Dynamical charge and pseudospin currents in graphene and possible Cooper pair formation

Abstract

Based on the quantum kinetic equations for systems with SU(2) structure, regularization-free density and pseudospin currents are calculated in graphene realized as the infinite mass-limit of electrons with quadratic dispersion and a proper spin-orbit coupling. Correspondingly the currents possess no quasiparticle part but only anomalous parts. The intraband and interband conductivities are discussed with respect to magnetic fields and magnetic domain puddles. It is found that the magnetic field and meanfield of domains can be represented by an effective Zeeman field. For large Zeeman fields the dynamical conductivities become independent of the density and are universal in this sense. The different limits of vanishing density, relaxation, frequency, and Zeeman field are not interchangeable. The optical conductivity agrees well with the experimental values using screened impurity scattering and an effective Zeeman field. The universal value of Hall conductivity is shown to be modified due to the Zeeman field. The pseudospin current reveals an anomaly since a quasiparticle part appears though it vanishes for particle currents. The density and pseudospin response functions to an external electric field are calculated and the dielectric function is discussed with respect to collective excitations. A frequency and wave-vector range is identified where the dielectric function changes sign and the repulsive Coulomb potential becomes effectively attractive allowing Cooper pairing.

Weyl systems: anomalous transport normally explained

“…With different choices of this vector we can describe the mean-field dynamics of great classes of systems as illustrated in table I. The idea is to realize graphene and Weyl Hamiltonians by the infinite-mass limit 99 which kills the quasiparticle energy ǫ k and leaves only the spin-orbit coupling of exactly the form of chiral Hamiltonian. The coupled kinetic equations of scalar and vector Wigner functions read 97…”

“…For this purpose we consider the limit of infinite mass of nonrelativstic particles which extinct the quasiparticle energy ǫ k → 0 and only the chiral Hamiltonian (17) remains with a proper choice of the vector selfenergy according to table I. This is the same procedure as was applied to describe graphene 99 and allows here to consider the kinetic equations for right and left-handed chiral particles Σ = ±vp. Let us focus on the right-handed ones since the final result can be translated for left-handed particles by v → −v.…”

“…Though it has been shown that (22) provide anomalous Hall conductivity 97 , spin-density waves 103 and graphene transport 99 directly, it is now useful to map this equation system to the helicity basis used in the literature. This will enlighten the connection to anomalous transport with Berry curvatures.…”

“…We will perform the derivation for the general Hamiltonian (17) such that large classes of systems are covered as illustrated in table I. In the end we will use the infinite-mass limit of nonrelativistic particles 99 to produce the chiral dispersion according to table I.…”

Exploring Anomalies by Many‐Body Correlations

“…and experimentally interpreted [ 11,15,16 ] as having observed a chiral anomaly. This has led to an enormous theoretical activity [ 17–19 ] describing, for example, anomalous transport, [ 20–25 ] the relation of chiral anomaly, and quantized Hall effects [ 26,27 ] up to chiral heat effect. [ 28 ]…”