All material bodies are surrounded by a fluctuating electromagnetic field because of the thermal and quantum fluctuations of the current density inside them. Close to the surface of planar sources (when the distance $d⪡{\ensuremath{\lambda}}_{T}=c\ensuremath{\hbar}∕{k}_{B}T$), thermal radiation can be spatially and temporally coherent if the surface can support surface modes like surface plasmon polaritons, surface phonon polaritons, or adsorbate vibrational modes. The fluctuating field is responsible for important phenomena such as radiative heat transfer, the van der Waals interaction, and the van der Waals friction between bodies. A general formalism for the calculation of the power spectral density for the fluctuating electromagnetic field is presented and applied to the radiative heat transfer and the van der Waals friction using both the semiclassical theory of the fluctuating electromagnetic field and quantum field theory. The radiative heat transfer and the van der Waals friction are greatly enhanced at short separations $(d⪡{\ensuremath{\lambda}}_{T})$ between the bodies due to the evanescent electromagnetic waves. Particularly strong enhancement occurs if the surface of the body can support localized surface modes like surface plasmons, surface polaritons, or adsorbate vibrational modes. An electromagnetic field outside a moving body can also be created by static charges which are always present on the surface of the body due to inhomogeneities, or due to a bias voltage. This electromagnetic field produces electrostatic friction which can be greatly enhanced if on the surface of the body there is a two-dimensional electron or hole system, or an incommensurate adsorbed layer of ions exhibiting acoustic vibrations. Applications of radiative heat transfer and noncontact friction to scanning probe spectroscopy are discussed. The theory gives a tentative explanation for the experimental noncontact friction data.

Near-field radiative heat transfer and noncontact friction

Semiconductor superlattices: a model system for nonlinear transport

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg–Landau theory, proximity and Josephson effects, etc.

Keldysh technique and non-linear σ-model: basic principles and applications

The single-particle energy spectra of graphene and its bilayer counterpart exhibit multiple degeneracies that arise through inherent symmetries. Interactions among charge carriers should spontaneously break these symmetries and lead to ordered states that exhibit energy gaps. In the quantum Hall regime, these states are predicted to be ferromagnetic in nature, whereby the system becomes spin polarized, layer polarized, or both. The parabolic dispersion of bilayer graphene makes it susceptible to interaction-induced symmetry breaking even at zero magnetic field. We investigated the underlying order of the various broken-symmetry states in bilayer graphene suspended between top and bottom gate electrodes. We deduced the order parameter of the various quantum Hall ferromagnetic states by controllably breaking the spin and sublattice symmetries. At small carrier density, we identified three distinct broken-symmetry states, one of which is consistent with either spontaneously broken time-reversal symmetry or spontaneously broken rotational symmetry.

http://yacoby.physics.harvard.edu/Publications/Broken-Symmetry%20States%20in%20Doubly%20Gated%20Suspended%20Bilayer%20Graphene_2010.pdf

Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene

An electronic double layer, subjected to a high magnetic field, can form an exciton condensate: a Bose–Einstein condensate of Coulomb-bound electron–hole pairs Now, exciton condensation is reported for a graphene/boron-nitride/graphene structure

/pdf/quantum-hall-drag-of-exciton-condensate-in-graphene-46xwwe1y4k.pdf

Quantum Hall drag of exciton condensate in graphene

Double-layer quantum Hall systems have interesting properties associated with interlayer correlations. At \ensuremath{\nu}=1/m where m is an odd integer they exhibit spontaneous symmetry breaking equivalent to that of spin 1/2 easy-plane ferromagents, 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.

Quantum ferromagnetism and phase transitions in double-layer quantum Hall systems

We derive and evaluate expressions for the frictional Coulomb drag between disordered two-dimensional electron-gas layers Our derivation is based on the memory-function formalism and the expression for the drag reduces to previously known results in the ballistic limit We find that Coulomb drag is appreciably enhanced by disorder at low temperatures when the mean free path within a layer is comparable to or shorter than the layer separation In high-mobility two-dimensional electron-gas systems, where the drag has been studied experimentally, the effect of disorder on the drag is negligible at attainable temperatures We predict that an enhancement due to disorder and a crossover in the temperature dependence and layer-separation dependence will be observable at low temperatures in moderate- and low-mobility samples

Coulomb drag between disordered two-dimensional electron-gas layers.

We derive and evaluate expressions for the electromagnetic coupling between a two-dimensional grating and a nearby two-dimensional electron gas. By considering both the thickness and the separation of the two systems as small compared with macroscopic wavelengths, a numerically tractable prescription for their mutual influence on an incident beam is developed. The theory is evaluated in several model calculations, which compare favorably with recent far-infrared transmission studies of cyclotron and magnetoplasmon resonances. The general need for a nonperturbative analysis is illustrated.

Theory of two-dimensional grating couplers

Correlation in double-layer two-dimensional electron-gas systems: Singwi-Tosi-Land-Sjölander theory at B=0.

We derive and evaluate expressions for the low-temperature dc equilibrium tunneling conductance between parallel two-dimensional electron systems. Our theory is based on a linear-response formalism and on impurity-averaged perturbation theory. The disorder broadening of features in the dependence of tunneling conductance on sheet densities and in-plane magnetic-field strengths is influenced both by the finite lifetime of electrons within the wells and by momentum-nonconserving tunneling events. Disorder vertex corrections are important only for weak in-plane magnetic fields and strong interwell impurity-potential correlations. We comment, on the basis of our results, on the possibility of using tunneling measurements to determine the lifetime of electrons in the quantum wells

Lian Zheng

Papers

Quantum ferromagnetism and phase transitions in double-layer quantum Hall systems

Coulomb drag between disordered two-dimensional electron-gas layers.

Theory of two-dimensional grating couplers

Correlation in double-layer two-dimensional electron-gas systems: Singwi-Tosi-Land-Sjölander theory at B=0.

Tunneling conductance between parallel two-dimensional electron systems.