arXiv subjects

B. I. Halperin

Publications and source records attributed to B. I. Halperin.

At least 37 records · Page 2Linked to original sources

arXiv2002

Quantum Hall Stripe Phases at Integer Filling Factors

We consider stripe formation in quantum Hall systems at integer filling factors. We use Hartree-Fock calculations to obtain the phase diagram of bilayer quantum Hall systems at $ν=4n+1$ in a tilted magnetic field. We derive and analyze an effective low energy theory for the stripe phases which may be present in such systems. We discuss the possibility of stripe formation in wide well systems in a tilted magnetic field and suggest that the resistance anisotropy, observed recently by W. Pan et.al. [phys. Rev. B 64 (2001) 121305], may be due to the existence of a skyrmion stripe phase.

cond-mat.mes-hall↗

arXiv2002

Which phase is measured in the mesoscopic Aharonov-Bohm interferometer?

Mesoscopic solid state Aharonov-Bohm interferometers have been used to measure the "intrinsic" phase, $α_{QD}$, of the resonant quantum transmission amplitude through a quantum dot (QD). For a two-terminal "closed" interferometer, which conserves the electron current, Onsager's relations require that the measured phase shift $β$ only "jumps" between 0 and $π$. Additional terminals open the interferometer but then $β$ depends on the details of the opening. Using a theoretical model, we present quantitative criteria (which can be tested experimentally) for $β$ to be equal to the desired $α_{QD}$: the "lossy" channels near the QD should have both a small transmission and a small reflection.

cond-mat.mes-hall↗

arXiv2001

Strong enhancement of drag and dissipation at the weak- to strong- coupling phase transition in a bi-layer system at a total Landau level filling nu=1

We consider a bi-layer electronic system at a total Landau level filling factor nu =1, and focus on the transition from the regime of weak inter-layer coupling to that of the strongly coupled (1,1,1) phase (or ''quantum Hall ferromagnet''). Making the assumption that in the transition region the system is made of puddles of the (1,1,1) phase embedded in a bulk of the weakly coupled state, we show that the transition is accompanied by a strong increase in longitudinal Coulomb drag, that reaches a maximum of approximately $h/2e^{2}$. In that regime the longitudinal drag is increased with decreasing temperature.

cond-mat.mes-hall↗

arXiv2001

Weak localization and conductance fluctuations of a chaotic quantum dot with tunable spin-orbit coupling

In a two-dimensional quantum dot in a GaAs heterostructure, the spin-orbit scattering rate is substantially reduced below the rate in a bulk two-dimensional electron gas [B.I. Halperin et al, Phys. Rev. Lett. 86, 2106 (2001)]. Such a reduction can be undone if the spin-orbit coupling parameters acquire a spatial dependence, which can be achieved, e.g., by a metal gate covering only a part of the quantum dot. We calculate the effect of such spatially non-uniform spin-orbit scattering on the weak localization correction and the universal conductance fluctuations of a chaotic quantum dot coupled to electron reservoirs by ballistic point contacts, in the presence of a magnetic field parallel to the plane of the quantum dot.

cond-mat.mes-hall↗

arXiv2001

Quasiparticle spectrum of d-wave superconductors in the mixed state: a large Fermi-velocity anisotropy study

The quasiparticle spectrum of a two-dimensional d-wave superconductor in the mixed state, H_c1 << H << H_c2, is studied for large values of the ``anisotropy ratio'' alpha_D = v_F/v_Delta. For a square vortex lattice rotated by 45 degrees from the quasiparticle anisotropy axes (and the usual choice of Franz--Tesanovic singular gauge transformation) we determine essential features of the band structure asymptotically for large alpha_D, using an effective one-dimensional model, and compare them to numerical calculations. We find that several features of the band structure decay to zero exponentially fast for large alpha_D. Using a different choice of singular gauge transformation, we obtain a different band structure, but still find qualitative agreement between the 1D and full 2D calculations. Finally, we distort the square lattice into a non-Bravais lattice. Both the one- and two-dimensional numerical calculations of the energy spectra show a gap around zero-energy, with our gauge choice, and the two excitation spectra agree reasonably well.

cond-mat.supr-con↗

arXiv2001

Effective action of a compressible QH state edge: application to tunneling

The electrodynamical response of the edge of a compressible Quantum Hall system affects tunneling into the edge. Using the composite Fermi liquid theory, we derive an effective action for the edge modes interacting with tunneling charge. This action generalizes the chiral Luttinger liquid theory of the Quantum Hall edge to compressible systems in which transport is characterized by a finite Hall angle. In addition to the standard terms, the action contains a dissipative term. The tunneling exponent is calculated as a function of the filling fraction for several models, including short-range and long-range Coulomb interaction. We find that tunneling exponents are robust and to a large extent insensitive to the particular model. We discuss recent tunneling measurements in the overgrown cleaved edge systems, and demonstrate that the profile of charge density near the edge is very sensitive to the parameters of the system. In general, the density is non-monotonic, and can deviate from the bulk value by up to 30%. Implications for the correspondence to the chiral Luttinger edge theories are discussed.

cond-mat.mes-hall↗

arXiv2001

Nonuniversal behavior of scattering between fractional quantum Hall edges

Among the predicted properties of fractional quantum Hall states are fractionally charged quasiparticles and conducting edge-states described as chiral Luttinger liquids. In a system with a narrow constriction, tunneling of quasi-particles between states at different edges can lead to resistance and to shot noise. The ratio of the shot noise to the backscattered current, in the weak scattering regime, measures the fractional charge of the quasi-particle, which has been confirmed in several experiments. However, the non-linearity of the resistance predicted by the chiral Luttinger liquid theory was apparently not observed in some of these cases. As a possible explanation for these discrepancies, we consider a model where a smooth edge profile leads to formation of additional edge states. Coupling between the current carrying edge mode and the additional phonon like mode can lead to {\it nonuniversal} exponents in the current-voltage characteristic, while preserving the ratio between shot noise and the back-scattered current, for weak backscattering. For special values of the coupling, one may obtain a linear I-V behavior.

cond-mat.mes-hall↗

arXiv2000

Spin orbit effects in a GaAs quantum dot in a parallel magnetic field

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. We argue that spin-orbit effects may become important in the presence of a large parallel magnetic field B_{||}, even if they are negligble for B_{||}=0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B_{||}. Our picture is consistent with the experimental observations of Folk et al.

cond-mat.mes-hall↗

arXiv2000

Fluctuating spin g-tensor in small metal grains

In the presence of spin-orbit scattering, the splitting of an energy level in a generic small metal grain due to the Zeeman coupling to a magnetic field B depends on the direction of B, as a result of mesoscopic fluctuations. The anisotropy is described by the eigenvalues g_j^2 (j=1,2,3) of a tensor G, corresponding to the (squares of) g-factors along three principal axes. We consider the statistical distribution of G and find that the anisotropy is enhanced by eigenvalue repulsion between the g_j.

cond-mat.mes-hall↗

arXiv2000

Quasiparticle Spectrum of d-wave Superconductors in the Mixed State

The quasiparticle spectrum of a two-dimensional d-wave superconductor in the mixed state, H_{c1} << H << H_{c2}, is studied both analytically and numerically using the linearized Bogoliubov-de Gennes equation. We consider various values of the "anisotropy ratio" v_F/v_Delta for the quasiparticle velocities at the Dirac points, and we examine the implications of symmetry. For a Bravais lattice of vortices, we find there is always an isolated energy-zero (Dirac point) at the center of the Brillouin zone, but for a non-Bravais lattice with two vortices per unit cell there is generally an energy gap. In both of these cases, the density of states should vanish at zero energy, in contrast with the semiclassical prediction of a constant density of states, though the latter may hold down to very low energies for large anisotropy ratios. This result is closely related to the particle-hole symmetry of the band structures in lattices with two vortices per unit cell. More complicated non-Bravais vortex lattice configurations with at least four vortices per unit cell can break the particle-hole symmetry of the linearized energy spectrum and lead to a finite density of states at zero energy.

cond-mat.supr-con↗

arXiv1999

Mesoscopic fluctuations of the ground state spin of a small metal particle

We study the statistical distribution of the ground state spin for an ensemble of small metallic grains, using a random-matrix toy model. Using the Hartree Fock approximation, we find that already for interaction strengths well below the Stoner criterion there is an appreciable probability that the ground state has a finite, nonzero spin. Possible relations to experiments are discussed.

cond-mat.mes-hall↗

arXiv1998

Half-filled Landau level as a Fermi liquid of dipolar quasiparticles

In this paper we study the relation between the conventional Fermion-Chern-Simons (FCS) theory of the half-filled Landau level (nu=1/2), and alternate descriptions that are based on the notion of neutral quasi-particles that carry electric dipole moments. We have previously argued that these two approaches are equivalent, and that e.g., the finite compressibility obtained in the FCS approach is also obtained from the alternate approach, provided that one properly takes into account a peculiar symmetry of the dipolar quasiparticles --- the invariance of their energy to a shift of their center of mass momentum. Here, we demonstrate the equivalence of these two approaches in detail. We first study a model where the charge and flux of each fermion is smeared over a radius Q^{-1} where results can be calculated to leading order in the small parameter Q/k_f. We study two dipolar-quasiparticle descriptions of the nu=1/2 state in the small-Q model and confirm that they yield the same density response function as in the FCS approach. We also study the single-particle Green's function and the effective mass, for one form of dipolar quasiparticles, and find the effective mass to be infra-red divergent, exactly as in the FCS approach. Finally, we propose a form for a Fermi-liquid theory for the dipolar quasiparticles, which should be valid in the physical case where Q is infinite.

cond-mat.mes-hall↗

arXiv1998

Density of states in the non-hermitian Lloyd model

We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find the localization length from the density of states of a non-hermitian random ``Hamiltonian''. However, finding the density of states of a non-hermitian random ``Hamiltonian'' remains an open problem, contrary to previous findings in the literature.

cond-mat.dis-nn↗

arXiv1998

Compressibility of a quantum Hall system at $ν= 1/2$

Despite the fact that composite fermions may be regarded as electrically neutral objects at Landua-level filling factor $ν=1/2$, carrying only an electric dipole moment, we argue that the long-wavelength compressibility of the system is finite.

cond-mat.mes-hall↗

arXiv1998

Parity Effect in a Small Superconducting Particle

Matveev and Larkin calculated the parity effect on the ground state energy of a small superconducting particle in the regimes where the mean level spacing is either large or small compared to the bulk gap. We perform a numerical calculation which extends their results into the intermediate regime, where the level spacing is of the same order as the bulk gap.

cond-mat.supr-con↗

arXiv1997

Tunneling into the edge of a compressible Quantum Hall state

We present a composite fermion theory of tunneling into the edge of a compressible quantum Hall system. The tunneling conductance is non-ohmic, due to slow relaxation of electromagnetic and Chern-Simons field disturbances caused by the tunneling electron. Universal results are obtained in the limit of a large number of channels involved in the relaxation. The tunneling exponent is found to be a continuous function of the filling factor nu, with a a slope that is discontinuous at nu=1/2 in the limit of vanishing bulk resistivity rho_xx. When nu corresponds to a principal fractional quantized Hall state, our results agree with the chiral Luttinger liquid theories of Wen, and Kane, Fisher and Polchinski.

cond-mat.mes-hall↗

arXiv1996

Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime

A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes. This explanation is based on the hypothesis that samples which show this behavior contain density inhomogeneities. Theory then relates the non-universal conductance peak-heights to the ``number of alternating percolation clusters'' of a continuum percolation model defined on the spatially-varying local carrier density. We discuss the statistical properties of the number of alternating percolation clusters for Corbino disc samples characterized by random density fluctuations which have a correlation length small compared to the sample size. This allows a determination of the statistical properties of the low-temperature conductance peak-heights of such samples. We focus on a range of filling fraction at the center of the plateau transition for which the percolation model may be considered to be critical. We appeal to conformal invariance of critical percolation and argue that the properties of interest are directly related to the corresponding quantities calculated numerically for bond-percolation on a cylinder. Our results allow a lower bound to be placed on the non-universal conductance peak-heights, and we compare these results with recent experimental measurements.

cond-mat.mes-hall↗

arXiv1996

Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field

We present a discussion of the linear thermoelectric response of an interacting electron gas in a quantizing magnetic field. Boundary currents can carry a significant fraction of the net current passing through the system. We derive general expressions for the bulk and boundary components of the number and energy currents. We show that the local current density may be described in terms of ``transport'' and ``internal magnetization'' contributions. The latter carry no net current and are not observable in standard transport experiments. We show that although Onsager relations cannot be applied to the local current, they are valid for the transport currents and hence for the currents observed in standard transport experiments. We relate three of the four thermoelectric response coefficients of a disorder-free interacting two-dimensional electron gas to equilibrium thermodynamic quantities. In particular, we show that the diffusion thermopower is proportional to the entropy per particle, and we compare this result with recent experimental observations.

cond-mat↗