Helical Gap Signatures in Nanowire Devices by Solving the 3D Schroedinger-Poisson Nonlinear Equation

We present an efficient framework for obtaining the conductance signatures of the helical gap. By simulating a nanowire quantum point contact (QPC) in an electrostatic environment, we can predict the geometrical and physical parameters that can guide experiments [1].

Our method features the self-consitent solution of the 3D Schroedinger-Poisson coupled equations. We use Kwant [2] for performing conductance calculations, and solving the Schroedinger equation with an implementation of the kernel polynomial method (KPM) [3].
We exploit KPM to obtain the local density of states as a function, and use it to find self-consistently [4] the solution to the Poisson equation [5].

The significant speedup gained with KPM and the self-consistent Poisson solver, allow us to compute the conductance for a wide range of gate voltages and magnetic fields, and to further explore the parameters space in magnetic field direction, spin-orbit strenght, and QPC lengths.


[1] J. Kammhuber et al., Nature Communications 8, 478 (2017);
A. Vuik et al., New J. Phys. 3, 033013 (2016).
[2] C. W. Groth et al., New J. Phys. 16, 063065 (2014).
[3] A. Weisse et al., Rev. Mod. Phys. 78, 275 (2006).
[4] A. Trellakis et al., Journal of Applied Physics 81, 7880 (1997).
[5] A. Logg, K. Mardal, and G. Wells, (Springer, 2012).