Electronic Excitations and Correlation Effects in Metals

Theoretical descriptions of the spectrum of electronic excitations in real metals have not yet reached a fully predictive, "first-principles" stage. In this paper we begin by presenting brief highlights of recent progress made in the evaluation of dynamical electronic response in metals. A comparison between calculated and measured spectra - we use the loss spectra of Al and Cs as test cases - leads us to the conclusion that, even in "weakly-correlated" metals, correlation effects beyond mean-field theory play an important role. Furthermore, the effects of the underlying band structure turn out to be significant. Calculations which incorporate the effects of both dynamical correlations and band structure from first principles are not yet available. As a first step towards such goal, we outline a numerical algorithm for the self-consistent solution of the Dyson equation for the one-particle Green's function. The self-energy is evaluated within the shielded-interaction approximation of Baym and Kadanoff. Our method, which is fully conserving, is a finite-temperature scheme which determines the Green's function and the self-energy at the Matsubara frequencies on the imaginary axis. The analytical continuation to real frequencies is performed via Pade approximants. We present results for the homogeneous electron gas which exemplify the importance of many-body self-consistency.Comment: 32 pages, 6 figures; "Fifty Years of the Correlation Problem", invited paper, to be published in Mol.Phy

Tunable Casimir repulsion with three dimensional topological insulators

In this Letter, we show that switching between repulsive and attractive Casimir forces by means of external tunable parameters could be realized with two topological insulator plates. We find two regimes where a repulsive (attractive) force is found at small (large) distances between the plates, canceling out at a critical distance. For a frequency range where the effective electromagnetic action is valid, this distance appears at length scales corresponding to $1-\epsilon(\omega) (2/\pi)\alpha\theta$.Comment: 9 pages, 5 figures, published version with auxiliary material. Featured in Physical Review Focu

Floquet Fractional Chern Insulator in Doped Graphene

Fractional Chern insulators are theoretically predicted states of electronic matter with emergent topological order. They exhibit the same universal properties as the fractional quantum Hall effect, but dispose of the need to apply a strong magnetic field. However, despite intense theoretical work, an experimental realization for these exotic states of matter is still lacking. Here we show that doped graphene turns into a fractional Chern insulator, when irradiated with high-intensity circularly polarized light. We derive the effective steady state band structure of light-driven graphene using Floquet theory and subsequently study the interacting system with exact numerical diagonalization. The fractional Chern insulator state equivalent to the 1/3 Laughlin state appears at 7/12 total filling of the honeycomb lattice (1/6 filling of the upper band). The state also features spontaneous ferromagnetism and is thus an example of the spontaneous breaking of a continuous symmetry along with a topological phase transition.Comment: 10 page

Pseudo-electromagnetic fields in topological semimetals

Dirac and Weyl semimetals, materials where electrons behave as relativistic fermions, react to position- and time-dependent perturbations, such as strain, as if emergent electromagnetic fields were applied. Since they differ from external electromagnetic fields in their symmetries and phenomenology they are called pseudo-electromagnetic fields, and enable a simple and unified description of a variety of inhomogeneous systems involving topological semimetals. We review the different physical ways to create effective pseudo-fields, their observable consequences as well as their similarities and differences compared to electromagnetic fields. Among these difference is their effect on quantum anomalies, the absence of a classical symmetry in the quantum theory, which we revisit from a quantum field theory and a semiclassical viewpoint. We conclude with predicted observable signatures of the pseudo-fields and the nascent experimental status.Comment: 18 pages, 6 (preliminary) figures. Original submitted version, comments welcom

Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementations

In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field $\mathbf{E}_5$, and also, the axial cyclotron orbits and chiral pseudo-magnetic effect due to the axial magnetic field $\mathbf{B}_5$.Comment: 16 pages, 6 figures, published versio