Spin-polarized tunneling into helical edge states: Asymmetry and conductances

Abstract

We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum spin Hall system. This problem arose in context of the spin and charge fractionalization of an injected electron. Renormalization of the dc conductances of the system is calculated in the fermionic approach and scattering states formalism. In lowest order of tunneling amplitude we confirm previous results for the scaling dependence of conductances. Going beyond the lowest order we show that interaction affects not only the total tunneling rate, but also the asymmetry of the injected current. The helical edge state forbids the backscattering, which leads to the possibility of two stable fixed points in renormalization group sense, in contrast to the Y-junction between the usual quantum wires.

Atomically Thin Quantum Spin Hall Insulators

“…[ 212 ] Thus, SP‐STM may be used as a detection tool for a given spin‐polarization or as a source to inject spin‐polarized currents into a helical edge. [ 208,210,211 ]…”

“…A remaining challenge in the study of 2D topological insulators is the unequivocal proof of spin-momentum locking, i.e., helicity at the edges of a QSH material. Theoretical proposals exist to detect helicity [208][209][210][211] by spin-polarized STM (SP-STM). SP-STM is based on tunneling of spin-polarized electrons from a magnetic probe tip, offering a high degree of spin polarization at atomic resolution.…”

“…[212] Thus, SP-STM may be used as a detection tool for a given spin-polarization or as a source to inject spin-polarized currents into a helical edge. [208,210,211] Several publications have since proposed [208,210,211] that fractionalized charge and spin excitations may be observable in spatially-separated electrical contacts on either side of a spinpolarized probe tip localized along the QSH edge. A schematic [210] showing the proposed helicity detection method using injected spin-polarized electrons into a QSH edge is shown in Figure 9A.…”

Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium

“…, and L (0) (x|y) is defined in (9). We dropped all unimportant labels here and introduced a dynamical factor Π(x|z…”

“…It was emphasised that preserving time-reversal symmetry inelastic scattering processes due to phonons can drastically influence the topologically protected transport properties. Such dissipative mechanisms induce backscattering in the presence of the Rashba spin orbit coupling [5] or the spin-polarized tunneling tip [9] which, in principle, might lead to significant corrections to measurable conductances or even to the existence of new fixed points in renormalization group sense.…”