arXiv subjects

N. R. Cooper

Publications and source records attributed to N. R. Cooper.

At least 73 records · Page 4Linked to original sources

arXiv2006

The longitudinal resistance of a quantum Hall system with a density gradient

Following recent experiments, we consider current flow in two dimensional electronic systems in the quantum Hall regime where a gradient in the electron density induces a spatial variation in the Hall resistivity. Describing the system in terms of a spatially varying local resistivity tensor, we show that in such a system the current density is generically non-uniform, with the current being pushed towards one side of the sample. We show that, for sufficiently large density gradient, the voltage along that side is determined by the change of the Hall resistivity, and is independent of the microscopic longitudinal resistivity, while the voltage on the opposite side is small and determined by both longitudinal and Hall resistivities. We solve some particular models in detail, and propose ways by which the microscopic longitudinal resistivity may be extracted from measurements of the longitudinal voltage on both sides of the sample.

cond-mat.mes-hall↗

arXiv2005

Virial theorems for vortex states in a confined Bose-Einstein condensate

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.

cond-mat.other↗

arXiv2005

Single vortex states in a confined Bose-Einstein condensate

It has been demonstrated experimentally that non-axially symmetric vortices precess around the centre of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S-vortex and the U-vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S-vortex has higher energy than the U-vortex in a rotating elongated condensate. We show that the S-vortex is related to the solitonic vortex which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S-vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.

cond-mat.other↗

arXiv2005

Quantum Hall states of atomic Bose gases: density profiles in single-layer and multi-layer geometries

We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multi-layer geometries. We show that, in a local density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multi-layered set-up we find different phases, depending on the strength of the inter-layer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling $t_{c_1}$. For tunneling well below $t_{c_1}$ one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids.

cond-mat.mes-hall↗

arXiv2005

Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2

Bosons in the lowest Landau level, such as rapidly-rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is 3/2. When a moderate amount of a longer-range (e.g. dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.

cond-mat.mes-hall↗

arXiv2005

Vortex Lattices in Rotating Atomic Bose Gases with Dipolar Interactions

We show that dipolar interactions have dramatic effects on the groundstates of rotating atomic Bose gases in the weak interaction limit. With increasing dipolar interaction (relative to the net contact interaction), the mean-field, or high filling fraction, groundstate undergoes a series of transitions between vortex lattices of different symmetries: triangular, square, ``stripe'', and ``bubble'' phases. We also study the effects of dipolar interactions on the quantum fluids at low filling fractions. We show that the incompressible Laughlin state at filling fraction $ν=1/2$ is replaced by compressible stripe and bubble phases.

cond-mat.mes-hall↗

arXiv2004

Edge excitations and Topological orders in rotating Bose gases

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.

cond-mat.mes-hall↗

arXiv2004

Density profiles for atomic quantum Hall states

We analyze density profiles for atomic quantum Hall states, which are expected to form in systems of rotating cold atoms in the high-rotation limit. For a two-dimensional (single-layer) system we predict a density landscape showing plateaus at quantized densities, signaling the formation of incompressible groundstates. For a set-up with parallel, coupled layers, we predict (i) at intermediate values of the inter-layer tunneling: a continuously varying density profile $ρ(z)$ across the layers, showing cusps at specific positions, (ii) at small values for the tunneling, quantum Hall-Mott phases, with individual layers at sharply quantized particle number, and plateaus in the density profile $ρ(z)$.

cond-mat.mes-hall↗

arXiv2004

Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates

We present the results of numerical calculations of the groundstates of weakly-interacting Bose-Einstein condensates containing large numbers of vortices. Our calculations show that these groundstates appear to be close to uniform triangular vortex lattices. However, slight deviations from a uniform triangular lattice have dramatic consequences on the overall particle distribution. In particular, we demonstrate that the overall particle distribution averaged on a lengthscale large compared to the vortex lattice constant is well approximated by a Thomas-Fermi profile.

cond-mat.mes-hall↗

arXiv2003

Interaction Effects at Crossings of Spin-Polarised One-Dimensional Subbands

We report conductance measurements of ballistic one-dimensional (1D) wires defined in GaAs/AlGaAs heterostructures in an in-plane magnetic field, B. When the Zeeman energy is equal to the 1D subband energy spacing, the spin-split subband N(up-spin) intersects (N+1)(down-spin), where N is the index of the spin-degenerate 1D subband. At the crossing of N=1(up-spin) and N=2(down-spin) subbands, there is a spontaneous splitting giving rise to an additional conductance structure evolving from the 1.5(2e^2/h) plateau. With further increase in B, the structure develops into a plateau and lowers to 2e^2/h. With increasing temperature and magnetic field the structure shows characteristics of the 0.7 structure. Our results suggest that at low densities a spontaneous spin splitting occurs whenever two 1D subbands of opposite spins cross.

cond-mat.mes-hall↗

arXiv2003

Exact Groundstates of Rotating Bose Gases close to a Feshbach Resonance

We study the groundstates of rotating Bose gases when interactions are affected by a nearby Feshbach resonance. We show that exact groundstates at high angular momentum can be found analytically for a general and realistic model for the resonant interactions. We identify parameter regimes where the exact groundstates are exotic fractional quantum Hall states, the excitations of which obey non-abelian exchange statistics.

cond-mat.mes-hall↗

arXiv2003

Free expansion of lowest Landau level states of trapped atoms: a wavefunction microscope

We show that for any lowest-Landau-level state of a trapped, rotating, interacting Bose gas, the particle distribution in coordinate space in a free expansion (time of flight) experiment is related to that in the trap at the time it is turned off by a simple rescaling and rotation. When the lowest-Landau-level approximation is valid, interactions can be neglected during the expansion, even when they play an essential role in the ground state when the trap is present. The correlations in the density in a single snapshot can be used to obtain information about the fluid, such as whether a transition to a quantum Hall state has occurred.

cond-mat.mes-hall↗

arXiv2002

Dissipative Transport in Quantum Hall Ferromagnets by Spinwave Scattering

We report on a study of the effect upon electrical transport of spinwave scattering from charged quasiparticles in nu=1 quantum Hall ferromagnets (QHFs), including both Heisenberg (single layer) and easy-plane (bilayer) cases. We derive a quantum Langevin equation to describe the resulting diffusive motion of the charged particle and use this to calculate the contribution to low temperature conductivity from a density of charged particles. This conductivity has a power law dependence upon temperature. The contribution is small at low temperatures increasing to a large value at relatively modest temperatures. We comment upon high temperature transport and upon the contribution of scattering to the width of the zero bias peak in inter-layer tunneling conductance.

cond-mat.mes-hall↗

arXiv2001

Stable Skyrmions in two-component Bose-Einstein condensates

We show that stable Skyrmions exist in two-component atomic Bose-Einstein condensates, in the regime of phase separation. Using full three-dimensional simulations we find the stable Skyrmions with topological charges Q=1 and 2, and compute their properties. With reference to these computations we suggest the salient features of an experimental setup in which they might realized.

cond-mat↗

arXiv2001

Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

We investigate the groundstates of weakly interacting bosons in a rotating trap as a function of the number of bosons, $N$, and the average number of vortices, $N_V$. We identify the filling fraction $ν\equiv N/N_V$ as the parameter controlling the nature of these states. We present results indicating that, as a function of $ν$, there is a zero temperature {\it phase transition} between a triangular vortex lattice phase, and strongly-correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.

cond-mat↗

arXiv1999

Large Skyrmions in an Al(0.13)Ga(0.87)As Quantum Well

We report tilted-field magnetotransport measurements of two-dimensional electron systems in a 200 Angstrom-wide Al(0.13)Ga(0.87)As quantum well. We extract the energy gap for the quantum Hall state at Landau level filling ν=1 as a function of the tilt angle. The relatively small effective Lande g-factor (g ~ 0.043) of the structure leads to skyrmionic excitations composed of the largest number of spins yet reported (s ~ 50). Although consistent with the skyrmion size observed, Hartree-Fock calculations, even after corrections, significantly overestimate the energy gaps over the entire range of our data.

cond-mat.mes-hall↗

arXiv1999

A Composite Fermion Description of Rotating Bose-Einstein Condensates

We study the properties of rotating Bose-Einstein condensates in parabolic traps, with coherence length large compared to the system size. In this limit, it has been shown that unusual groundstates form which cannot be understood within a conventional many-vortex picture. Using comparisons with exact numerical results, we show that these groundstates can be well-described by a model of non-interacting ``composite fermions''. Our work emphasises the similarities between the novel states that appear in rotating Bose-Einstein condensates and incompressible fractional quantum Hall states.

cond-mat↗

arXiv1999

``Smoke Rings'' in Ferromagnets

It is shown that bulk ferromagnets support propagating non-linear modes that are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These are circular loops of {\it magnetic} vorticity which travel at constant velocity parallel to their axis of symmetry. The topological structure of the continuum theory has important consequences for the properties of these magnetic vortex rings. One finds that there exists a sequence of magnetic vortex rings that are distinguished by a topological invariant (the Hopf invariant). We present analytical and numerical results for the energies, velocities and structures of propagating magnetic vortex rings in ferromagnetic materials.

cond-mat↗