Full electrical control of charge and spin conductance through interferometry of edge states in topological insulators

Fabrizio Dolcini

Phys. Rev. B 83, 165304 – Published 7 April 2011

Abstract

We investigate electron interferometry of edge states in topological insulators. We show that when interboundary coupling is induced at two quantum point contacts of a four terminal setup, both Fabry-Pérot-like and Aharonov-Bohm-like loop processes arise. These underlying interference effects lead to a full electrically controllable system, where the magnitude of charge and spin linear conductances can be tuned by gate voltages, without applying magnetic fields. In particular we find that, under appropriate conditions, interboundary coupling can lead to negative values of the conductance. Furthermore, the setup also allows to selectively generate pure charge or pure spin currents by choosing the voltage bias configuration.

Received 19 November 2010

DOI:https://doi.org/10.1103/PhysRevB.83.165304

Authors & Affiliations

Fabrizio Dolcini^*

Dipartimento di Fisica del Politecnico di Torino, I-10129 Torino, Italy

^*fabrizio.dolcini@polito.it

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Vol. 83, Iss. 16 — 15 April 2011

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Images

Figure 1
Schematic description of the proposed four terminal setup, where edge states flow at the top and bottom boundaries of a TI quantum well. Blue (red) lines denote spin- $↑$ ( $↓$ ) edge channels and are slightly separated for illustrative reasons. The dashed box denotes the scattering region where interboundary tunneling occurs at two QPCs, located around positions $x_{a}$ and $x_{b}$ and separated by a distance $L = x_{b} - x_{a}$ . Two gate voltages $V_{g, T}$ and $V_{g, B}$ shift the edge state momenta in the top and bottom regions between the QPCs, modifying the electron phase in the loop processes induced by tunneling. No magnetic flux is present.Reuse & Permissions
Figure 2
The two types of basic interference processes allowed by time reversal symmetry of the system. (a) An example of loop process induced by the spin-preserving tunneling terms Eq. (2), reminiscent of a Fabry-Pérot interferometer. The electron flows rightward in the top boundary and leftward in the bottom boundary, so that the loop interference phase is $ϕ_{FP} = e (V_{g, T} + V_{g, B}) L / ℏ v_{F}$ . (b) An example of loop processes induced by the spin-flipping tunneling terms Eq. (3), reminiscent of an electrostatic Aharonov-Bohm interferometer. The electron maintains the motion direction both in the top boundary and in the bottom boundary, so that the loop interference phase is $ϕ_{AB} = e (V_{g, T} - V_{g, B}) L / ℏ v_{F}$ . A similar loop connects terminal 2 to 3. In general multiloop processes, where the two processes interplay, are also possible.Reuse & Permissions
Figure 3
Charge-bias configuration (C) [see Eq. (28)]. The conductance (31) is plotted as a function of the FP phase $ϕ_{FP} = e (V_{g, T} + V_{g, B}) L / ℏ v_{F}$ , for different values of single QPC “horizontal” transmission, namely $T_{12}^{a} = 0.04$ (solid curve), $0.15$ (dashed curve), and $0.48$ (dashed-dotted curve), corresponding to spin-preserving tunneling amplitudes $γ_{p} = 0.1, 0.2, 0.4$ , respectively, and to spin-flipping amplitude $γ_{f} = 0.1$ . The FP interference pattern allows to switch from the “off” state (minima) to the “on” state (maxima) by operating with the gate voltages. In configuration (C) the conductance is independent of the AB phase $ϕ_{FP} = e (V_{g, T} - V_{g, B}) L / ℏ v_{F}$ .Reuse & Permissions
Figure 4
Spin-bias configuration (S) [see Eq. (29)]. The conductance $G^{(S)}$ (in units of $e^{2} / h$ ) is plotted as a function of the FP phase $ϕ_{FP} = e (V_{g, T} + V_{g, B}) L / ℏ v_{F}$ and the AB phase $ϕ_{AB} = e (V_{g, T} - V_{g, B}) L / ℏ v_{F}$ . The tunneling amplitudes for spin-preserving and spin-flipping processes are $γ_{p} = 0.4$ and $γ_{f} = 0.2$ . By tuning the gate voltages one can control both magnitude and sign of the conductance. Negative conductance values originate from spin-flipping interboundary coupling.Reuse & Permissions
Figure 5
Slice plots of Fig. 4. The conductance (33) in the spin-bias configuration (S) is plotted as a function of the AB phase $ϕ_{AB}$ , for different values of the FP phase $ϕ_{FP}$ , namely $ϕ_{FP} = 0$ (solid curve), $π / 2$ (dashed curve), and $π$ (dash-dotted curve). The dependence of $G^{(S)}$ on $ϕ_{AB}$ results in an AB modulation of the $ϕ_{FP}$ -dependent Fabry-Pérot pattern, and regions of negative conductance arise.Reuse & Permissions

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