Revealing the Spin-Orbit Interaction in InAs nanowires

Revealing the Spin-Orbit Interaction in InAs nanowires

Vectorial control of the spin-orbit interaction in suspended InAs nanowires

1A. Iorio, 1,2M. Rocci, 1L. Bours, 1M. Carrega, 1V. Zannier, 1L. Sorba, 1S. Roddaro, 1F. Giazotto, 1E. Strambini1NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy2Francis Bitter Magnet Laboratory and Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

IntroductionSpin-orbit interaction (SOI) is a relativistic effect that couples electron momentum (orbit) and magnetic moment (spin) when moving in an electric field.

It allows for the electrical control over the electron spin in spintronic devices1 or spin-orbit qubits.2 Moreover it is an essential ingredient in nanowire (NW) based system for realizing Majorana bound states.3

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Motivations • Debated origin of the SOI in InAs nanowires (Rashba, Dresselhaus, etc.).• Role of the substrate in pinning the SO-field.4

• Missing evidence of a rotation of the SO-field by external electric fields.• Unclear influence of the 3D-confinment potential in the magnetoconductance.

A suspended InAs nanowire (in red), with two side gates (in yellow) and four ohmic contacts (in blue).

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EWeak anti-localizationIn diffusive systems with strong SOI, the interference of electrons moving along time-reversed paths allows to quantify the electron coherence length lφ and spin-relaxation length lSO. This effect, namely weak anti-localization (WAL), results in a peak in the magnetoconductance at B=0 (a), allows to quantify lφ, lSO (b) and the strength of SOI.

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a) b)Nanowire symmetriesThe WAL is studied in the 3D space by changing the orientation of the magnetic field B. When B lies in the plane orthogonal to the NW, the WAL clearly reflects the 6-fold periodicity of its hexagonal confinment potential since the suspension preserves the NW intrinsic symmetries (c, d).

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c) d)Vectorial control of the SOIIn the presence of an external electric field induced by two side gates, the NW 6-fold degeneracies are removed as demonstrated by the angular map of the WAL (e). A vectorial tuning of lSO is then achieved (f) and a rotation of the SO-field can be induced by varying the strenght of the external electric field (g).

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http : //web.nano.cnr. i t /sqe l /

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Conclusions• Vector-field investigation of WAL in suspended NWs.

First angular mapping of WAL and first WAL study on a suspended NW. WAL is non trivially affected by geometrical boundaries and carrier transport dynamics.

• No pinning of the spin-orbit field.Rashba SOI related only to the confining electric field.

• Vectorial control of the SOI by electric fields.

Evidence of an enhancement and a vectorial evolution of the SOI.

References

Nano Letters 2019 19 (2), 652-657DOI: 10.1021/acs.nanolett.8b02828

(1) Datta, S.; Das, B. Electronic analog of the electro-optic modulator. Applied Physics Letters 1990, 56, 665–667.(2) Nadj-Perge, S.; Frolov, S. M.; Bakkers, E. P. a. M.; Kouwenhoven, L. P. Spin–orbit qubit in a semiconductor nanowire. Nature 2010, 468, 1084.(3) Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Reports on Progress in Physics 2012, 75, 076501.(4) Nadj-Perge, S.; Pribiag, V. S.; van den Berg, J. W. G.; Zuo, K.; Plissard, S. R.; Bakkers, E. P. A. M.; Frolov, S. M.; Kouwenhoven, L. P. Spectroscopy of Spin-Orbit Quantum Bits in Indium Antimonide Nanowires. Physical Review Letters 2012, 108, 166801.

1A. Iorio, 3O. Durante, 3R. Citro, 4S. Bergeret, 4C. Sanz Fernández, 1A. Braggio, 1,2M. Rocci, 1N. Ligato, 1L. Sorba, 1F. Giazotto, and 1E. Strambini

IntroductionIn the Josephson effect1, the supercurrent that flows through a weak-link is described by the conventional current-phase relation (CPR):

IJ = IC sin(φ)An anomalous regime is theoretically preditcted if time-reversal and parity symmetries are broken2, as in the presence of a Zeeman field and strong SOI. In this case, an anomalous supercurrent can flow even when the superconducting phase difference φ=02:

IJ = IC sin(φ+φ0)

Motivations • There is only little experimental evidence of φ0-junctions in complex structures.3, 4

• Parity of the φ0-shift has never been investigated.• φ0-junctions can be used as phase batteries in superconducting circuits.

Anomalous φ0-shift in hybrid InAs nanowire SQUID

A single InAs nanowire (in red) is embedded in an aluminum ring (in blue) thus defining an hybrid SQUID.

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CPR in a SQUID

A SQUID is a phase-sensitive interferometer made by two weak-links embdedded in a superconducting ring. By piercing it with different magnetic fluxes, the I-V characteristics of the SQUID show a typical Φ0-periodic interference pattern (a) that allows to detect φ0-shifts in the weak-links (b).

IS(Φ) = 2IC |cos(πΦ/Φ0+φ)|a) b)

Breaking time-reversal and parity symmetriesBy applying an external in-plane magnetic field Bin perpendicular to the NW axis, an anomalous shift can be induced (c, d). The observed continuous shift shows however an intrinsic hysteretic contribution as a function of Bin (e). This spurious term can be isolated by turning off Bin after each sweep (f).

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Anomalous φ0-shiftThe φ0-shift is then isolated by subtracting the two contributions of (e) and (f) and shows no more hysteresis in the field (g). It can be tuned up to ±π/2 with a large magnetic field and its odd parity is in agreement with the theoretical prediction.2

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1NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy2Francis Bitter Magnet Laboratory and Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA3Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno and CNR-SPIN, 84084 Fisciano (Salerno), Italy4Donostia International Physics Center (DIPC), Manuel de Lardizabal 5, E-20018 San Sebastian, Spain

Conclusions• Experimental observation of the anomalous φ0-shift.

Direct observation of the anomalous φ0-shift in a hybrid SQUID with straightforward geometry.

• Parity of the φ0-shift in the Zeeman field.

First experimental confirmation of the odd parity φ0-shift in Bin.

• Hysteretic contribution in the anomalous phase.

The hysteretic behavior at Bin=0 observed in the anomalous phase can be exploited for phase batteries and persistent memories.

References

A. Iorio et al., Anomalous φ0-shift in hybrid InAs nanowire SQUID, in submission (2019). (1) Josephson, B. D. Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251–253 (1962).(2) Bergeret, F. S. & Tokatly, I. V. Theory of diffusive φ0 josephson junctions in the presence of spin-orbit coupling. EPL 110, 57005 (2015).(3) Szombati, D. B. et al. Josephson φ0-junction in nanowire quantum dots. Nature Physics 12, 568 EP (2016)(4) Assouline, A. et al. Spin-orbit induced phase-shift in Bi2Se3 josephson junctions. Nature Communications 10, 126 (2019).