Tunnel junction of helical edge states: Determining and controlling spin-preserving and spin-flipping processes through transconductance

Abstract

When a constriction is realized in a 2D quantum spin Hall system, electron tunneling between helical edge states occurs via two types of channels allowed by time-reversal symmetry, namely spin-preserving ({p}) and spin-flipping ({f}) tunneling processes. Determining and controlling the effects of these two channels is crucial to the application of helical edge states in spintronics. We show that, despite the Hamiltonian terms describing these two processes do not commute, the scattering matrix entries of the related 4-terminal setup always factorize into products of p-terms and f-terms contributions. Such factorization provides an operative way to determine the transmission coefficient $T_p$ and $T_f$ related to each of the two processes, via transconductance measurements. Furthermore, these transmission coefficients are also found to be controlled independently by a suitable combination of two gate voltages applied across the junction. This result holds for an arbitrary profile of the tunneling amplitudes, including disorder in the tunnel region, enabling us to discuss the effect of the finite length of the tunnel junction, and the space modulation of both magnitude and phase of the tunneling amplitudes.

16 pages, 8 figures. Extended Discussion Section, updated reference list

References in corpus (30)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Dissipationless Quantum Spin Current at Room Temperature
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Nonlocal edge state transport in the quantum spin Hall state
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Corner Junction as a Probe of Helical Edge States
• Tunneling between edge states in a quantum spin Hall system
• Full electrical control of Charge and Spin conductance through Interferometry of Edge States in Topological Insulators
• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
• Tunneling between helical edge states through extended contacts
• Spintronics and spincaloritronics in topological insulators
• Tunneling of Dirac electrons through spatial regions of finite mass
• Generating and controlling spin-polarized currents induced by a quantum spin Hall antidot
• Oscillatory non-linear conductance of an interacting quantum wire with an impurity
• Thermopower and the Mott formula for a Majorana edge state
• Dephasing of spin and charge interference in helical Luttinger liquids
• Coherent tunnelling across a quantum point contact in the quantum Hall regime
• Multiple Andreev reflections in a quantum dot coupled to superconductors: Effects of spin-orbit coupling
• Transport phenomena in helical edge states interferometers. A Green's function approach
• Finite frequency noise in a quantum point contact between helical edge states
• Current-voltage correlations in interferometers

Cited by in corpus (23)

• Interacting topological edge channels
• Spin-thermoelectric transport induced by interactions and spin-flip processes in two dimensional topological insulators
• Nonlinear spin-thermoelectric transport in two-dimensional topological insulators
• Photoexcitation of electron wave packets in quantum spin Hall edge states: effects of chiral anomaly from a localised electric pulse
• Polarized heat current generated by quantum pumping in two-dimensional topological insulators
• Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires
• Noise and current correlations in tunnel junctions of Quantum Spin Hall edge states
• Controllable spin entanglement production in a quantum spin Hall ring
• Magnetic AC control of the spin textures in a helical Luttinger liquid
• Signatures of Jackiw-Rebbi resonance in the thermal conductance of topological Josephson junctions with magnetic islands
• Fabry-Pérot resonant vortices and magnetoconductance in topological insulator constrictions with magnetic barriers
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Effects of disorder on electron tunneling through helical edge states
• Interaction effects in non-equilibrium transport properties of a four-terminal topological corner junction
• Detailed study of nonlinear cooling with two-terminal configurations of topological edge states
• Emission of entangled Kramers pairs from a helical mesoscopic capacitor
• Transport through a quantum spin Hall antidot as a spectroscopic probe of spin textures
• A topological current divider
• Transport in quantum spin Hall edges in contact to a quantum dot
• Interference effects induced by a precessing easy-plane magnet coupled to a helical edge state
• Confinement versus interface bound states in spin-orbit coupled nanowires
• Manipulation of helical states revealed by crossed Andreev reflection
• Lifting topological protection in a quantum spin Hall insulator by edge coupling