Abstract

Quantum wires or quantum point contacts (QPCs) built from two
dimensional materials, like bilayer graphene (BLG), might pave the
way towards quantum circuits. We consider a gate defined BLG based
quantum wire with a perpendicular magnetic field and both supercon-
ducting and non superconducting leads. In the superconducting regime
we study the magnetic interference pattern in rectangular junctions
by means of a semi-classical model [1]. A similar study was recently con-
ducted on BLG QPCs, where it could be shown, that a variation in the
gate potentials leads to a tailoring of the supercurrent [2]. Here we find a
dependence on the aspect ratio, where reflections at the side edges are
of high importance in narrow junctions, but not in wide ones. In the
normal conducting regime, we investigate the quantized conductance
due to finite size effects and the emergence of Landau levels. We find
an accidental degeneracy for wide channels and large gaps, as proposed by [3].
The experimental confirmation in the case of BLG QPCs was recently given in [4].
The conduction plateaus of height 4 e^2/h are clearly visible and the first step
has a height of 8 e^2/h for certain values of the splitgate. The conditions
for this accidental degeneracy can be expressed analytically by means
of the effective two band Hamiltonian.

[1] H. Meier, V. I. Fal'ko and L. I. Glazman, Phys. Rev. B 93, 184506 (2016).


[2] R. Kraft et al., NatureCommunication 9, 1722, 1722 (2018).


[3] A. Knothe and V. Fal'ko, Phys. Rev. B 98, 155435 (2018).


[4] R. Kraft et al., Phys. Rev. Lett. 121, 257709 (2018).