asymptotic particles which are half as many in number. The two kinds of particles are related by a complicated transformation. The main purpose of this note is to highlight the relationship between asymptotic and half-asymptotic particles. The relevance of our findings to higher dimensions is briefly discussed.

cond-mat.str-el↗

arXiv2004

Ballistic Quantum Dots with Disorder and Interactions: A numerical study on the Robnik-Berry billiard

In previous work we have found a regime in ballistic quantum dots where interelectron interactions can be treated asymptotically exactly as the Thouless number $g$ of the dot becomes very large. However, this work depends on some assumptions concerning the renormalization group and various properties of the dot obeying Random Matrix Theory predictions at scales of the order of the Thouless energy. In this work we test the validity of those assumptions by considering a particular ballistic dot, the Robnik-Berry billiard, numerically. We find that almost all of our predictions based on the earlier work are borne out, with the exception of fluctuations of certain matrix elements of interaction operators. We conclude that, at least in the Robnik-Berry billiard, one can trust the results of our previous work at a qualitative and semi-quantitative level.

cond-mat.mes-hall↗

arXiv2004

Interplay between the mesoscopic Stoner and Kondo effects in quantum dots

We consider electrons confined to a quantum dot interacting antiferromagnetically with a spin-$\half$ Kondo impurity. The electrons also interact among themselves ferromagnetically with a dimensionless coupling $\tilde{J}$, where $\tilde{J}=1$ denotes the bulk Stoner transition. We show that as $\tilde{J}$ approaches 1 there is a regime with enhanced Kondo correlations, followed by one where the Kondo effect is destroyed and impurity is spin polarized opposite to the dot electrons. The most striking signature of the first, Stoner-enhanced Kondo regime, is that a Zeeman field increases the Kondo scale, in contrast to the case for noninteracting dot electrons. Implications for experiments are discussed.

cond-mat.mes-hall↗

arXiv2004

Random Matrix Crossovers and Quantum Critical Crossovers for Interacting Electrons in Quantum Dots

Quantum dots with large Thouless number $g$ embody a regime where both disorder and interactions can be treated nonperturbatively using large-N techniques (with $N=g$) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a new, tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at the new energy scale. The nonperturbative physics of this regime can only be described by the large-N approach, as we illustrate with two experimentally relevant examples.

cond-mat.mes-hall↗