arXiv subjects

S. M. Girvin

Publications and source records attributed to S. M. Girvin.

At least 181 records · Page 10Linked to original sources

arXiv1996

Phonon Emission from a 2D Electron Gas: Evidence of Transition to the Hydrodynamic Regime

Using as a thermometer the temperature dependent magneto-transport of a two-dimensional electron gas, we find that effective temperature scales with current as $T_{\rm e} \sim I^a$, where $a=0.4 \pm 2\%$ in the {\it Shubnikov de-Haas} regime, and $0.53 \pm 2\%$ in both the {\it integer and fractional} quantum Hall effect. This implies the phonon energy emission rate changes from the expected $P\sim T^5$ to $P\sim T^4$. We explain this, as well as the dramatic enhancement in phonon emission efficiency using a hydrodynamic model.

cond-mat↗

arXiv1995

The effect of inter-edge Coulomb interactions on the transport between quantum Hall edge states

In a recent experiment, Milliken {\em et al.} demonstrated possible evidence for a Luttinger liquid through measurements of the tunneling conductance between edge states in the $ν=1/3$ quantum Hall plateau. However, at low temperatures, a discrepancy exists between the theoretical predictions based on Luttinger liquid theory and experiment. We consider the possibility that this is due to long-range Coulomb interactions which become dominant at low temperatures. Using renormalization group methods, we calculate the cross-over behaviour from Luttinger liquid to the Coulomb interaction dominated regime. The cross-over behaviour thus obtained seems to resolve one of the discrepancies, yielding good agreement with experiment.

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arXiv1995

Hydrodynamics of Spatially Ordered Superfluids

We derive the hydrodynamic equations for the supersolid and superhexatic phases of a neutral two-dimensional Bose fluid. We find, assuming that the normal part of the fluid is clamped to an underlying substrate, that both phases can sustain third-sound modes and that in the supersolid phase there are additional modes due to the superfluid motion of point defects (vacancies and interstitials).

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arXiv1995

Random Bonds and Topological Stability in Gapped Quantum Spin Chains

We study the effects of random bonds on spin chains that have an excitation gap in the absence of randomness. The dimerized spin-1/2 chain is our principal example. Using an asymptotically exact real space decimation renormalization group procedure, we find that dimerization is a relevant perturbation at the random singlet fixed point. For weak dimerization, the dimerized chain is in a Griffiths phase with short range spin-spin correlations and a divergent susceptibility. The string topological order, however, is not destroyed by bond randomness and dimerization is stabilized by the confinement of topological defects. We conjecture that random integer spin chains in the Haldane phase exhibit similar thermodynamic and topological properties.

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arXiv1995

Multi-Component Quantum Hall Systems: The Sum of their Parts and More

The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons have degrees of freedom in addition to the two-dimensional orbital degree of freedom. We will be primarily interested in the situation where a finite number of states, most-commonly two, are available for each orbital state within a degenerate Landau level and will refer to these systems as multi-component systems. Physical realizations of the additional degree of freedom include the electron spin, the valley index in multi-valley semiconductors, and the layer index in multiple-quantum-well systems. The consideration of multi-component systems expands the taxonomy of incompressible states and fractionally charged excitations, and for example, leads to the appearance of fractions with even denominators. More interestingly, it also leads us to new physics, including novel spontaneously broken symmetries and in some cases, finite temperature phase transitions. We present an introduction to this rich subject.

cond-mat↗

arXiv1995

Critical Behaviour of Superfluid $^4$He in Aerogel

We report on Monte Carlo studies of the critical behaviour of superfluid $^4$He in the presence of quenched disorder with long-range fractal correlations. According to the heuristic argument by Harris, uncorrelated disorder is irrelevant when the specific heat critical exponent $α$ is negative, which is the case for the pure $^4$He. However, experiments on helium in aerogel have shown that the superfluid density critical exponent $ζ$ changes. We hypothesize that this is a cross-over effect due to the fractal nature of aerogel. Modelling the aerogel as an incipient percolating cluster in 3D and weakening the bonds at the fractal sites, we perform XY-model simulations, which demonstrate an increase in $ζ$ from $0.67 \pm 0.005 $ for the pure case to an apparent value of $0.722\pm 0.005$ in the presence of the fractal disorder, provided that the helium correlation length does not exceed the fractal correlation length.

cond-mat↗

arXiv1994

Aharonov-Bohm Oscillations in a One-Dimensional Wigner Crystal-Ring

We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux and temperature dependence of the persistent current in a perfect ring is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects --- the reduced barrier height for macroscopic tunneling and loss of quantum coherence --- may result in a sharp peak in the temperature dependence. The character of the macroscopic quantum tunneling of a Wigner crystal ring is dictated by the strength of pinning. At strong pinning the tunneling of a rigid Wigner crystal chain is highly inhomogeneous, and the persistent current has a well-defined peak at $T\sim 0.5\ \hbar s/L$ independent of the barrier height ($s$ is the sound velocity of the Wigner crystal, $L$ is the length of the ring). In the weak pinning regime, the Wigner crystal tunnels through the barrier as a whole and if $V_p>T_0$ the effect of the barrier is to suppress the current amplitude and to shift the crossover temperature from $T_0$ to $T^*\simeq \sqrt{V_{p}T_{0}}$. ($V_{p}$ is the amplitude of the pinning potential, $T_{0} =\hbar v_{F}/L ,\; v_{F}\sim \hbar/ma $ is the drift velocity of a Wigner crystal ring with lattice spacing $a$). For very weak pinning, $V_p\ll T_0$, the influence of the barrier on the persistent current of a Wigner crystal ring is negligibly small.

cond-mat↗

arXiv1994

Fractional Spin for Quantum Hall Effect Quasiparticles

We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. The presence of such a spin $S$ is suggested by the spin-statistics relation $S=θ/2π$, with $θ$ being the statistical angle, and, on a sphere, is required for consistent quantization of one or more quasiparticles. By performing Berry-phase calculations for quasiparticles on a sphere we find that there are two terms, of different origin, that couple to the curvature and can be interpreted as parts of the quasiparticle spin. One, due to self-interaction, has the same value for both the quasihole and quasielectron, and fulfills the spin-statistics relation. The other is a kinematical effect and has opposite signs for the quasihole and quasielectron. The total spin thus agrees with a generalized spin-statistics theorem $(S_{qh} + S_{qe})/2 = θ/2π$. On the plane, we do not find any corresponding terms.

cond-mat↗

arXiv1994

Current--Voltage Characteristics of Two--Dimensional Vortex Glass Models

We have performed Monte Carlo simulations to determine current--voltage characteristics of two different vortex glass models in two dimensions. The results confirm the conclusions of earlier studies that there is a transition at $T=0$. In addition we find that, as $T\to 0$, the linear resistance vanishes exponentially, and the current scale, $J_{nl}$, where non-linearities appear in the $I$--$V$ characteristics varies roughly as $T^3$, quite different from the predictions of conventional flux creep theory, $J_{nl} \sim T$. The results for the two models agree quite well with each other, and also agree fairly well with recent experiments on very thin films of YBCO.

cond-mat↗

arXiv1994

Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions

At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs can be neutral or carry charge e. We derive an effective low-energy action and use it to discuss the charged and collective neutral excitations of the system. We have obtained the parameters of the Landau-Ginzburg functional from first-principles estimates and from finite-size exact diagonalization studies. We use these results to estimate the dependence of the critical temperature for the Kosterlitz-Thouless phase transition on layer separation.

cond-mat↗

arXiv1994

Persistent Current of a One-Dimensional Wigner Crystal-Ring

We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux- and temperature dependence of the persistent current is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier, that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects --- a reduced barrier height for macroscopic tunneling and a loss of quantum coherence --- results in a sharp peak in the temperature dependence, which for a rigid Wigner crystal appears at $T\sim 0.5\ \hbar s/L$, ($s$ is the sound velocity of the Wigner crystal, $L$ is the length of the ring).

cond-mat↗

arXiv1994

Superhexatics

We develop a theory for a novel state of ${}^4$He films, that possesses off diagonal order (as in the superfluid state), as well as hexatic or bond orientational order. Within our description, both the hexatic and superfluid transitions are still of the Kosterlitz-Thouless type, but the superfluid stiffness is sensitive to the hexatic transition. We briefly discuss the possible relevance of this work to recent experiments on submonolayer helium films.

cond-mat↗

arXiv1993

Universal conductivity in the boson Hubbard model in a magnetic field

The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical $XY$-model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of magnetic field is characterized by the frustration $f$. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent $z$, the correlation length exponent $ν$, and the universal conductivity $σ^*$. For the disorder-free model with $f=1/2$, we obtain $z \approx 1$, $1/ν\approx 1.5$, and $σ^*/σ_Q =0.52 \pm 0.03 $ where $σ_Q$ is the quantum conductance. We also study the case with $f=1/3$, in which we find $σ^*/σ_Q = 0.83 \pm 0.06 $. The value of $σ^*$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find $z=1.07 \pm 0.03$, $ν\approx 1$, and $σ^*/σ_Q= 0.27 \pm 0.04$ for the case $f=0$, and $z=1.14 \pm 0.03$, $ν\approx 1$, and $σ^*/σ_Q= 0.49 \pm 0.04$ for the case $f=1/2$.

cond-mat↗

arXiv1993

Quantum Ferromagnetism and Phase Transitions in Double-Layer Quantum Hall Systems

Double layer quantum Hall systems have interesting properties associated with interlayer correlations. At $ν=1/m$ where $m$ is an odd integer they exhibit spontaneous symmetry breaking equivalent to that of spin $1/2$ easy-plane ferromagnets, with the layer degree of freedom playing the role of spin. We explore the rich variety of quantum and finite temperature phase transitions in these systems. In particular, we show that a magnetic field oriented parallel to the layers induces a highly collective commensurate-incommensurate phase transition in the magnetic order.

cond-mat↗

arXiv1993

The superconductor-insulator transition in 2D dirty boson systems

Universal properties of the zero temperature superconductor-insulator transition in two-dimensional amorphous films are studied by extensive Monte Carlo simulations of bosons in a disordered medium. We report results for both short-range and long-range Coulomb interactions for several different points in parameter space. In all cases we observe a transition from a superconducting phase to an insulating Bose glass phase. {}From finite-size scaling of our Monte Carlo data we determine the universal conductivity $σ^*$ and the critical exponents at the transition. The result $σ^* = (0.55 \pm 0.06) (2e)^2/h$ for bosons with long-range Coulomb interaction is roughly consistent with experiments reported so far. We also find $σ^* = (0.14 \pm 0.03) (2e)^2/h$ for bosons with short-range interactions.

cond-mat↗

arXiv1993

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $ν= 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.

cond-mat↗

arXiv1993

Soluble `Supersymmetric' Quantum XY Model

We present a `supersymmetric' modification of the $d$-dimensional quantum rotor model whose ground state is exactly soluble. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The Hamiltonian contains three-site terms which are relevant: they change the universality class of the transition from that of the ($d+1$)--- to the $d$-dimensional classical XY model. The metallic phase has algebraic ODLRO but the superfluid density is identically zero. Variational wave functions for single-particle and collective excitations are presented.

cond-mat↗

arXiv1992

Flux Pinning and Phase Transitions in Model High-Temperature Superconductors with Columnar Defects

We calculate the degree of flux pinning by defects in model high-temperature superconductors (HTSC's). The HTSC is modeled as a three-dimensional network of resistively-shunted Josephson junctions in an external magnetic field, corresponding to a HTSC in the extreme Type-II limit. Disorder is introduced either by randomizing the coupling between grains (Model A disorder) or by removing grains (Model B disorder). Three types of defects are considered: point disorder, random line disorder, and periodic line disorder; but the emphasis is on random line disorder. Static and dynamic properties of the models are determined by Monte Carlo simulations and by solution of the analogous coupled overdamped Josephson equations in the presence of thermal noise. Random line defects considerably raise the superconducting transition temperature T$_c(B)$, and increase the apparent critical current density J$_c(B,T)$, in comparison to the defect-free crystal. They are more effective in these respects than a comparable volume density of point defects, in agreement with the experiments of Civale {\it et al}. Periodic line defects commensurate with the flux lattice are found to raise T$_c(B)$ even more than do random line defects. Random line defects are most effective when their density approximately equals the flux density. Near T$_c(B)$, our static and dynamic results appear consistent with the anisotropic Bose glass scaling hypotheses of Nelson and Vinokur, but with possibly different critical indices:

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