Confinement versus interface bound states in spin-orbit coupled nanowires

Abstract

Semiconductor nanowires with strong Rashba spin-orbit coupling are currently on the spotlight of several research fields such as spintronics, topological materials and quantum computation. While most theoretical models assume an infinitely long nanowire, in actual experimental setups the nanowire has a finite length, is contacted to metallic electrodes and is partly covered by gates. By taking these effects into account through an inhomogeneous spin-orbit coupling profile, we show that in general two types of bound states arise in the nanowire, namely confinement bound states and interface bound states. The appearance of confinement bound states, related to the finite length of the nanowire, is favoured by a mismatch of the bulk band bottoms characterizing the lead and the nanowire, and occurs even in the absence of magnetic field. In contrast, an interface bound states may only appear if a magnetic field applied perpendicularly to the spin-orbit field direction overcomes a critical value, and is favoured by an alignment of the band bottoms of the two regions across the interface. We describe in details the emergence of these two types of bound states, pointing out their differences. Furthermore, we show that when a nanowire portion is covered by a gate the application of a magnetic field can change the nature of the electronic ground state from a confinement to an interface bound state, determining a redistribution of the electron charge.

The Dirac paradox in 1 + 1 dimensions and its realization with spin–orbit coupled nanowires

“…Indeed the huge advances of gating techniques enable one to realize different gate potentials to various portions of the NWs [38][39][40][41][42][43], thereby locally varying the magnitude and even the sign of the RSOC [44][45][46][47][48][49][50][51][52][53][54][55][56][57]. The overall system can thus be described by a inhomogeneous spin-orbit coupling α(x) and the Hamiltonian ( 36) is generalized to [63][64][65][66][67][68][69][70][71]…”

Electron transport in quantum channels with spin-orbit interaction: Effects of the sign of the Rashba coupling and applications to nanowires

“…Recent studies suggest that a different scenario may emerge in the presence of inhomogeneous RSOC profile. A junction between two regions with opposite RSOC signs, for instance, exhibits interesting spectral and equilibrium properties at the interface, such as localized bound states 55,56 and orthogonal spin polarization 57 , which look surprisingly similar to the ones of the topological phase. In experimental implementations, where the RSOC can be locally controlled by gates, these inhomogeneous configurations can be realized by coupling various gates along the NW, providing an additional knob to control the electrical current flowing through the NW setup.…”

Electron transport in quantum channels with spin–orbit interaction: effects of the sign of the Rashba coupling and applications to nanowires

“…Recent studies suggest that a different scenario may emerge in the presence of inhomogeneous RSOC profile. A junction between two regions with opposite RSOC signs, for instance, exhibits interesting spectral and equilibrium properties at the interface, such as localized bound states [58,59] and orthogonal spin polarization [60], which look surprisingly similar to the ones of the topological phase. In experimental implementations, where the RSOC can be locally controlled by gates, these inhomogeneous configurations can be realized by coupling various gates along the NW, providing an additional knob to control the electrical current flowing through the NW setup.…”