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Spin-orbit interaction in a dual gated InAs/GaSb quantum well
A. Beukman et al. (Kouwenhoven Group) arXiv: Logo of PASPS9 conference Kris Cerveny Friday Group Meeting Talk
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Introduction Motivation: Experiment: InAs and GaSb have strong SOI
Rashba strength tunable with gating for InAs Control of SOI necessary for spintronic devices Strong SOI + large g-factor + inducible superconductivity ingredients for topological superconducting phase Experiment: Investigates SOI in dual-gated InAs/GaSb quantum well Tune between single and double carrier regimes ( ๐ โ and ๐ โ + holes) Analyze difference in density of SO split bands Extract zero-field density difference โ ๐ ๐๐น SOI near hybridization gap
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InAs/GaSb DQW InAs + GaSb ๏จ Interesting band structure [1]
GaSb valence band maximum higher in energy than InAs conduction band minimum [2] Energy range where ๐ โ in InAs coexist with holes from the GaSb Strong coupling ๏จ ๐ โ -hole hybridization ๏จ gap when ๐ ๐ โ โ ๐ โ [1] F. Qu et al., PRL 115, (2015) [2] H. Kroemer, Physica E 20 (2004)
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Sample 20ฮผm x 80ฮผm Hall bar 300mK Measurements
GaSb substrate lattice matched with subsequent layers ๏จ no need for thick buffer as with GaAs ๏จ better coupling between BG and wells! [1] F. Qu et al., PRL 115, (2015)
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๐
๐ฅ๐ฅ as function of ๐ ๐ก๐/๐๐
2T out of plane magnet High ๐
๐ฅ๐ฅ (dashed lines) ๏ ๐ธ ๐น inside gap Green line separates single- and dual-carrier regimes Line ฮ: ๐ โ mobility highest Line ฮฮ: close to hybridization gap
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Electron-only Regime Trace along line ฮ (fixed density)
Trends from 1-10: Extra frequency peak Asymmetry between beats (amplitude and oscillation #) Decreased spacing of peaks (decreasing โณ ๐ ๐๐น ) Increasing # of oscillations in A & B ๏ nodes pushed to lower B fields Clear SdH oscillations in ๐
๐ฅ๐ฅ ๏ beating pattern as function of ๐ต โฅ SdH osc. for each spin band periodic in 1 ๐ต ๐ ๐ = ๐โ ๐ ๐ โ System favors one SO eigenstate ๏จ โณ ๐ ๐๐น = ๐ 2 โ ๐ 1 ๏จ โณ ๐ธ ๐๐น๐๐ =โณ ๐ ๐๐น ( ๐ โ ๐ โ 2 ) โ1
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Center Frequency Peak Emergent central peak does not correspond to a density 3 possible mechanisms can cause extra freq. components: Magnetic inter-subband scattering Magnetophonon resonances Magnetic breakdown: ๏ Carriers tunneling between spin polarized Fermi-surfaces Emergent central peak does not correspond to a density 3 possible mechanisms can cause extra freq. components: Magnetic inter-subband scattering Magnetophonon resonances Magnetic breakdown [Schematics] W. G. Chambers, Proc. Phys. Soc., Vol 84, 1964
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Simulation vs Measurement
Parameter tuning yields: ๐ผ 1 =75 ๐๐๐โซ ๐ฝ 1 =28.5 ๐๐๐โซ ๐ธ ๐ =๐ ๐๐๐ฝ โซ ๐ Solve for LL energies and extract ๐ ๐ฅ๐ฅ ๐ต ๐ง ๐ผ 10 =53๐ ๐๐โซ ๐ฝ 10 =28.5 ๐๐๐โซ ๐ธ ๐๐ =๐ ๐๐๐ฝ โซ ๐ In 2D systems: ๐ฝ= ๐ ๐ง 2 ๐พ ; ๐ ๐ง 2 โ ๐ ๐ 2 Compare data to QM LL simulations with the MB mechanism [4] ๏จ Valid for infinite square wellโฆ ๐ โ =0.04 ๐ 0 ; ๐ โ =โ11.5 Cubic Dresselhaus term set to zero for good fits!?!? [4] R. Winkler, Spin-orbit Coupling Effects in Two-dimensional Electron and Hole Systems, Springer 2003
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Two Carrier Regime ๐ โ in InAs present with holes in GaSb simultaneously Investigate influence of hybridization on โ ๐ ๐๐น through magnetoresistance traces on line ฮฮ Hole concentration increases from point 1 to 13 ๏ 13: ๐ โ โ ๐ ๐ โ ๐ธ ๐น near hybrid. gap
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Magnetoresistance Data
Traces with and without beating โ ๐ ๐๐น,1โ3 =1.7โ m โ2 โ ๐ ๐๐น,4โ5 ๏ no beating ๏ no ZFDD extractable Non-monotonic behavior! Band structure calculations agree qualitatively for first 10 points
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Lack of Beating Two possible reasons:
Strong asymmetry between spin species determines visibility ( ๐ด ๐ข๐ โซ ๐ด ๐๐๐ค๐ ) ๐ด ๐๐๐ป โ ๐๐ต ๐ โ 3 expโก โ๐ ๐ ๐ ๐ [5] When approaching hybrid. gap ๐ โ and ๐ are very dissimilar ๏ visibility reduced below experimental detection limits Energy window with single spin band present [6] No beating possible They can not determine which is the cause [5] J. Luo et al., PRB, 41, (1990) [6] F. Nichele et al., ArXiv (2016),
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Conclusion Study of SOI in InAs/GaSb DQW by top and back gating
Tunable in electron-only regime ๏จ extract Rashba and Dresselhaus Non-monotonic spin splitting behavior in two carriers regime ๏จ crossing of spin bands due to hybridization
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Thanks for listening!!
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๐ต โฅ =2T
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Christopher Schierholz โ Rashba Spin-Orbit Interaction in Low and High Magnetic Fields
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