Enhancement of spin-orbit interaction and the effect of interface diffusion in quaternary InGaAsP/InGaAs heterostructures

Makoto Kohda and Junsaku Nitta

Phys. Rev. B 81, 115118 – Published 15 March 2010

Abstract

The enhancement of spin-orbit interaction due to simultaneous control of both valence-band offset and electron probability density of the conduction band in a quaternary InGaAsP/InGaAs heterointerface is demonstrated. Weak antilocalization is measured to determine the strength of the Rashba spin-orbit interaction with different gate bias voltages and analyzed by quantum correction of the conductance developed by L. E. Golub [Phys. Rev. B 71, 235310 (2005)]. The Rashba spin-orbit interaction parameter is increased up to $α = 10.4 \times 10^{- 12} eV m$ with sheet carrier density $N_{s} = 2 \times 10^{11} {cm}^{- 2}$ . To confirm such a strong effective magnetic field by comparison with the Zeeman energy, we also measure weak antilocalization in the presence of the in-plane magnetic field. A weak antilocalization signal remains up to $B_{∥} = 3.0 T$ , resulting in direct evidence of strong spin-orbit interaction in the InGaAsP/InGaAs heterostructure. By taking the interface diffusion at the InGaAsP/InGaAs into account, the obtained Rashba spin-orbit interaction parameter $α$ is found to be quantitatively consistent with theoretical calculation derived from the $k \cdot p$ theory.

Received 3 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.115118

Authors & Affiliations

Makoto Kohda^1,2,* and Junsaku Nitta¹

¹Department of Materials Science, Tohoku University, 6-6-02 Aramaki-Aza Aoba, Aoba-ku, Sendai 980-8579, Japan
²PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

^*makoto@material.tohoku.ac.jp

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Vol. 81, Iss. 11 — 15 March 2010

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Images

Figure 1
(Color online) Energy-band profiles of conduction $(Γ_{6})$ , valence $(Γ_{8})$ , and spin split-off $(Γ_{7})$ bands in ${In}_{0.52} {Al}_{0.48} As / 5 nm {({In}_{0.53} {Ga}_{0.47} As)}_{0.41} {(In P)}_{0.59} / 10 nm {In}_{0.8} {Ga}_{0.2} As / 3 nm {({In}_{0.52} {Al}_{0.48} As)}_{0.3} {({In}_{0.53} {Ga}_{0.47} As)}_{0.7} / {In}_{0.52} {Al}_{0.48} As$ 2DEG structures calculated by the Poisson-Schrödinger equation. Each line correspond to $Γ_{6}$ (top), $Γ_{8}$ (middle), and $Γ_{7}$ (bottom) bands, respectively, whose energies are based on the position of Fermi energy $E_{F}$ . Solid and dashed lines are the band structure under the gate bias voltage of $V_{g} = - 4.5$ and $+ 2.5 V$ , respectively. Normalized electron probability density ${| Ψ |}^{2}$ is also shown.Reuse & Permissions
Figure 2
(Color online) Schematic band structure and electron probability density for enhancing the interface contribution of Rashba SOI parameter. $Δ E_{Γ 6}$ , $Δ E_{Γ 8}$ , and $Δ E_{Γ 7}$ are band offset energies of conduction, valence, and spin split-off bands at the interface, respectively. $E_{F} - E_{Γ 8}^{Q W} (z_{n})$ $[E_{F} - E_{Γ 7}^{Q W} (z_{n})]$ is the band-gap energy in a quantum well between Fermi level and valence band [spin split-off band].Reuse & Permissions
Figure 3
(Color online) Measured magnetoconductances in 10 nm ${In}_{0.8} {Ga}_{0.2} As$ , 5 nm ${In}_{0.8} {Ga}_{0.2} As$ , and 10 nm ${In}_{0.53} {Ga}_{0.47} As$ QWs. Carrier densities between three samples are adjusted to $N_{s} = 4.11 \times 10^{11} {cm}^{- 2}$ by gate bias at $T = 0.3 K$ . Conductance is plotted in units of $e^{2} / 2 π h$ .Reuse & Permissions
Figure 4
(Color online) Perpendicular magnetic field dependence of conductance in 10 nm ${In}_{0.53} {Ga}_{0.47} As$ QW under different in-plane magnetic fields $B_{∥}$ from 0.2 to 3.0 T at $T = 4.3 K$ .Reuse & Permissions
Figure 5
(Color online) Experimental results (gray circles) of the quantum correction of the conductivity $Δ σ$ in units of $e^{2} / 2 π h$ for (a) 10 nm ${In}_{0.8} {Ga}_{0.2} As$ , (b) 5 nm ${In}_{0.8} {Ga}_{0.2} As$ , and (c) 10 nm ${In}_{0.53} {Ga}_{0.47} As$ QWs with different gate bias voltages at $T = 0.3 K$ . The curves are offset for clarity. Corresponding carrier density $N_{s}$ for the gate bias is also shown. The solid lines represent the best fits to the experimental results using the Golub theory (Ref. 31). (d) Carrier density dependence of transport magnetic field $B_{t r}$ (closed symbols) and characteristic magnetic field of spin-relaxation length $B_{s o}$ (open symbols). $B_{t r}$ is calculated from mean free path and $B_{s o}$ is derived from the ILP theory (Ref. 30).Reuse & Permissions
Figure 6
(Color online) Carrier density dependence of the Rashba SOI parameter $α$ by fitting the experimental results with the Golub theory (closed circles) and calculated results from the $k \cdot p$ theory (lines and open circles) for (a) 10 nm ${In}_{0.8} {Ga}_{0.2} As$ , (b) 5 nm ${In}_{0.8} {Ga}_{0.2} As$ , and (c) 10 nm ${In}_{0.53} {Ga}_{0.47} As$ QWs. Solid lines and open circles represent theoretical results with no interface diffusion and 1 nm interface diffusion at ${({In}_{0.53} {Ga}_{0.47} As)}_{0.41} {(InP)}_{0.59} / {In}_{y} {Ga}_{1 - y} As$ heterostructure, respectively. Closed triangles are the results in ${In}_{0.52} {Al}_{0.48} As / {In}_{0.8} {Ga}_{0.2} As$ QW (Refs. 33, 34). Open squares and triangles are ${In}_{0.53} {Ga}_{0.47} As / {In}_{0.77} {Ga}_{0.23} As$ QW which obtained the largest $α$ and $d α / d N_{s}$ in the WAL measurement (Ref. 32).Reuse & Permissions

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