The functional renormalization group (RG) in combination with Fermi surface patching is a well-established method for studying Fermi liquid instabilities of correlated electron systems. In this article, we further develop this method and combine it w
ith mean-field theory to approach multiband systems with spin-orbit coupling, and we apply this to a tight-binding Rashba model with an attractive, local interaction. The spin dependence of the interaction vertex is fully implemented in a RG flow without SU(2) symmetry, and its momentum dependence is approximated in a refined projection scheme. In particular, we discuss the necessity of including in the RG flow contributions from both bands of the model, even if they are not intersected by the Fermi level. As the leading instability of the Rashba model, we find a superconducting phase with a singlet-type interaction between electrons with opposite momenta. While the gap function has a singlet spin structure, the order parameter indicates an unconventional superconducting phase, with the ratio between singlet and triplet amplitudes being plus or minus one on the Fermi lines of the upper or lower band, respectively. We expect our combined functional RG and mean-field approach to be useful for an unbiased theoretical description of the low-temperature properties of spin-based materials.
The derivation of Lorentz-covariant generalizations of Ohms law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative r
oute to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor $chi^mu_ u$ relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohms law, we prove the validity of Ohms law in every inertial frame. We further use the universal relation between $chi^mu_ u$ and the microscopic conductivity tensor $sigma_{kell}$ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohms law.
In this article, we put forward a new approach to electrodynamics of materials. Based on the identification of induced electromagnetic fields as the microscopic counterparts of polarization and magnetization, we systematically employ the mutual funct
ional dependencies of induced, external and total field quantities. This allows for a unified, relativistic description of the electromagnetic response without assuming the material to be composed of electric or magnetic dipoles. Using this approach, we derive universal (material-independent) relations between electromagnetic response functions such as the dielectric tensor, the magnetic susceptibility and the microscopic conductivity tensor. Our formulae can be reduced to well-known identities in special cases, but more generally include the effects of inhomogeneity, anisotropy, magnetoelectric coupling and relativistic retardation. If combined with the Kubo formalism, they would also lend themselves to the ab initio calculation of all linear electromagnetic response functions.
We study the magneto-optical (MO) response of polar semiconductor BiTeI with giant bulk Rashba spin splitting at various carrier densities. Despite being non-magnetic, the material is found to yield a huge MO activity in the infrared region under mod
erate magnetic fields (<3 T). By comparison with first-principles calculations, we show that such an enhanced MO response is mainly due to the intraband transitions between the Rashba-split bulk conduction bands in BiTeI, which give rise to distinct novel features and systematic doping dependence of the MO spectra. We further predict an even more pronounced enhancement in the low-energy MO response and dc Hall effect near the crossing (Dirac) point of the conduction bands.
