Weak anti-localization of two-dimensional holes in germanium beyond the diffusive regime

Chou, C. -T.; Jacobson, N. T.; Moussa, J. E.; Baczewski, A. D.; Chuang, Y.; Liu, C. -Y.; Li, J. -Y.; Lu, T. M.

doi:10.1039/C8NR05677C

Title: Weak anti-localization of two-dimensional holes in germanium beyond the diffusive regime

Journal Article · 18 September 2018 · Nanoscale

DOI: https://doi.org/10.1039/C8NR05677C · OSTI ID:1477314

Chou, C. -T. ^[1]; Jacobson, N. T. ^[2]; Moussa, J. E. ^[2]; Baczewski, A. D. ^[2]; Chuang, Y. ^[1]; Liu, C. -Y. ^[1]; Li, J. -Y. ^[3];

^[2]

National Taiwan Univ., Taipei (Taiwan)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
National Taiwan Univ., Taipei (Taiwan); National Nano Device Labs., Hsinchu (Taiwan)

Gate-controllable spin-orbit coupling is often one requisite for spintronic devices. For practical spin field-effect transistors, another essential requirement is ballistic spin transport, where the spin precession length is shorter than the mean free path such that the gate-controlled spin precession is not randomized by disorder. In this letter, we report the observation of a gate-induced crossover from weak localization to weak anti-localization in the magneto-resistance of a high-mobility twodimensional hole gas in a strained germanium quantum well. From the magneto-resistance, we extract the phase-coherence time, spin-orbit precession time, spin-orbit energy splitting, and cubic Rashba coefficient over a wide density range. The mobility and the mean free path increase with increasing hole density, while the spin precession length decreases due to increasingly stronger spin-orbit coupling. As the density becomes larger than , 6 x 10¹¹cm^-2, the spin precession length becomes shorter than the mean free path, and the system enters the ballistic spin transport regime. We also report here the numerical methods and code developed for calculating the magnetoresistance in the ballistic regime, where the commonly used HLN and ILP models for analyzing weak localization and anti-localization are not valid. These results pave the way toward siliconcompatible spintronic devices.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1477314

Alternate ID(s):: OSTI ID: 1474007

Report Number(s):: SAND-2018-10483J; 668122

Journal Information:: Nanoscale, Vol. 10, Issue 44; ISSN 2040-3364

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 9 works

Citation information provided by
Web of Science

References (47)

Spin-orbit interaction in a two-dimensional electron gas in a InAs/AlSb quantum well with gate-controlled electron density Heida, J. P.; van Wees, B. J.; Kuipers, J. J. Physical Review B, Vol. 57, Issue 19 https://doi.org/10.1103/PhysRevB.57.11911	journal	May 1998
Rashba Spin-Orbit Coupling Probed by the Weak Antilocalization Analysis in InAlAs / InGaAs / InAlAs Quantum Wells as a Function of Quantum Well Asymmetry Koga, Takaaki; Nitta, Junsaku; Akazaki, Tatsushi Physical Review Letters, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevLett.89.046801	journal	July 2002
Narrow heavy-hole cyclotron resonances split by the cubic Rashba spin-orbit interaction in strained germanium quantum wells Failla, M.; Myronov, M.; Morrison, C. Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.045303	journal	July 2015
The Effect of Spin Splitting on the Metallic Behavior of a Two-Dimensional System Papadakis, S. J. Science, Vol. 283, Issue 5410 https://doi.org/10.1126/science.283.5410.2056	journal	March 1999
Weak localization in thin films Bergmann, Gerd Physics Reports, Vol. 107, Issue 1 https://doi.org/10.1016/0370-1573(84)90103-0	journal	May 1984
Observation of Rashba zero-field spin splitting in a strained germanium 2D hole gas Morrison, C.; Wiśniewski, P.; Rhead, S. D. Applied Physics Letters, Vol. 105, Issue 18 https://doi.org/10.1063/1.4901107	journal	November 2014
Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures Lutchyn, Roman M.; Sau, Jay D.; Das Sarma, S. Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevLett.105.077001	journal	August 2010
Spin-orbit interaction in InSb nanowires van Weperen, I.; Tarasinski, B.; Eeltink, D. Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/PhysRevB.91.201413	journal	May 2015
All-electric quantum point contact spin-polarizer Debray, P.; Rahman, S. M. S.; Wan, J. Nature Nanotechnology, Vol. 4, Issue 11 https://doi.org/10.1038/nnano.2009.240	journal	September 2009
Quantum Spin Hall Effect in Graphene Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.226801	journal	November 2005
Spin orientation of holes in quantum wells Winkler, R.; Culcer, Dimitrie; Papadakis, S. J. Semiconductor Science and Technology, Vol. 23, Issue 11 https://doi.org/10.1088/0268-1242/23/11/114017	journal	October 2008
Large Rashba Splitting in InAs Quantum Wells due to Electron Wave Function Penetration into the Barrier Layers Grundler, Dirk Physical Review Letters, Vol. 84, Issue 26 https://doi.org/10.1103/PhysRevLett.84.6074	journal	June 2000
Observation of spin precession in GaAs inversion layers using antilocalization Dresselhaus, P. D.; Papavassiliou, C. M. A.; Wheeler, R. G. Physical Review Letters, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevLett.68.106	journal	January 1992
Spin-Orbit Interaction and Magnetoresistance in the Two Dimensional Random System Hikami, S.; Larkin, A. I.; Nagaoka, Y. Progress of Theoretical Physics, Vol. 63, Issue 2 https://doi.org/10.1143/PTP.63.707	journal	February 1980
Electronic analog of the electro‐optic modulator Datta, Supriyo; Das, Biswajit Applied Physics Letters, Vol. 56, Issue 7 https://doi.org/10.1063/1.102730	journal	February 1990
Anomalous Rashba spin splitting in two-dimensional hole systems Winkler, R.; Noh, H.; Tutuc, E. Physical Review B, Vol. 65, Issue 15 https://doi.org/10.1103/PhysRevB.65.155303	journal	March 2002
Experimental Evidence of Cubic Rashba Effect in an Inversion-Symmetric Oxide Nakamura, H.; Koga, T.; Kimura, T. Physical Review Letters, Vol. 108, Issue 20 https://doi.org/10.1103/PhysRevLett.108.206601	journal	May 2012
Strong spin-orbit interactions and weak antilocalization in carbon-doped p -type Ga As ∕ Al x Ga 1 − x As heterostructures Grbić, Boris; Leturcq, Renaud; Ihn, Thomas Physical Review B, Vol. 77, Issue 12 https://doi.org/10.1103/PhysRevB.77.125312	journal	March 2008
Anomalous spin precession and spin Hall effect in semiconductor quantum wells Bi, Xintao; He, Peiru; Hankiewicz, E. M. Physical Review B, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevB.88.035316	journal	July 2013
Spin--Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems Winkler, Roland; Höhler, Gerhard; Kühn, Johann H. Springer Tracts in Modern Physics, Vol. 191 https://doi.org/10.1007/b13586	book	January 2003
Hole weak anti-localization in a strained-Ge surface quantum well Mizokuchi, R.; Torresani, P.; Maurand, R. Applied Physics Letters, Vol. 111, Issue 6 https://doi.org/10.1063/1.4997411	journal	August 2017
Negative differential Rashba effect in two-dimensional hole systems Habib, B.; Tutuc, E.; Melinte, S. Applied Physics Letters, Vol. 85, Issue 15 https://doi.org/10.1063/1.1806543	journal	October 2004
Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained- Ge / SiGe Quantum Well Moriya, Rai; Sawano, Kentarou; Hoshi, Yusuke Physical Review Letters, Vol. 113, Issue 8 https://doi.org/10.1103/PhysRevLett.113.086601	journal	August 2014
Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures Sau, Jay D.; Lutchyn, Roman M.; Tewari, Sumanta Physical Review Letters, Vol. 104, Issue 4 https://doi.org/10.1103/PhysRevLett.104.040502	journal	January 2010
Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System Wunderlich, J.; Kaestner, B.; Sinova, J. Physical Review Letters, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevLett.94.047204	journal	February 2005
Nonmonotonically tunable Rashba spin-orbit coupling by multiple-band filling control in SrTiO 3 -based interfacial d -electron gases Liang, Haixing; Cheng, Long; Wei, Laiming Physical Review B, Vol. 92, Issue 7 https://doi.org/10.1103/PhysRevB.92.075309	journal	August 2015
Majorana fermions in a tunable semiconductor device Alicea, Jason Physical Review B, Vol. 81, Issue 12 https://doi.org/10.1103/PhysRevB.81.125318	journal	March 2010
Tunable Spin-Splitting and Spin-Resolved Ballistic Transport in GaAs/AlGaAs Two-Dimensional Holes Lu, J. P.; Yau, J. B.; Shukla, S. P. Physical Review Letters, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevLett.81.1282	journal	August 1998
Gate-Controlled Spin-Orbit Quantum Interference Effects in Lateral Transport Miller, J. B.; Zumbühl, D. M.; Marcus, C. M. Physical Review Letters, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevLett.90.076807	journal	February 2003
Spin-Orbit Coupling Effects in Zinc Blende Structures Dresselhaus, G. Physical Review, Vol. 100, Issue 2 https://doi.org/10.1103/PhysRev.100.580	journal	October 1955
Theory of interface roughness scattering in quantum wells Penner, U.; Rücker, H.; Yassievich, I. N. Semiconductor Science and Technology, Vol. 13, Issue 7 https://doi.org/10.1088/0268-1242/13/7/009	journal	July 1998
Spin Hall Effect Hirsch, J. E. Physical Review Letters, Vol. 83, Issue 9 https://doi.org/10.1103/PhysRevLett.83.1834	journal	August 1999
Gate Control of Spin-Orbit Interaction in an Inverted I n 0.53 G a 0.47 As/I n 0.52 A l 0.48 As Heterostructure Nitta, Junsaku; Akazaki, Tatsushi; Takayanagi, Hideaki Physical Review Letters, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevLett.78.1335	journal	February 1997
Gate-Controlled Spin-Orbit Interaction in a Parabolic GaAs / AlGaAs Quantum Well Studer, M.; Salis, G.; Ensslin, K. Physical Review Letters, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevLett.103.027201	journal	July 2009
Nondiffusive weak localization in two-dimensional systems with spin-orbit splitting of the spectrum Glazov, M. M.; Golub, L. E. Semiconductors, Vol. 40, Issue 10 https://doi.org/10.1134/S1063782606100150	journal	October 2006
Effects of surface tunneling of two-dimensional hole gases in undoped Ge/GeSi heterostructures Su, Yi-Hsin; Chuang, Yen; Liu, Chia-You Physical Review Materials, Vol. 1, Issue 4 https://doi.org/10.1103/PhysRevMaterials.1.044601	journal	September 2017
All-electric all-semiconductor spin field-effect transistors Chuang, Pojen; Ho, Sheng-Chin; Smith, L. W. Nature Nanotechnology, Vol. 10, Issue 1 https://doi.org/10.1038/nnano.2014.296	journal	December 2014
Control of Spin Precession in a Spin-Injected Field Effect Transistor Koo, H. C.; Kwon, J. H.; Eom, J. Science, Vol. 325, Issue 5947 https://doi.org/10.1126/science.1173667	journal	September 2009
Spin-Filter Device Based on the Rashba Effect Using a Nonmagnetic Resonant Tunneling Diode Koga, Takaaki; Nitta, Junsaku; Takayanagi, Hideaki Physical Review Letters, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevLett.88.126601	journal	March 2002
Spin-Transistor Electronics: An Overview and Outlook Sugahara, Satoshi; Nitta, Junsaku Proceedings of the IEEE, Vol. 98, Issue 12 https://doi.org/10.1109/JPROC.2010.2064272	journal	December 2010
Spin hall Effect Schliemann, John International Journal of Modern Physics B, Vol. 20, Issue 09 https://doi.org/10.1142/s021797920603370x	journal	April 2006
Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained-Ge/SiGe Quantum Well Moriya, Rai; Sawano, Kentarou; Hoshi, Yusuke Universität Regensburg https://doi.org/10.5283/epub.30750	text	January 2014
Majorana fermions in a tunable semiconductor device Alicea, Jason arXiv https://doi.org/10.48550/arxiv.0912.2115	text	January 2009
Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures Lutchyn, Roman M.; Sau, Jay D.; Sarma, S. Das arXiv https://doi.org/10.48550/arxiv.1002.4033	text	January 2010
Anomalous Rashba spin splitting in two-dimensional hole systems Winkler, R.; Noh, H.; Tutuc, E. arXiv https://doi.org/10.48550/arxiv.cond-mat/0106246	text	January 2001
Negative differential Rashba effect in two-dimensional hole systems Habib, B.; Tutuc, E.; Melinte, S. arXiv https://doi.org/10.48550/arxiv.cond-mat/0409372	text	January 2004
Spin Hall effect Hirsch, J. E. arXiv https://doi.org/10.48550/arxiv.cond-mat/9906160	text	January 1999

Cited By (2)

Single and double hole quantum dots in strained Ge/SiGe quantum wells Hardy, Will J.; Harris, C. Thomas; Su, Yi-Hsin Nanotechnology, Vol. 30, Issue 21 https://doi.org/10.1088/1361-6528/ab061e	journal	March 2019
Single and Double Hole Quantum Dots in Strained Ge/SiGe Quantum Wells Hardy, Will J.; Harris, C. Thomas; Su, Yi-Hsin arXiv https://doi.org/10.48550/arxiv.1808.07077	text	January 2018