Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids

In a fluid subject to a magnetic field the viscous stress tensor has a dissipationless antisymmetric component controlled by the so-called Hall viscosity. We here propose an all-electrical scheme that allows a determination of the Hall viscosity of a two-dimensional electron liquid in a solid-state device.Comment: 12 pages, 4 figure

Helicons in Weyl semimetals

Helicons are transverse electromagnetic waves propagating in three-dimensional (3D) electron systems subject to a static magnetic field. We present a theory of helicons propagating through a 3D Weyl semimetal. Our approach relies on the evaluation of the optical conductivity tensor from semiclassical Boltzmann transport theory, with the inclusion of certain Berry curvature corrections that have been neglected in the earlier literature (such as the one due to the orbital magnetic moment). We demonstrate that the axion term characterizing the electromagnetic response of Weyl semimetals dramatically alters the helicon dispersion with respect to that in nontopological metals. We also discuss axion-related anomalies that appear in the plasmon dispersion relation.Comment: 5 pages, 1 figur

Magnetic hallmarks of viscous electron flow in graphene

We propose a protocol to identify spatial hallmarks of viscous electron flow in graphene and other two-dimensional viscous electron fluids. We predict that the profile of the magnetic field generated by hydrodynamic electron currents flowing in confined geometries displays unambiguous features linked to whirlpools and backflow near current injectors. We also show that the same profile sheds light on the nature of the boundary conditions describing friction exerted on the electron fluid by the edges of the sample. Our predictions are within reach of vector magnetometry based on nitrogen-vacancy centers embedded in a diamond slab mounted onto a graphene layer.Comment: 5 pages, 6 figure

Spin-resolved optical conductivity of two-dimensional group-VIB transition-metal dichalcogenides

We present an ab-initio study of the spin-resolved optical conductivity of two-dimensional (2D) group-VIB transition-metal dichalcogenides (TMDs). We carry out fully-relativistic density-functional-theory calculations combined with maximally localized Wannier functions to obtain band manifolds at extremely high resolutions and focus on the photo-response of 2D TMDs to circularly-polarized light in a wide frequency range. We present extensive numerical results for monolayer TMDs involving molybdenum and tungsten combined with sulphur and selenium. Our numerical approach allows us to locate with a high degree of accuracy the positions of the points in the Brillouin zone that are responsible for van Hove singularities in the optical response. Surprisingly, some of the saddle points do not occur exactly along high-symmetry directions in the Brillouin zone, although they happen to be in their close proximity.Comment: 9 pages, 5 figure

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov - de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by J. C. Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic- oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment.Comment: 20 pages, 2 figures, 22 reference

Electron hydrodynamics dilemma: whirlpools or no whirlpools

In highly viscous electron systems such as, for example, high quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow. In this work, we study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge

The LHeC Detector

The Large Hadron Electron Collider (LHeC) is a proposed upgrade to the LHC, to provide high energy, high luminosity electron-proton collisions to run concurrently with Phase 2 of the LHC. The baseline design of a detector for the LHeC is described, driven by the requirements from the projected physics programme and including some preliminary results from first simulations.Comment: 6 pages, proceedings of parallel talk at Deep Inelastic Scattering 2013, 22-26 April 2013, Marseilles, Franc

Electron density distribution and screening in rippled graphene sheets

Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.Comment: 13 pages, 13 figures, submitted. High-quality figures can be requested to the author

Theory of integer quantum Hall polaritons in graphene

We present a theory of the cavity quantum electrodynamics of the graphene cyclotron resonance. By employing a canonical transformation, we derive an effective Hamiltonian for the system comprised of two neighboring Landau levels dressed by the cavity electromagnetic field (integer quantum Hall polaritons). This generalized Dicke Hamiltonian, which contains terms that are quadratic in the electromagnetic field and respects gauge invariance, is then used to calculate thermodynamic properties of the quantum Hall polariton system. Finally, we demonstrate that the generalized Dicke description fails when the graphene sheet is heavily doped, i.e. when the Landau level spectrum of 2D massless Dirac fermions is approximately harmonic. In this case we `integrate out' the Landau levels in valence band and obtain an effective Hamiltonian for the entire stack of Landau levels in conduction band, as dressed by strong light-matter interactions.Comment: 20 pages, 7 figure

Many-body effective mass enhancement in a two-dimensional electron liquid

Motivated by a large number of recent magnetotransport studies we have revisited the problem of the microscopic calculation of the quasiparticle effective mass in a paramagnetic two-dimensional (2D) electron liquid (EL). Our systematic study is based on a generalized $GW$ approximation which makes use of the many-body local fields and takes advantage of the results of the most recent QMC calculations of the static charge- and spin-response of the 2D EL. We report extensive calculations for the many-body effective mass enhancement over a broad range of electron densities. In this respect we critically examine the relative merits of the on-shell approximation, commonly used in weak-coupling situations, {\it versus} the actual self-consistent solution of the Dyson equation. We show that already for $r_s \simeq 3$ and higher, a solution of the Dyson equation proves here necessary in order to obtain a well behaved effective mass. Finally we also show that our theoretical results for a quasi-2D EL, free of any adjustable fitting parameters, are in good qualitative agreement with some recent measurements in a GaAs/AlGaAs heterostructure.Comment: 12 pages, 3 figures, CMT28 Conference Proceedings, work related to cond-mat/041226