Chiral Magnetic Effect of Hot Electrons.

We propose a way to observe the chiral magnetic effect in noncentrosymmetric Weyl semimetals under the action of a strong electric field, via the nonlinear part of their I-V characteristic that is odd in the external magnetic field, or odd-in-magnetic field voltages in electrically open circuits. This effect relies on valley-selective heating in such materials, which, in general, leads to nonequilibrium valley population imbalances. In the presence of an external magnetic field, such a valley-imbalanced Weyl semimetal will, in general, develop an electric current along the direction of the magnetic field-the chiral magnetic effect. We also discuss a specific experimental setup to observe the chiral magnetic effect of hot electrons.

Two-Particle Collisional Coordinate Shifts and Hydrodynamic Anomalous Hall Effect in Systems without Lorentz Invariance.

We show that electrons undergoing a two-particle collision in a crystal experience a coordinate shift that depends on their single-particle Bloch wave functions and derive a gauge-invariant expression for such a shift, valid for arbitrary band structures and arbitrary two-particle interaction potentials. As an application of the theory, we consider two-particle coordinate shifts for Weyl fermions in space of three spatial dimensions. We demonstrate that such shifts in general contribute to the anomalous Hall conductivity of a clean electron liquid.

Dynamic Chiral Magnetic Effect and Faraday Rotation in Macroscopically Disordered Helical Metals.

We develop an effective medium theory for electromagnetic wave propagation through gapless nonuniform systems with a dynamic chiral magnetic effect. The theory allows us to calculate macroscopic-disorder-induced corrections to the values of optical, as well as chiral magnetic conductivities. In particular, we show that spatial fluctuations of the optical conductivity induce corrections to the effective value of the chiral magnetic conductivity. The absolute value of the effect varies strongly depending on the system parameters, but yields the leading frequency dependence of the polarization rotation and circular dichroism signals. Experimentally, these corrections can be observed as features in the Faraday rotation angle near frequencies that correspond to the bulk plasmon resonances of a material. Such features are not expected to be present in single-crystal samples.

Anomalous Hall Effect in Type-I Weyl Metals.

We study the ac anomalous Hall conductivity σ_{xy}(ω) of a Weyl semimetal with broken time-reversal symmetry. Even in the absence of free carriers these materials exhibit a "universal" anomalous Hall response determined solely by the locations of the Weyl nodes. We show that the free carriers, which are generically present in an undoped Weyl semimetal, give an additional contribution to the ac Hall conductivity. We elucidate the phy146sical mechanism of the effect and develop a microscopic theory of the free carrier contribution to σ_{xy}(ω). The latter can be expressed in terms of a small number of parameters (the electron velocity matrix, the Fermi energy µ, and the "tilt" of the Weyl cone). The resulting σ_{xy}(ω) has resonant features at ω∼2µ which may be used to separate the free carrier response from the filled-band response using, for example, Kerr effect measurements. This may serve as a diagnostic tool to characterize the doping of individual valleys.

Topological magnetoelectric effect decay.

We address the influence of realistic disorder and finite doping on the effective magnetic monopole induced near the surface of an ideal topological insulator (TI) by currents that flow in response to a suddenly introduced external electric charge. We show that when the longitudinal conductivity σ(xx)=g(e(2)/h)≠0, the apparent position of a magnetic monopole initially retreats from the TI surface at speed v(M)=αcg, where α is the fine structure constant and c is the speed of light. For the particular case of TI surface states described by a massive Dirac model, we further find that the temperature T=0 Hall currents vanish when the external potential is screened.

Geometric phase for nonlinear oscillators from perturbative renormalization group.

We formulate a renormalization-group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous models with time-independent parameters, as well as nonautonomous models with slowly varying parameters. We show that the renormalization-group equations for the nonautonomous case can be used to determine the geometric phase acquired by the oscillator during the change of its parameters. We illustrate the obtained results by applying them to the Van der Pol and Van der Pol-Duffing models.

Interaction-induced topological insulator states in strained graphene.

The electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for both studying the Dirac fermions in new regimes and for new device applications. Certain natural configurations of strain generate large nearly uniform pseudomagnetic fields, which have opposite signs in the two valleys, and give rise to flat spin- and valley-degenerate pseudo-Landau levels (PLLs). Here we consider the effect of the Coulomb interactions in strained graphene with a uniform pseudomagnetic field. We show that the spin or valley degeneracies of the PLLs get lifted by the interactions, giving rise to topological insulator states. In particular, when a nonzero PLL is quarter or three-quarter filled, an anomalous quantum Hall state spontaneously breaking time-reversal symmetry emerges. At half-filled PLLs, a weak spin-orbital interaction stabilizes the time-reversal-symmetric quantum spin-Hall state. These many-body states are characterized by the quantized conductance and persist to a high temperature scale set by the Coulomb interactions, which we estimate to be a few hundreds Kelvin at moderate strain values. At fractional fillings, fractional quantum Hall states breaking valley symmetry emerge. These results suggest a new route to realizing robust topological states in mesoscopic graphene.

Ordering of magnetic impurities and tunable electronic properties of topological insulators.

We study collective behavior of magnetic adatoms randomly distributed on the surface of a topological insulator. Interactions of an ensemble of adatoms are frustrated, as the RKKY-type interactions of two adatom spins depend on the directions of spins relative to the vector connecting them. We show that at low temperatures the frustrated RKKY interactions give rise to two phases: an ordered ferromagnetic phase with spins pointing perpendicular to the surface, and a disordered spin-glass-like phase. The two phases are separated by a quantum phase transition driven by the magnetic exchange anisotropy. The ordered phase breaks time-reversal symmetry spontaneously, driving the surface states into a gapped state, which exhibits an anomalous quantum Hall effect and provides a realization of the parity anomaly. We find that the magnetic ordering is suppressed by potential scattering.

Conductance of d-wave superconductor/normal metal/d-wave superconductor junctions.

We develop a theory of the conductance of superconductor/normal metal/superconductor junctions in the case where the superconducting order parameter has d-wave symmetry. At low temperature the conductance is proportional to the square root of the inelastic electron relaxation time in the bulk of the superconductor. As a result it turns out to be much larger than the conductance of the normal part of the junction.

Suppression of superconductivity in disordered interacting wires.

We study superconductivity suppression due to thermal fluctuations in disordered wires using the replica nonlinear sigma-model (NLsigmaM). We show that in addition to the thermal phase slips there is another type of fluctuations that result in a finite resistivity. These fluctuations are described by saddle points in NLsigmaM and cannot be treated within the Ginzburg-Landau approach. The contribution of such fluctuations to the wire resistivity is evaluated with exponential accuracy. The magnetoresistance associated with this contribution is negative.

Coulomb-blockade-induced bound quasiparticle states in a double-island structure.

We determine the low temperature shape of the Coulomb-blockade staircase in a superconducting double-island device. For an odd number of electrons, in the ground state the intrinsic quasiparticle is bound to the tunneling contact. For a single channel contact the gap between the ground state and the continuum of excited states is of the order of the Josephson energy E(J). The temperature dependence of the Coulomb-blockade step width is nonmonotonic, with the minimal width occurring at T(i) approximately E(J)/ln(square root DeltaE(J)/delta), where Delta and delta are, respectively, the superconducting gap and mean level spacing in the island. For an even number of electrons, the Coulomb enhancement of the Josephson energy is shown to be significantly stronger than that for a single grain coupled to a lead. If the electrostatic energy favors a single broken Cooper pair, the resulting quasiparticles are bound to the contact at T=0.