D. A. Pesin

Spintronics and pseudospintronics in graphene and topological insulators

The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin-relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analogue of giant magnetoresistance in bilayer graphene.

Mott physics and band topology in materials with strong spin–orbit interaction

Mott insulators are driven by strong Coulomb repulsion and topological insulators by strong spin–orbit coupling. Although these effects are normally in competition, in some cases the Coulomb interaction can enhance the effects of spin–orbit coupling. Together these interactions could lead to gapless spin-only excitations on the surface of a strongly correlated insulator.

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.

Quantum kinetic theory of current-induced torques in Rashba ferromagnets

Motivated by recent experimental studies of thin-film devices containing a single ferromagnetic layer, we develop a quantum kinetic theory of current-induced magnetic torques in Rashba-model ferromagnets. We find that current-induced spin-densities that are responsible for the switching behavior are due most essentially to spin-dependent quasiparticle lifetimes and derive analytic expressions for relevant limits of a simple model. Quantitative model parameter estimates suggest that spin-orbit coupling in the adjacent metal normal magnetic layer plays an essential role in the strength of the switching effect.

Interaction-enhanced coherence between two-dimensional Dirac layers

We estimate the strength of interaction-enhanced coherence between two graphene or topological insulator surface-state layers by solving imaginary-axis gap equations in the random phase approximation. Using a self-consistent treatment of dynamic screening of Coulomb interactions in the gapped phase, we show that the excitonic gap can reach values on the order of the Fermi energy at strong interactions. The gap is discontinuous as a function of interlayer separation and effective fine structure constant, revealing a first order phase transition between effectively incoherent and interlayer coherent phases. To achieve the regime of strong coherence the interlayer separation must be smaller than the Fermi wavelength, and the extrinsic screening of the medium embedding the Dirac layers must be negligible. In the case of a graphene double-layer we comment on the supportive role of the remote

Interaction-induced topological insulator states in strained graphene.

\pi

Chiral magnetic effect and natural optical activity in metals with or without Weyl points

-bands neglected in the two-band Dirac model.

Photogalvanic effect in Weyl semimetals

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.

Density response in Weyl metals

We consider the phenomenon of natural optical activity, and related chiral magnetic effect in metals with low carrier concentration. To reveal the correspondence between the two phenomena, we compute the optical conductivity of a noncentrosymmetric metal to linear order in the wave vector of the light wave, specializing to the low-frequency regime. We show that it is the orbital magnetic moment of quasiparticles that is responsible for the natural optical activity, and thus the chiral magnetic effect. While for purely static magnetic fields the chiral magnetic effect is known to have a topological origin and to be related to the presence of Berry curvature monopoles (Weyl points) in the band structure, we show that the existence of Berry monopoles is not required for the dynamic chiral magnetic effect to appear; the latter is thus not unique to Weyl metals. The magnitude of the dynamic chiral magnetic effect in a material is related to the trace of its gyrotropic tensor. We discuss the conditions under which this trace is non-zero; in noncentrosymmetric Weyl metals it is found to be proportional to the energy-space dipole moment of Berry curvature monopoles. The calculations are done within both the semiclassical kinetic equation, and Kubo linear response formalisms, with coincident results.

Density, spin, and pairing instabilities in polarized ultracold Fermi gases

We theoretically study the impact of impurities on the photogalvanic effect (PGE) in Weyl semimetals with weakly tilted Weyl cones. Our calculations are based on a two-nodes model with an inversion symmetry breaking offset and we employ a kinetic equation approach in which both optical transitions as well as particle-hole excitations near the Fermi energy can be taken into account. We focus on the parameter regime with a single photoactive node and control the calculation in small impurity concentration. Internode scattering is treated generically and therefore our results allow to continuously interpolate between the cases of short range and long range impurities. We find that the time evolution of the circular PGE may be nonmonotonic for intermediate internode scattering. Furthermore, we show that the tilt vector introduces three additional linearly independent components to the steady state photocurrent. Amongst them, the photocurrent in direction of the tilt takes a particular role inasmuch it requires elastic internode scattering or inelastic intranode scattering to be relaxed. It may therefore be dominant. The tilt also generates skew scattering which leads to a current component perpendicular to both the incident light and the tilt. We extensively discuss our findings and comment on the possible experimental implications.