Abstract

Topological protection of edge state in quantum spin Hall systems relies only on time-reversal symmetry. Hence, S z conservation on the edge can be relaxed which can have an interferometric manifestation in terms of spin Berry phase. Primarily it could lead to the generation of spin Berry phase arising from a closed loop dynamics of electrons. Our work provides a minimal framework to generate and detect these effects by employing both spin-unpolarized and spin-polarized leads. We show that spin-polarized leads could lead to resonances or anti-resonances in the two-terminal conductance of the interferometer. We further show that the positions of these anti-resonances (as a function of energy of the incident electron) get shifted owing to the presence of spin Berry phase. Finally, we present simulations of a device setup using KWANTpackage which put our theoretical predictions on firm footing.

Highlights

  • Birth of topological insulators [1,2,3,4,5] has marked a new realm in the field of condensed matter research and nucleated a number of experimental activities [6,7,8] in a quest for materials relevant for exploring the topological aspects of such systems in the past decades

  • These edge modes have conserved spin quantum number Sz locked with their momentum, viz., if ↑ spins (Sz = +1) flow along +k, called right movers, ↓ spins (Sz = −1) would flow along −k, called left movers, ensued from time-reversal symmetry—a phenomenon known as quantum spin Hall (QSH) effect [1,11,12,13,14,15,16]

  • The present paper explores the consequences of relaxing the Sz conservation by considering a generic profile of the spin-orbit (SO) field along a pristine edge

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Summary

INTRODUCTION

Birth of topological insulators [1,2,3,4,5] has marked a new realm in the field of condensed matter research and nucleated a number of experimental activities [6,7,8] in a quest for materials relevant for exploring the topological aspects of such systems in the past decades. The tunability of the orientation of the spin would result in modulations of the phase which manifest as oscillations in the current through the interferometer and can be visualized as stretching and shrinking the above mentioned area on the Bloch sphere by changing T1 or T2 or both in a controlled manner This discussion provides us with a clear picture regarding the generation and detection of a finite SB phase in such a two-path interferometer geometry.

SCATTERING THROUGH SPIN-ORBIT BARRIERS AND SPIN BERRY PHASE
SB PHASE AND TRANSFER MATRIX
SB PHASE AND ITS INTERFEROMETRIC MANIFESTATION
Interferometry with polarized leads
First scenario: both leads local parallel
NUMERICAL ANALYSIS USING KWANT
DISCUSSION AND CONCLUSION

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