πSpin Berry Phase in a Quantum-Spin-Hall-Insulator-Based Interferometer: Evidence for the Helical Spin Texture of the Edge States

Abstract

The quantum spin Hall insulator is characterized by helical edge states, with the spin polarization of the electron being locked to its direction of motion. Although the edge-state conduction has been observed, unambiguous evidence of the helical spin texture is still lacking. Here, we investigate the coherent edge-state transport in an interference loop pinched by two point contacts. Because of the helical character, the forward interedge scattering enforces a π spin rotation. Two successive processes can only produce a nontrivial 2π or trivial 0 spin rotation, which can be controlled by the Rashba spin-orbit coupling. The nontrivial spin rotation results in a geometric π Berry phase, which can be detected by a π phase shift of the conductance oscillation relative to the trivial case. Our results provide smoking gun evidence for the helical spin texture of the edge states. Moreover, it also provides the opportunity to all electrically explore the trajectory-dependent spin Berry phase in condensed matter.

Supercurrent switch in π topological junctions based upon a narrow quantum spin Hall insulator

“…Therefore, the helical edge states have not only the physical significance but also important applications in topological superconducting spintronics and topological quantum computation 1 – 4 . Besides, while the edge-state conduction 3 , 4 and the spin polarization of the edge current 6 have been verified, a direct evidence for the helical spin texture of the edge states remains a challenge 7 . For a narrow QSH insulator with two edges getting close to each other, the overlap between edge states from opposite edges produces an energy gap, leading to the so-called interedge coupling, although the intraedge backscattering is still forbidden 8 .…”

“…For a narrow QSH insulator with two edges getting close to each other, the overlap between edge states from opposite edges produces an energy gap, leading to the so-called interedge coupling, although the intraedge backscattering is still forbidden 8 . Resultantly, the properties of QSH insulator can be greatly modified and one remarkable property is the elastic interedge backscattering between the edge states at the two sides 7 – 9 .…”

“…However, in the present structure, compared with the case of no interedge coupling, since there is no difference between the spin-up and -down electrons, the 0 − π transition tuned by the gate voltage V g should be just originated from the interedge coupling, which induces an additional π phase difference in I ( ϕ ). Specifically, in the context of the interedge coupling, the interedge backscattering between the edge states at two sides can occur at the interface between the left (right) and middle regions, but the intraedge backscattering is still prevented on account of the helical nature of the edge states 7 – 9 . The wave from the AR at interface x = 0 in edge 1 and that from the interedge backscattering at the interface in edge 2 are destructively coherent, leading to the additional π phase difference and the resultant 0 − π transition modulated by V g .…”

Manipulation and Characterization of the Valley-Polarized Topological Kink States in Graphene-Based Interferometers

“…In this Letter, we study the quantum interference of the Aharanov-Bohm (AB) interferometer [19,33] composed of topological kink states locating at the domain walls of graphene systems [see Fig.1]. Both the magnetic field and the gate voltage can be utilized to manipulate these kink states, which only allow for the valley polarized propagation and interference.…”

Berry Curvature and Topology in Low-Dimensional Crystals

“…An alternative setup for the detection of the π-Berry phase was proposed in Ref. [101], with the interferometer based on a quantum spin-Hall (QSH) insulator. The QSH insulator [21] is a time-reversal symmetric topological state of matter which possesses in gap helical edge states: at each edge of the system there are two counter-propagating states with opposite spin projections.…”