Three- and low-dimensional inorganic semiconductors

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.

Thermoelectric response of an interacting two-dimensional electron gas in a quantizing magnetic field

The condensation of excitons, bound electron-hole pairs in a solid, into a coherent collective electronic state was predicted more than 50 years ago. Perhaps surprisingly, the phenomenon was first observed in a system consisting of two closely spaced parallel two-dimensional electron gases in a semiconductor double quantum well. At an appropriate high magnetic field and low temperature, the bilayer electron system condenses into a state resembling a superconductor, only with the Cooper pairs replaced by excitons consisting of electrons in one layer bound to holes in the other. In spite of being charge neutral, the transport of excitons within the condensate gives rise to several spectacular electrical effects. This article describes these phenomena and examines how they inform our understanding of this unique phase of quantum electronic matter.

/pdf/exciton-condensation-in-bilayer-quantum-hall-systems-4ovvayqrsx.pdf

Exciton Condensation in Bilayer Quantum Hall Systems

The Nernst effect is the transverse electric field produced by a longitudinal thermal gradient in the presence of a magnetic field. At the beginning of this century, Nernst experiments on cuprates were analyzed assuming that: (i) the contribution of quasi-particles to the Nernst signal is negligible; and (ii) Gaussian superconducting fluctuations cannot produce a Nernst signal well above the critical temperature. Both these assumptions were contradicted by subsequent experiments. This paper reviews experiments documenting multiple sources of a Nernst signal, which, according to the Bridgman relation, measures the flow of transverse entropy caused by a longitudinal particle flow. Along the lines of Landauer's approach to transport phenomena, the magnitude of the transverse magneto-thermoelectric response is linked to the quantum of thermoelectric conductance and a number of material-dependent length scales: the mean free path, the Fermi wavelength, the de Broglie thermal wavelength and the superconducting coherence length. Extremely mobile quasi-particles in dilute metals generate a widely-documented Nernst signal. Fluctuating Cooper pairs in the normal state of superconductors have been found to produce a detectable Nernst signal with an amplitude conforming to the Gaussian theory, first conceived by Ussishkin, Sondhi and Huse. In addition to these microscopic sources, mobile Abrikosov vortices, mesoscopic objects simultaneously carrying entropy and magnetic flux, can produce a sizeable Nernst response. Finally, in metals subject to a magnetic field strong enough to truncate the Fermi surface to a few Landau tubes, each exiting tube generates a peak in the Nernst response. The survey of these well-established sources of the Nernst signal is a helpful guide to identify the origin of the Nernst signal in other controversial cases.

http://iopscience.iop.org/article/10.1088/0034-4885/79/4/046502/pdf

Nernst effect in metals and superconductors: a review of concepts and experiments.

The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.

/pdf/fibonacci-anyons-from-abelian-bilayer-quantum-hall-states-4zobjwh5ua.pdf

Fibonacci Anyons From Abelian Bilayer Quantum Hall States

Anomalous temperature dependence of the correlated ν=1 quantum Hall effect in bilayer electron systems

Measured diffusion thermopower of a low-disorder two-dimensional hole system in the extreme quantum limit is used to probe the thermal properties of the recently proposed particle-flux composite fermions (CF's). The data are consistent with the CF's exhibiting the integral quantum Hall effect away from filling factor nu=1/2. The magnitudes of the thermopower maxima between the fractional quantum Hall states yield an estimate for the CF Landau-level broadening Gamma(CF) which agrees well with Gamma(CF) deduced from the analysis of the excitation energy gaps for the fractional liquid states.

Thermopower of Composite Fermions

Measurements of the reflection and transmission coefficients of ballistic two‐dimensional electrons by a potential barrier, induced via a surface gate, reveal that both coefficients vary gradually with the barrier height when it is less then the electron Fermi energy. Superimposed on the gradual variation, oscillatory structure which are consistent with interference resonances are also observed. The data imply that the potential barrier seen by the two‐dimensional electrons is sharp compared to the electron wavelength.

Quantum reflection and transmission of ballistic two‐dimensional electrons by a potential barrier

Magnetotransport of a low-disorder triple-layer electron system in perpendicular or parallel magnetic fields

One-component to two-component transitions of fractional quantum Hall states in a wide quantum well

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