arXiv subjects

Florian Geissler

Publications and source records attributed to Florian Geissler.

21 records · Page 2Linked to original sources

arXiv2016

Evidence for broken Galilean invariance at the quantum spin Hall edge

We study transport properties of the helical edge channels of a quantum spin Hall (QSH) insulator, in the presence of electron-electron interactions and weak, local Rashba spin-orbit coupling. The combination of the two allows for inelastic backscattering that does not break time-reversal symmetry (TRS), resulting in interaction-dependent power law corrections to the conductance. Here, we use a non-equilibrium Keldysh formalism to describe the situation of a long, one-dimensional edge channel coupled to external reservoirs, where the applied bias is the leading energy scale. By calculating explicitly the corrections to the conductance up to fourth order of the impurity strength, we analyse correlated single- and two-particle backscattering processes on a microscopic level. Interestingly, we show that the modeling of the leads together with the breaking of Galilean invariance has important consequences on the transport properties. Such breaking occurs, because the Galilean invariance of the bulk spectrum transforms into an emergent Lorentz invariance of the edge spectrum. With this broken Galilean invariance at the QSH edge, we find a contribution to single particle backscattering with a very low power scaling, while in the presence of Galilean invariance the leading contribution would be due to correlated two-particle backscattering only. This difference is further reflected in different values of the Fano factor of the shot noise, an experimentally observable quantity. The described behaviour is specific to the Rashba scatterer, and does not occur in the case of backscattering off a time-reversal breaking, magnetic impurity.

cond-mat.mes-hall↗

arXiv2014

Random Rashba spin-orbit coupling at the quantum spin Hall edge

We study a one-dimensional helical system with random Rashba spin-orbit coupling. Using renor- malization group methods, we derive a consistent set of flow equations governing the important con- trol parameters of the backscattering process. Thereby, we prove the existence of disorder-induced two-particle backscattering that can even be non-local in space. This analysis allows us to derive the scaling form of the conductance at low temperatures. We find that two-particle backscattering due to random spin-orbit coupling differs from the one off a single Rashba impurity by both the scaling of the conductance with the temperature and the relevance of the backscattering operators.

cond-mat.mes-hall↗

arXiv2013

Group theoretical and topological analysis of the quantum spin Hall effect in silicene

Silicene consists of a monolayer of silicon atoms in a buckled honeycomb structure. It was recently discovered that the symmetry of such a system allows for interesting Rashba spin-orbit effects. A perpendicular electric field is able to couple to the sublattice pseudospin, making it possible to electrically tune and close the band gap. Therefore, external electric fields may generate a topological phase transition from a topological insulator to a normal insulator (or semimetal) and vice versa. The contribution of the present article to the study of silicene is twofold: First, we perform a group theoretical analysis to systematically construct the Hamiltonian in the vicinity of the $K$ points of the Brillouin zone and discover a new, but symmetry allowed term. Subsequently, we identify a tight binding model that corresponds to the group theoretically derived Hamiltonian near the $K$ points. Second, we start from this tight binding model to analyze the topological phase diagram of silicene by an explicit calculation of the $Z_2$ topological invariant of the band structure. To this end, we calculate the $Z_2$ topological invariant of the honeycomb lattice in a manifestly gauge invariant way which allows us to include $S_z$ symmetry breaking terms -- like Rashba spin orbit interaction -- into the topological analysis. Interestingly, we find that the interplay of two Rashba terms can generate a non-trivial quantum spin Hall phase in silicene. This is in sharp contrast to the more extensively studied honeycomb system graphene where Rashba spin orbit interaction is known to compete with the quantum spin Hall effect in a potentially detrimental way.

cond-mat.mes-hall↗