skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Valley dependent anisotropic spin splitting in silicon quantum dots

Abstract

Spin qubits hosted in silicon (Si) quantum dots (QD) are attractive due to their exceptionally long coherence times and compatibility with the silicon transistor platform. To achieve electrical control of spins for qubit scalability, recent experiments have utilized gradient magnetic fields from integrated micro-magnets to produce an extrinsic coupling between spin and charge, thereby electrically driving electron spin resonance (ESR). However, spins in silicon QDs experience a complex interplay between spin, charge, and valley degrees of freedom, influenced by the atomic scale details of the confining interface. We report experimental observation of a valley dependent anisotropic spin splitting in a Si QD with an integrated micro-magnet and an external magnetic field. We show by atomistic calculations that the spin-orbit interaction (SOI), which is often ignored in bulk silicon, plays a major role in the measured anisotropy. Moreover, inhomogeneities such as interface steps strongly affect the spin splittings and their valley dependence. This atomic-scale understanding of the intrinsic and extrinsic factors controlling the valley dependent spin properties is a key requirement for successful manipulation of quantum information in Si QDs.

Authors:
ORCiD logo [1];  [2];  [2];  [3];  [4];  [4];  [4];  [4]; ORCiD logo [4];  [4];  [2]; ORCiD logo [1]
  1. Purdue Univ., West Lafayette, IN (United States). Electrical and Computer Engineering and Network for Computational Nanotechnology
  2. Delft Univ. of Technology (Netherlands). QuTech and Kavli Inst. of Nanoscience
  3. Delft Univ. of Technology (Netherlands). QuTech and Kavli Inst. of Nanoscience; AGH - Univ. of Science and Technology, Krakow (Poland). Academic Centre for Materials and Nanotechnology
  4. Univ. of Wisconsin, Madison, WI (United States)
Publication Date:
Research Org.:
Univ. of Wisconsin, Madison, WI (United States). Materials Research Science and Engineering Center (MRSEC)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); US Army Research Office (ARO); National Science Foundation (NSF); European Research Council (ERC)
Contributing Org.:
Purdue Univ., West Lafayette, IN (United States). Network for Computational Nanotechnology (nanoHUB.org)
OSTI Identifier:
1460097
Grant/Contract Number:  
FG02-03ER46028; W911NF-12-0607; DMR-1121288; EEC-0228390
Resource Type:
Accepted Manuscript
Journal Name:
npj Quantum Information
Additional Journal Information:
Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2056-6387
Publisher:
Nature Partner Journals
Country of Publication:
United States
Language:
English
Subject:
77 NANOSCIENCE AND NANOTECHNOLOGY; 97 MATHEMATICS AND COMPUTING

Citation Formats

Ferdous, Rifat, Kawakami, Erika, Scarlino, Pasquale, Nowak, Michal P., Ward, D. R., Savage, D. E., Lagally, M. G., Coppersmith, S. N., Friesen, Mark, Eriksson, Mark A., Vandersypen, Lieven M. K., and Rahman, Rajib. Valley dependent anisotropic spin splitting in silicon quantum dots. United States: N. p., 2018. Web. doi:10.1038/s41534-018-0075-1.
Ferdous, Rifat, Kawakami, Erika, Scarlino, Pasquale, Nowak, Michal P., Ward, D. R., Savage, D. E., Lagally, M. G., Coppersmith, S. N., Friesen, Mark, Eriksson, Mark A., Vandersypen, Lieven M. K., & Rahman, Rajib. Valley dependent anisotropic spin splitting in silicon quantum dots. United States. doi:10.1038/s41534-018-0075-1.
Ferdous, Rifat, Kawakami, Erika, Scarlino, Pasquale, Nowak, Michal P., Ward, D. R., Savage, D. E., Lagally, M. G., Coppersmith, S. N., Friesen, Mark, Eriksson, Mark A., Vandersypen, Lieven M. K., and Rahman, Rajib. Tue . "Valley dependent anisotropic spin splitting in silicon quantum dots". United States. doi:10.1038/s41534-018-0075-1. https://www.osti.gov/servlets/purl/1460097.
@article{osti_1460097,
title = {Valley dependent anisotropic spin splitting in silicon quantum dots},
author = {Ferdous, Rifat and Kawakami, Erika and Scarlino, Pasquale and Nowak, Michal P. and Ward, D. R. and Savage, D. E. and Lagally, M. G. and Coppersmith, S. N. and Friesen, Mark and Eriksson, Mark A. and Vandersypen, Lieven M. K. and Rahman, Rajib},
abstractNote = {Spin qubits hosted in silicon (Si) quantum dots (QD) are attractive due to their exceptionally long coherence times and compatibility with the silicon transistor platform. To achieve electrical control of spins for qubit scalability, recent experiments have utilized gradient magnetic fields from integrated micro-magnets to produce an extrinsic coupling between spin and charge, thereby electrically driving electron spin resonance (ESR). However, spins in silicon QDs experience a complex interplay between spin, charge, and valley degrees of freedom, influenced by the atomic scale details of the confining interface. We report experimental observation of a valley dependent anisotropic spin splitting in a Si QD with an integrated micro-magnet and an external magnetic field. We show by atomistic calculations that the spin-orbit interaction (SOI), which is often ignored in bulk silicon, plays a major role in the measured anisotropy. Moreover, inhomogeneities such as interface steps strongly affect the spin splittings and their valley dependence. This atomic-scale understanding of the intrinsic and extrinsic factors controlling the valley dependent spin properties is a key requirement for successful manipulation of quantum information in Si QDs.},
doi = {10.1038/s41534-018-0075-1},
journal = {npj Quantum Information},
number = 1,
volume = 4,
place = {United States},
year = {2018},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 8 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Coupled Spin and Valley Physics in Monolayers of MoS 2 and Other Group-VI Dichalcogenides
journal, May 2012


Spintronics: Fundamentals and applications
journal, April 2004


Spin and valley-orbit splittings in Si Ge Si heterostructures
journal, June 2006


An addressable quantum dot qubit with fault-tolerant control-fidelity
journal, October 2014

  • Veldhorst, M.; Hwang, J. C. C.; Yang, C. H.
  • Nature Nanotechnology, Vol. 9, Issue 12
  • DOI: 10.1038/nnano.2014.216

Second-Harmonic Coherent Driving of a Spin Qubit in a Si/SiGe Quantum Dot
journal, September 2015


Quantum control and process tomography of a semiconductor quantum dot hybrid qubit
journal, July 2014


Magnetic field dependence of valley splitting in realistic Si∕SiGe quantum wells
journal, November 2006

  • Friesen, Mark; Eriksson, M. A.; Coppersmith, S. N.
  • Applied Physics Letters, Vol. 89, Issue 20
  • DOI: 10.1063/1.2387975

Valley splitting in strained silicon quantum wells modeled with 2° miscuts, step disorder, and alloy disorder
journal, February 2007

  • Kharche, Neerav; Prada, Marta; Boykin, Timothy B.
  • Applied Physics Letters, Vol. 90, Issue 9
  • DOI: 10.1063/1.2591432

Spintronics: A Spin-Based Electronics Vision for the Future
journal, November 2001

  • Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.
  • Science, Vol. 294, Issue 5546, p. 1488-1495
  • DOI: 10.1126/science.1065389

Spin and pseudospins in layered transition metal dichalcogenides
journal, April 2014

  • Xu, Xiaodong; Yao, Wang; Xiao, Di
  • Nature Physics, Vol. 10, Issue 5
  • DOI: 10.1038/nphys2942

Dressed photon-orbital states in a quantum dot: Intervalley spin resonance
journal, April 2017


Morphology of monatomic step edges on vicinal Si(001)
journal, November 1993


Atomistic Simulation of Realistically Sized Nanodevices Using NEMO 3-D—Part I: Models and Benchmarks
journal, September 2007


Quantum computation with quantum dots
journal, January 1998


Spin-orbit splitting in crystalline and compositionally disordered semiconductors
journal, July 1977


Spins in few-electron quantum dots
journal, October 2007


Electronic analog of the electro‐optic modulator
journal, February 1990

  • Datta, Supriyo; Das, Biswajit
  • Applied Physics Letters, Vol. 56, Issue 7
  • DOI: 10.1063/1.102730

Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers
journal, June 2013

  • Gong, Zhirui; Liu, Gui-Bin; Yu, Hongyi
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3053

Valley-Based Noise-Resistant Quantum Computation Using Si Quantum Dots
journal, March 2012


Coherent singlet-triplet oscillations in a silicon-based double quantum dot
journal, January 2012

  • Maune, B. M.; Borselli, M. G.; Huang, B.
  • Nature, Vol. 481, Issue 7381
  • DOI: 10.1038/nature10707

Coherent Single Electron Spin Control in a Slanting Zeeman Field
journal, January 2006


Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots
journal, September 2005


Disorder-induced valley-orbit hybrid states in Si quantum dots
journal, July 2013


Universal quantum computing with spin and valley states
journal, August 2012


Electric field effect on electron spin splitting in Si Ge Si quantum wells
journal, April 2008


A CMOS silicon spin qubit
journal, November 2016

  • Maurand, R.; Jehl, X.; Kotekar-Patil, D.
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms13575

A valley–spin qubit in a carbon nanotube
journal, July 2013

  • Laird, E. A.; Pei, F.; Kouwenhoven, L. P.
  • Nature Nanotechnology, Vol. 8, Issue 8
  • DOI: 10.1038/nnano.2013.140

Hybrid Spin and Valley Quantum Computing with Singlet-Triplet Qubits
journal, October 2014


Spin splitting in symmetrical SiGe quantum wells
journal, March 2004


Two-axis control of a singlet-triplet qubit with an integrated micromagnet
journal, August 2014

  • Wu, X.; Ward, D. R.; Prance, J. R.
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 33
  • DOI: 10.1073/pnas.1412230111

Electrically driven spin qubit based on valley mixing
journal, February 2017


Spin-orbit coupling and operation of multivalley spin qubits
journal, November 2015


Driven coherent oscillations of a single electron spin in a quantum dot
journal, August 2006

  • Koppens, F. H. L.; Buizert, C.; Tielrooij, K. J.
  • Nature, Vol. 442, Issue 7104
  • DOI: 10.1038/nature05065

Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot
journal, August 2014


Valley polarization assisted spin polarization in two dimensions
journal, June 2015

  • Renard, V. T.; Piot, B. A.; Waintal, X.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8230