Transport phenomena in helical edge state interferometers: A Green's function approach

Abstract

We analyze the current and the shot-noise of an electron interferometer made of the helical edge states of a two-dimensional topological insulator within the framework of non-equilibrium Green's functions formalism. We study in detail setups with a single and with two quantum point contacts inducing scattering between the different edge states. We consider processes preserving the spin as well as the effect of spin-flip scattering. In the case of a single quantum point contact, a simple test based on the shot-noise measurement is proposed to quantify the strength of the spin-flip scattering. In the case of two single point contacts with the additional ingredient of gate voltages applied within a finite-size region at the top and bottom edges of the sample, we identify two type of interference processes in the behavior of the currents and the noise. One of such processes is analogous to that taking place in a Fabry-Pérot interferometer, while the second one corresponds to a configuration similar to a Mach-Zehnder interferometer. In the helical interferometer these two processes compete.

Noise and current correlations in tunnel junctions of quantum spin Hall edge states

“…For the DQPC setup, P p exhibits a pattern characterized by a period E L related to the distance between the two point-contacts, and by a width of the minima related to the reflection of each individual QPC [see Fig.4(a)], in agreement with the results of Ref. [37]. By setting V p to the minima values (17), the spin-flipping partition noise can be straightforwardly detected and tuned with the spin gate V f , within the spin-bias configuration of the terminals [see Fig.4(b)].…”

“…14, 16 The value of the spin-flipping magnitude |Γ f | is typically smaller than |Γ p | by a factor 3 to 4 only. 28,29,35,37,39 Then, within the suitable voltage bias configurations discussed above, the two partition noises P p and P f can be tuned with varying the charge and spin gate voltages V p and V f in the meV regime. Similarly, in the DQPC setup the individual PQC reflection is controlled by the constrictions, and a distance of about 1µm between the two QPCs leads to a pattern for P p and P f that has a typical period of a few meV.…”

“…[24][25][26][27] For the helical states, a constriction in the QSH bar causes a local wavefunction overlap 28,29 that is known to yield two types of tunneling processes. [29][30][31][32][33][34][35][36][37][38][39] The first type is the customary spin-preserving (p) process, where an electron tunnels across the junction maintaining its spin orientation, and thereby reversing its group velocity. The second type is less conventional and is a spin-flipping (f ) process, where a tunneling electron reverses its spin orientation maintaining its group velocity: it mainly originates from the interplay between bulk-inversion asymmetry and wavefunction overlap, even in absence of magnetic coupling.…”

Shot noise in the edge states of 2D topological insulators

“…Therefore, a comparison of its theoretical value with the experimental data could allow one to understand the mechanism of conductance suppression in topological insulators. So far, only several theoretical papers on the noise in topological insulators were published, and most of them considered the electron tunneling from one edge of the sample to another [15][16][17][18]. These authors neglected the scattering in the edge states themselves and these states were assumed to be noiseless.…”

Nonlinear spin-thermoelectric transport in two-dimensional topological insulators

“…A feasible possibility is the application of local potentials to form quantum antidots. More generally, the presence of constrictions in two-dimensional topological insulators have been proposed to give rise to coherent oscillations [18], transformations between ordinary and topological regimes [19], peaks of noise correlations [20], metal-to-insulator quantum phase transitions [21], nonequilibrium fluctuation relations [22], braiding of Majorana fermions [23], competition between Fabry-Pérot and Mach-Zehnder processes [24], control of edge magnetization [25], and detection of Kondo clouds [26]. Interestingly, König et al have experimentally demonstrated [27] the local manipulation of helical states with back-gate electrodes.…”