Observation of a one-dimensional spin–orbit gap in a quantum wire

Abstract

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 magnitude [1]. Following this remarkable success, the field of 'spintronics' or spin-based electronics [1,2,3] is moving beyond effects based on local spin polarisation and is turning its attention to spin-orbit interaction (SOI) effects, which hold promise for the production, detection and manipulation of spin currents, allowing coherent transmission of information within a device [1,2]. While SOIinduced spin transport effects have been observed in two-and three-dimensional samples, these have been subtle and elusive, often detected only indirectly in electrical transport or else with more sophisticated techniques [4,5,6,7,8,9]. Here we present the first observation of a predicted 'spinorbit gap' in a one-dimensional sample, where counter-propagating spins, constituting a spin current, are accompanied by a clear signal in the easily-measured linear conductance of the system [10,11].We first introduce the class of phenomena we dub 'the one-dimensional spin-orbit gap' using a simple example adapted from Ref. [10], then describe our experiment in detail, and finally present a more elaborate model which captures most of the features seen in our data.The spin-orbit interaction is a relativistic effect where a charged particle moving in an electric field experiences an effective magnetic field which couples to its spin [12]. In semiconductor heterostructures, the electric field can arise as a result of either the lack of an inversion centre in the crystal (bulk inversion asymmetry, BIA) or a lack of symmetry in an external confining potential (structural inversion asymmetry, SIA) due to crystal interfaces or additional structures such as metallic gates [13]. The strength of the resulting effective magnetic field is proportional to both the particle's momentum and the original electric field.Consider a spin-degenerate one-dimensional subband with a Hamiltonian H 0 = 2 k 2 2m , where is Planck's constant, k the particle's momentum and m its mass ( Figure 1a). The leading order SO contribution to the Hamiltonian iswhere − → σ is the particle's spin, V the electrostatic potential and β a material-dependent parameter [14]. This term breaks the spin-degeneracy of the system and results in two spinful subbands separated by a lateral (wave vector) shift as shown in Figure 1b.Despite this rather striking change in the band structure, measurements of conductance through the system cannot distinguish the situation shown in Figure 1b from the case where the spins are degenerate. In both cases the edges of the two spin subbands occur at the same energy, so in both cases the conductance rises by G 0 = 2e 2 /h when the Fermi level of the system is tuned through this energy (e.g. by applying a voltage to a nearby gate) [15,16,17]. (Figure 1d.) To detect the SO shift in a transport measurement, a different approach is needed.Note that the spins as shown in Figure ...

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

“…More recently, ballistic spin resonance due to an intrinsically oscillating spin-orbit field has been experimentally realized in a quantum wire 8 . The observation of the 'one-dimensional spin-orbit gap' in quantum wires has also been reported recently 9 . Both of these experiments highlight the use of spin-orbit effects in quantum wires as a means to control the spin of carriers, an important ingredient for potential spintronic applications.…”

g-factor anisotropy of hole quantum wires induced by Rashba interaction

“…[12][13][14] By further confining the hole gas, it is possible to generate nanostructures with the shape of quantum wires. [15][16][17] In this case, the splitting varies, in principle, with both wire and magnetic field orientations. [3][4][5][6] There are few theoretical analyses of the spin splittings in hole quantum wires.…”

The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles

“…In semiconductors with strong spin-orbit (SO) interactions the two spin branches are separated in momentum space, but SO interactions do not lift the Kramer's degeneracy. However, in a magnetic field B⊥B so there is a range of energies where double degeneracy is lifted [16], see schematic in Fig 1c. If the Fermi energy E F is tuned to be within this single-mode range of energies, E Z > ∆ 2 + E 2 F , (where ∆ is the proximity gap, E Z = gµ B B/2 is the Zeeman energy, µ B is the Bohr magneton, and g is the Landé g-factor), the proximity effect from a conventional s-wave superconductor induces p-wave pairing in the semiconductor material and drives the system into a topological superconducting state which supports Majorana particles. Theoretically, it has been predicted that proper conditions for this to occur can be realized in 2D [15,17] and, most relevant to the current work, in 1D systems [1,2].…”