Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.Comment: 18 pages, 8 figure

First-Principles Wannier Functions of Silicon and Gallium Arsenide

We present a self-consistent, real-space calculation of the Wannier functions of Si and GaAs within density functional theory. We minimize the total energy functional with respect to orbitals which behave as Wannier functions under crystal translations and, at the minimum, are orthogonal. The Wannier functions are used to calculate the total energy, lattice constant, bulk modulus, and the frequency of the zone-center TO phonon of the two semiconductors with the accuracy required nowadays in ab-initio calculations. Furthermore, the centers of the Wannier functions are used to compute the macroscopic polarization of Si and GaAs in zero electric field. The effective charges of GaAs, obtained by finite differentiation of the polarization, agree with the results of linear response theory.Comment: 12 pages, 2 PostScript figures, RevTeX, to appear in Physical Review

Electron energy spectrum and the Berry phase in graphite bilayer

We emphasize that there exist four Dirac-type points in the electron-energy spectrum of a graphite bilayer near the point K of its Brillouin zone. One of the Dirac points is at the point K, and three Dirac points lie nearby. Each of these three points generates the Berry phase $\pi$, while the Dirac point at K gives the phase $-\pi$. It is these four points that determine the Berry phase in the bilayer. If an electron orbit surrounds all these points, the Berry phase is equal to $2\pi$.Comment: 4 pages, 2 figures, submitted to Phys. Rev. B ; expande

Mott scattering at the interface between a metal and a topological insulator

We compute the spin-active scattering matrix and the local spectrum at the interface between a metal and a three-dimensional topological band insulator. We show that there exists a critical incident angle at which complete (100%) spin flip reflection occurs and the spin rotation angle jumps by $\pi$. We discuss the origin of this phenomena, and systematically study the dependence of spin-flip and spin-conserving scattering amplitudes on the interface transparency and metal Fermi surface parameters. The interface spectrum contains a well-defined Dirac cone in the tunneling limit, and smoothly evolves into a continuum of metal induced gap states for good contacts. We also investigate the complex band structure of Bi$_2$Se$_3$.Comment: published versio

Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect

We propose a gauge invariant expression for the side jump associated with scattering between particular Bloch states. Our expression for the side jump follows from the Born series expansion for the scattering T-matrix in powers of the strength of the scattering potential. Given our gauge invariant side jump expression, it is possible to construct a semiclassical Boltzmann theory of the anomalous Hall effect which expresses all previously identified contributions in terms of gauge invariant quantities and does not refer explicitly to off-diagonal terms in the density-matrix response.Comment: 6 pages, 1 fugure. submitted to PR

Optical injection and terahertz detection of the macroscopic Berry curvature

We propose an experimental scheme to probe the Berry curvature of solids. Our method is sensitive to arbitrary regions of the Brillouin zone, and employs only basic optical and terahertz techniques to yield a background free signal. Using semiconductor quantum wells as a prototypical system, we discuss how to inject Berry curvature macroscopically, and probe it in a way that provides information about the underlying microscopic Berry curvature.Comment: 4 pages, accepted in Physical Review Letter

Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass

We study the behaviour of the expectation value of the acceleration of a particle in a one-dimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states that include the interband mixing induced by the force. This approach allows us to understand the behaviour of the wavepacket, which responds with a mass that is initially the bare mass, and subsequently oscillates around the value predicted by the effective mass. If Zener tunneling can be neglected, the expression obtained for the acceleration of the particle is valid over timescales of the order of a Bloch oscillation, which are of interest for experiments with cold atoms in optical lattices. We discuss how these oscillations can be tuned in an optical lattice for experimental detection.Comment: 15 pages, 12 figure

Anatomy of the quantum melting of the two dimensional Wigner crystal

The Fermi liquid-Wigner crystal transition in a two dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum Monte Carlo calculations. Recently, we proposed (Phys. Rev. Lett. 94, 046801 (2005)) that for intermediate densities, a hybrid phase (with the symmetry of the crystal but otherwise liquid like properties) is more stable than both the liquid and the crystal phase. Here we confirm this result both in the thermodynamic and continuum limit. The liquid-hybrid transition takes place at rs=31.5 +/- 0.5. We find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature. We discuss the implications of our results for various transition scenarii (quantum hexatic phase, supersolid, multiple exchange, microemulsions) proposed in the literature.Comment: 14 pages, 16 figure

Existence of the Stark-Wannier quantum resonances

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.Comment: 30 pages, 1 figur

Noncommutative geometry for three-dimensional topological insulators

We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.Comment: 41 pages, 3 figure