Electron-electron interactions and two-dimensional-two-dimensional tunneling

Long-Range Photon Fluctuations Enhance Photon-Mediated Electron Pairing and Superconductivity

Recently, the possibility of inducing superconductivity for electrons in two-dimensional materials has been proposed via cavity-mediated pairing. The cavity-mediated electron-electron interactions are long range, which has two main effects: firstly, within the standard BCS-type pairing mediated by adiabatic photons, the superconducting critical temperature depends polynomially on the coupling strength, instead of the exponential dependence characterizing the phonon-mediated pairing; secondly, as we show here, the effect of photon fluctuations is significantly enhanced. These mediate novel non-BCS-type pairing processes, via nonadiabatic photons, which are not sensitive to the electron occupation but rather to the electron dispersion and lifetime at the Fermi surface. Therefore, while the leading temperature dependence of BCS pairing comes from the smoothening of the Fermi-Dirac distribution, the temperature dependence of the fluctuation-induced pairing comes from the electron lifetime. For realistic parameters, also including cavity loss, this results in a critical temperature which can be more than 1 order of magnitude larger than the BCS prediction. Moreover, a finite average number of photons (as can be achieved by incoherently pumping the cavity) adds to the fluctuations and leads to a further enhancement of the critical temperature.

Hydrodynamics of electrons in graphene

Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the 'phase diagram' of graphene, and the inevitable presence of impurities and phonons in experimental systems. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics.

Smearing of the two-dimensional Kohn anomaly in a nonquantizing magnetic field: implications for interaction effects

Thermodynamic and transport characteristics of a clean two-dimensional interacting electron gas are shown to be sensitive to the weak perpendicular magnetic field even at temperatures much higher than the cyclotron energy, when the quantum oscillations are completely washed out. We demonstrate this sensitivity for two interaction-related characteristics: electron lifetime and the tunnel density of states. The origin of the sensitivity is traced to the field-induced smearing of the Kohn anomaly; this smearing is the result of curving of the semiclassical electron trajectories in magnetic field.

Optical conductivity of a two-dimensional electron liquid with spin-orbit interaction

The interplay of electron-electron interactions and spin-orbit coupling leads to a new contribution to the homogeneous optical conductivity of the electron liquid. The latter is known to be insensitive to many-body effects for a conventional electron system with parabolic dispersion. The parabolic spectrum has its origin in the Galilean invariance which is broken by spin-orbit coupling. This opens up a possibility for the optical conductivity to probe electron-electron interactions. We analyze the interplay of interactions and spin-orbit coupling and obtain optical conductivity beyond RPA.