Effect of Rashba spin-orbit coupling on magnetotransport in $\mathrm{InGaAs}∕\mathrm{InP}$ quantum wire structures

The Rashba spin-orbit coupling in $\mathrm{InGaAs}∕\mathrm{InP}$ quantum wire structures with a width varying between $1\mu \mathrm{m}$ and $400\mathrm{nm}$ is investigated. For all quantum wire structures a clear beating pattern in the oscillations of the magnetoresistance owing to the presence of Rashba spin-orbit coupling is observed. By applying a bias voltage to a gate electrode covering the wires it was possible to control the magnitude of the spin-orbit coupling. For the narrowest wire the effect of the confining potential on the sublevel spectrum could be resolved in the magnetoresistance oscillations. It is found that the node of the beating pattern shifts towards larger magnetic fields with decreasing wire width. The corresponding increase of the Rashba spin-orbit coupling parameter is explained by the effect of the confining potential of the wire.

Figure 1

(Color online) Schematic illustration of the wire structure. The two-dimensional electron gas is located in the strained ${\mathrm{In}}_{0.77}{\mathrm{Ga}}_{0.23}\mathrm{As}$ layer. The widths $w$ of the wires were $400$, $600\mathrm{nm}$, and $1\mu \mathrm{m}$, respectively.

Figure 2

(Color online) Magnetoresistance of a $400\mathrm{nm}$ wide wire structure. The gate voltage $V_g$ was set to $+1.0$, $-1.0$, $-2.0$, and $-3.0\mathrm{V}$. The inset shows the magnetoresistance as a function of the inverse magnetic field for a gate voltage of $+1.0$ and $0\mathrm{V}$. Here, the slowly varying background resistance was subtracted. The upper curve was shifted by $0.3k\Omega$. The node positions are indicated by arrows.

Figure 3

(Color online) (a) Magnetoresistance as a function of the magnetic field and the gate voltage. Lighter areas correspond to higher resistance values. (b) Fast Fourier transform in $1∕B$ of the magnetoresistance at 0, $-1$, $-2$, and $-3\mathrm{V}$ as a function of the characteristic field $B_c$. (c) Rashba coupling parameter $\alpha$ extracted from the fast Fourier transform spectra shown in (b).

Figure 4

(Color online) Magnetoresistance oscillations of the $400$, $600\mathrm{nm}$, and $1\mu \mathrm{m}$ wide wires as a function of the inverse magnetic field and of the gate voltage. Lighter areas correspond to higher resistance values. The position of the node of the beating pattern is indicated by an arrow. The measurement temperature was $0.6\mathrm{K}$. The slowly varying background resistance was subtracted.

Figure 5

(Color online) Sublevel index vs inverse magnetic fields of the 600 (a) and $400\mathrm{nm}$ wide (b) quantum wires at various gate voltages. The node position is indicated by an arrow.