We consider the classical magnetoresistance of a Weyl metal in which the electron Fermi surface possess nonzero fluxes of the Berry curvature. Such a system may exhibit large negative magnetoresistance with unusual anisotropy as a function of the angle between the electric and magnetic fields. In this case the system can support a new type of plasma waves. These phenomena are consequences of chiral anomaly in electron transport theory.PACS numbers: 72.10.Bg Materials with nontrivial topological properties have attracted considerable interest after the discovery of topological insulators [1]. One type of such materials is the so-called Weyl semimetals, characterized by the the presence of points of band touching (Dirac points) [2][3][4][5][6][7][8][9][10]. In this paper, we study the metallic counterparts of these materials-the Weyl metals, where Dirac points are hidden inside a Fermi surface. We show that these materials may exhibit large negative magnetoresistance with unusual anisotropy. We also find a new type of plasma waves in these systems.At low magnetic field B and at relatively high temperature Landau quantization can be neglected, and electron transport in metals can be described using the semiclassical Boltzmann kinetic equationHere n p (r, t) is the electron distribution function, p is the quasimomentum, I coll {n p } is the collision integral, andṙThe last, "anomalous," term in Eq. (2a), proportional to the Berry curvaturewas introduced in Ref. [11]. (See also reviews on the subject in Refs. [12,13].) In systems with time-reversal symmetry Ω p = Ω −p , while in centro-symmetric systems Ω p = −Ω −p . Thus, in systems which are both time-and centro-symmetric Ω p = 0. In this case the magneto-resistance described by Eq. (1) is positive and is governed by the parameter (ω c τ tr ) 2 [14]. Here ω c is the cyclotron frequency and τ tr is the electron transport mean free path. The Berry curvature is divergence-free except at isolated points in p space, which are associated with band degeneracies. As a result, in the case where the electronic spectrum has several valleys, they can be characterized by integers (see, for example, Ref.[15])Here the index "i" labels the valleys, dS is the elementary area vector. Nonzero values of k (i) are realized if near the degeneracy points, electrons can be described by the massless Dirac Hamiltonian [27] H = ±vσ ·P.(5)A is the momentum operator, A is the vector potential, σ is the operator of pseudospin, v is the quasiparticle velocity, and the signs ± correspond to the different chiralities of the Weyl fermions.It is well known that massless Dirac fermions exhibit chiral anomaly which can be understood in the language of level crossing in the presence of a magnetic field [16]. According to the Nielsen-Ninomiya theorem [17], the number of valleys with opposite chiralities (positive and negative values of k (i) ) should be equal, and so i k (i) = 0. Recently, gapless semiconductors with topologically protected Dirac points (Weyl semimetals) have attracted significant atten...

Motivated by recent efforts to achieve cold fermions pairing, we study the nonadiabatic regime of the Bardeen-Cooper-Schrieffer state formation. After the interaction is turned on, at times shorter than the quasiparticle energy relaxation time, the system oscillates between the superfluid and normal state. The collective nonlinear evolution of the BCS-Bogoliubov amplitudes u(p), v(p), along with the pairing function Delta, is shown to be an integrable dynamical problem which admits single soliton and soliton train solitons. We interpret the collective oscillations as Bloch precession of Anderson pseudospins, where each soliton causes a pseudospin 2pi Rabi rotation.

We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, κ. This is in striking contrast to the Stokes flow, in which the resistance is independent of κ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance.

We present an overview of the measured transport properties of the two dimensional electron fluids in high mobility semiconductor devices with low electron densities, and of some of the theories that have been proposed to account for them. Many features of the observations are not easily reconciled with a description based on the well understood physics of weakly interacting quasiparticles in a disordered medium. Rather, they reflect new physics associated with strong correlation effects, which warrant further study.

We consider adiabatic charge transport through mesoscopic metallic samples caused by a periodically changing external potential. We find that both the amplitude and the sign of the charge transferred through a sample per period are random sample specific quantities. The characteristic magnitude of the charge is determined by the quantum interference. [S0031-9007(98) PACS numbers: 72.15.Rn Let us apply an external potential f͑r, t͒, which is changing slowly and periodically in time to a metallic sample. This potential causes finite net charge Q transported across the sample per period. This phenomenon, known as adiabatic charge transport [1], has been investigated in several papers [1][2][3][4] for a closed system characterized by its ground state wave function corresponding to the instantaneous value of the external potential f͑r, t͒. However, in real experimental situations exact eigenfunctions of electrons are ill defined: The electron energy levels are broadened due to inelastic processes at T fi 0, and, in the case of an open system, are further broadened due to finite dwell time.Here we present a theory of adiabatic charge transport in "open mesoscopic systems." We demonstrate that at low T both the magnitude and the sign of Q are sample specific quantities. The typical value of Q in disordered (chaotic) systems turns out to be determined by quantum interference effects. We evaluate this value and find that it is much larger than the one in ballistic systems. This enhancement manifests of the well-known fact that at low temperatures, all electronic characteristics of mesoscopic samples are extremely sensitive to changes in the scattering potential [5][6][7][8].Let us start with a qualitative picture of the mesoscopic adiabatic charge transport. The wave functions of electrons in disordered systems exhibit sample specific spatial fluctuations. Therefore, the spatial electron density profile is changing slowly in time, together with the external potential f͑r, t͒. According to the continuity relation, variation of the charge density in time requires currents in the system. The question arises: What is the condition for a total charge transfer during one period to be nonzero? Let the pumping potential f͑r, t͒ be characterized by a finite set of functions g͑t͒ ͕g a ͑t͖͒, a 1, . . . , m, which are periodic with the same period t 0 :f͑r, t͒ f͑ ͑ ͑r, g͑t͒͒ ͒ ͒ X a f a ͑r͒g a ͑t͒ .The time evolution of the functions g͑t͒ represents a motion of a point in m dimensional space M . Because of the periodicity of f͑r, t͒, the trajectory C of this point is closed. The above-mentioned currents lead to Q fi 0, provided C encloses a finite area in M. This requires that m $ 2.To calculate Q we will use the Keldysh technique for the Green function matrix equation [9] ͑i≠ t 2 H 0 2 f͑r, t͒͒Ĝ͑r, rwhereĜ is a 2 3 2 matrix, G 11 0, G 12 G A , G 21 G R , and G 22 G K , with G R,A,K being the retarded, advanced, and Keldysh Green functions, respectively. H 0 is the Hamiltonian for electrons which includes impurity scattering po...