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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 ( π β and π β + holes) Analyze difference in density of SO split bands Extract zero-field density difference β π ππΉ SOI near hybridization gap
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InAs/GaSb DQW InAs + GaSb ο¨ Interesting band structure [1]
GaSb valence band maximum higher in energy than InAs conduction band minimum [2] Energy range where π β in InAs coexist with holes from the GaSb Strong coupling ο¨ π β -hole hybridization ο¨ gap when π π β β π β [1] F. Qu et al., PRL 115, (2015) [2] H. Kroemer, Physica E 20 (2004)
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Sample 20ΞΌm x 80ΞΌm Hall bar 300mK Measurements
GaSb substrate lattice matched with subsequent layers ο¨ no need for thick buffer as with GaAs ο¨ better coupling between BG and wells! [1] F. Qu et al., PRL 115, (2015)
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π
π₯π₯ as function of π π‘π/ππ
2T out of plane magnet High π
π₯π₯ (dashed lines) ο πΈ πΉ inside gap Green line separates single- and dual-carrier regimes Line Ξ: π β mobility highest Line ΞΞ: close to hybridization gap
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Electron-only Regime Trace along line Ξ (fixed density)
Trends from 1-10: Extra frequency peak Asymmetry between beats (amplitude and oscillation #) Decreased spacing of peaks (decreasing β³ π ππΉ ) Increasing # of oscillations in A & B ο nodes pushed to lower B fields Clear SdH oscillations in π
π₯π₯ ο beating pattern as function of π΅ β₯ SdH osc. for each spin band periodic in 1 π΅ π π = πβ π π β System favors one SO eigenstate ο¨ β³ π ππΉ = π 2 β π 1 ο¨ β³ πΈ ππΉππ =β³ π ππΉ ( π β π β 2 ) β1
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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: ο 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: πΌ 1 =75 πππβ« π½ 1 =28.5 πππβ« πΈ π =π πππ½ β« π Solve for LL energies and extract π π₯π₯ π΅ π§ πΌ 10 =53π ππβ« π½ 10 =28.5 πππβ« πΈ ππ =π πππ½ β« π In 2D systems: π½= π π§ 2 πΎ ; π π§ 2 β π π 2 Compare data to QM LL simulations with the MB mechanism [4] ο¨ Valid for infinite square wellβ¦ π β =0.04 π 0 ; π β =β11.5 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 π β in InAs present with holes in GaSb simultaneously Investigate influence of hybridization on β π ππΉ through magnetoresistance traces on line ΞΞ Hole concentration increases from point 1 to 13 ο 13: π β β π π β πΈ πΉ near hybrid. gap
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Magnetoresistance Data
Traces with and without beating β π ππΉ,1β3 =1.7β m β2 β π ππΉ,4β5 ο no beating ο 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 ( π΄ π’π β« π΄ πππ€π ) π΄ πππ» β ππ΅ π β 3 expβ‘ βπ π π π [5] When approaching hybrid. gap π β and π are very dissimilar ο 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 ο¨ extract Rashba and Dresselhaus Non-monotonic spin splitting behavior in two carriers regime ο¨ crossing of spin bands due to hybridization
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Thanks for listening!!
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π΅ β₯ =2T
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Christopher Schierholz β Rashba Spin-Orbit Interaction in Low and High Magnetic Fields
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