arXiv subjects

N. R. Cooper

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

80 records · Page 5Linked to original sources

arXiv1998

Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect

A branch of uniformly-propagating solitary waves of planar ferromagnets is identified. The energy dispersion and structures of the solitary waves are determined for an isotropic ferromagnet as functions of a conserved momentum. With increasing momentum, their structure undergoes a transition from a form ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An instability to the formation of these solitary waves is shown to provide a mechanism for the electric field-induced breakdown of the spin-polarized quantum Hall effect.

cond-mat.mes-hall↗

arXiv1996

Skyrmions in Quantum Hall Systems with Realistic Force-Laws

We study the charged excitations of quantum Hall systems at integer filling fractions $ν=2n+1$, for a force-law that takes account of the finite width of the electron gas. For typical values of this width, in the limit of vanishing Zeeman energy we find that the low-energy excitations are ``skyrmions'' not only at $ν=1$ but also at higher filling fractions. Our results lead to the prediction that, in typical samples, abrupt transitions to charged excitations with very large spins should be observable at filling fractions higher than $ν=1$ if the Zeeman energy is reduced sufficiently.

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

Theory of Photoluminescence of the $ν=1$ Quantum Hall State: Excitons, Spin-Waves and Spin-Textures

We study the theory of intrinsic photoluminescence of two-dimensional electron systems in the vicinity of the $ν=1$ quantum Hall state. We focus predominantly on the recombination of a band of initial ``excitonic states'' that are the low-lying energy states of our model at $ν=1$. It is shown that the recombination of excitonic states can account for recent observations of the polarization-resolved spectra of a high-mobility GaAs quantum well. The asymmetric broadening of the spectral line in the $σ_-$ polarization is explained to be the result of the ``shake-up'' of spin-waves upon radiative recombination of excitonic states. We derive line shapes for the recombination of excitonic states in the presence of long-range disorder that compare favourably with the experimental observations. We also discuss the stabilities and recombination spectra of other (``charged'') initial states of our model. An additional high-energy line observed in experiment is shown to be consistent with the recombination of a positively-charged state. The recombination spectrum of a negatively-charged initial state, predicted by our model but not observed in the present experiments, is shown to provide a direct measure of the formation energy of the smallest ``charged spin-texture'' of the $ν=1$ state.

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↗

arXiv1996

Theory of Exciton Recombination from the Magnetically Induced Wigner Crystal

We study the theory of itinerant-hole photoluminescence of two-dimensional electron systems in the regime of the magnetically induced Wigner crystal. We show that the exciton recombination transition develops structure related to the presence of the Wigner crystal. The form of this structure depends strongly on the separation $d$ between the photo-excited hole and the plane of the two-dimensional electron gas. When $d$ is small compared to the magnetic length, additional peaks appear in the spectrum due to the recombination of exciton states with wavevectors equal to the reciprocal lattice vectors of the crystal. For $d$ larger than the magnetic length, the exciton becomes strongly confined to an interstitial site of the lattice, and the structure in the spectrum reflects the short-range correlations of the Wigner crystal. We derive expressions for the energies and the radiative lifetimes of the states contributing to photoluminescence, and discuss how the results of our analysis compare with experimental observations.

cond-mat↗

arXiv1995

Non-Universal Behavior of Finite Quantum Hall Systems as a Result of Weak Macroscopic Inhomogeneities

We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights $σ_{xx}^{\rm max}$ compared to the universal values previously predicted for infinite homogeneous samples. This effect is expected to occur for the conductivity peaks measured in standard experimental geometries such as the Hall bar and the Corbino disc. At the lowest temperatures, the decrease in $σ_{xx}^{\rm max}(T)$ is found to saturate at values proportional to the difference between the adjacent plateaus in $σ_{xy}$, with a prefactor which depends on the particular realization of disorder in the sample. We argue that this provides a possible explanation of the ``non-universal scaling'' of $σ_{xx}^{\rm max}$ observed in a number of experiments. We also predict an enhancement of the ``non-local'' resistance due to the macroscopic inhomogeneities. We argue that, in the Hall bar with a sharp edge, the enhanced ``non-local'' resistance and the size corrections to the ``local'' resistance $R_{xx}$ are directly related. Using this relation, we suggest a method by which the finite-size corrections may be eliminated from $R_{xx}$ and $R_{xy}$ in this case.

cond-mat↗

arXiv1994

Theory of Spin-Split Cyclotron Resonance in the Extreme Quantum Limit

We present an interpretation of recent cyclotron resonance experiments on the two-dimensional electron gas in GaAs/AlGaAs heterostructures. We show that the observed dependence of the resonance spectrum on Landau level occupancy and temperature arises from the interplay of three factors: spin-splitting of the cyclotron frequency; thermal population of the two spin states; and coupling of the resonances for each spin orientation by Coulomb interactions. In addition, we derive an $f$-sum rule which allows spin polarisation to be determined directly from resonance spectra.

cond-mat↗