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We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80 $mu$eV by the displacement field. We assign this gate-tunable subband-splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addition, we observe the existence of a spin-polarized channel of 6 e$^2$/h at high in-plane magnetic field and of signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.
Understanding the flow of spins in magnetic layered structures has enabled an increase in data storage density in hard drives over the past decade of more than two orders of magnitude1. Following this remarkable success, the field of spintronics or s
We study conductance across a twisted bilayer graphene coupled to single-layer graphene leads in two setups: a flake of graphene on top of an infinite graphene ribbon and two overlapping semi-infinite graphene ribbons. We find conductance strongly de
We have fabricated and studied a ballistic one-dimensional p-type quantum wire using an undoped AlGaAs/GaAs heterostructure. The absence of modulation doping eliminates remote ionized impurity scattering and allows high mobilities to be achieved over
We report a change of three orders of magnitudes in the resistance of a suspended bilayer graphene flake which varies from a few k$Omega$s in the high carrier density regime to several M$Omega$s around the charge neutrality point (CNP). The correspon
A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D Hamiltonian