A capacitance spectroscopy-based platform for realizing gate-defined electronic lattices

Hensgens, T.; Mukhopadhyay, U.; Barthelemy, P.; Vermeulen, R. F.  L.; Schouten, R. N.; Fallahi, S.; Gardner, G. C.; Reichl, C.; Wegscheider, W.; Manfra, M. J.; Vandersypen, L. M.  K.

doi:10.1063/1.5046796

Title: A capacitance spectroscopy-based platform for realizing gate-defined electronic lattices

Journal Article · Thu Sep 27 00:00:00 EDT 2018 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.5046796· OSTI ID:1527168

Hensgens, T. ^[1]; Mukhopadhyay, U. ^[1]; Barthelemy, P. ^[1]; Vermeulen, R. F. L. ^[1]; Schouten, R. N. ^[1]; Fallahi, S. ^[2]; Gardner, G. C. ^[2]; Reichl, C. ^[3]; Wegscheider, W. ^[4]; Manfra, M. J. ^[2];

^[1]

Delft Univ. of Technology (Netherlands)
Purdue Univ., West Lafayette, IN (United States)
Swiss Federal Inst. of Technology (ETH), Zurich (Switzerland)
Solid State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland

Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a wide host of quantum phases. Capacitance spectroscopy demonstrates a technique that allows one to directly probe the density of states of such two-dimensional electron systems. Here, we present a measurement and fabrication scheme that builds on capacitance spectroscopy and allows for the independent control of density and periodic potential strength imposed on a two-dimensional electron gas. We characterize disorder levels and (in)homogeneity and develop and optimize different gating strategies at length scales where interactions are expected to be strong. A continuation of these ideas might see to fruition the emulation of interaction-driven Mott transitions or Hofstadter butterfly physics

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Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Swiss National Science Foundation (SNSF); Netherlands Organization of Scientific Research (NWO)

Grant/Contract Number:: SC0006671

OSTI ID:: 1527168

Alternate ID(s):: OSTI ID: 1474208

Journal Information:: Journal of Applied Physics, Vol. 124, Issue 12; ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (35)

Energy gaps of the two-dimensional electron gas explored with equilibrium tunneling spectroscopy Ashoori, R. C.; Lebens, J. A.; Bigelow, N. P. Physical Review B, Vol. 48, Issue 7 https://doi.org/10.1103/PhysRevB.48.4616	journal	August 1993
Collective Coulomb blockade in an array of quantum dots: A Mott-Hubbard approach Stafford, C. A.; Das Sarma, S. Physical Review Letters, Vol. 72, Issue 22 https://doi.org/10.1103/PhysRevLett.72.3590	journal	May 1994
Gate-Defined Quantum Dots in Intrinsic Silicon Angus, Susan J.; Ferguson, Andrew J.; Dzurak, Andrew S. Nano Letters, Vol. 7, Issue 7 https://doi.org/10.1021/nl070949k	journal	July 2007
Automated capacitance bridge Cavicchi, R. E.; Silsbee, R. H. Review of Scientific Instruments, Vol. 59, Issue 1 https://doi.org/10.1063/1.1140002	journal	January 1988
Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices Yu, G. L.; Gorbachev, R. V.; Tu, J. S. Nature Physics, Vol. 10, Issue 7 https://doi.org/10.1038/nphys2979	journal	June 2014
Evidence of Hofstadter's Fractal Energy Spectrum in the Quantized Hall Conductance Albrecht, C.; Smet, J. H.; von Klitzing, K. Physical Review Letters, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevLett.86.147	journal	January 2001
Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices Dean, C. R.; Wang, L.; Maher, P. Nature, Vol. 497, Issue 7451 https://doi.org/10.1038/nature12186	journal	May 2013
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan Nature, Vol. 496, Issue 7444 https://doi.org/10.1038/nature12066	journal	April 2013
Cloning of Dirac fermions in graphene superlattices Ponomarenko, L. A.; Gorbachev, R. V.; Yu, G. L. Nature, Vol. 497, Issue 7451 https://doi.org/10.1038/nature12187	journal	May 2013
Sharp tunnelling resonance from the vibrations of an electronic Wigner crystal Jang, Joonho; Hunt, Benjamin M.; Pfeiffer, Loren N. Nature Physics, Vol. 13, Issue 4 https://doi.org/10.1038/nphys3979	journal	December 2016
Metal-insulator transitions Imada, Masatoshi; Fujimori, Atsushi; Tokura, Yoshinori Reviews of Modern Physics, Vol. 70, Issue 4, p. 1039-1263 https://doi.org/10.1103/RevModPhys.70.1039	journal	October 1998
Two-Dimensional Mott-Hubbard Electrons in an Artificial Honeycomb Lattice Singha, A.; Gibertini, M.; Karmakar, B. Science, Vol. 332, Issue 6034, p. 1176-1179 https://doi.org/10.1126/science.1204333	journal	June 2011
Theory of magnetotransport in two-dimensional electron systems subjected to weak two-dimensional superlattice potentials Pfannkuche, Daniela; Gerhardts, Rolf R. Physical Review B, Vol. 46, Issue 19 https://doi.org/10.1103/PhysRevB.46.12606	journal	November 1992
Fractal Energy Spectrum of a Polariton Gas in a Fibonacci Quasiperiodic Potential Tanese, D.; Gurevich, E.; Baboux, F. Physical Review Letters, Vol. 112, Issue 14 https://doi.org/10.1103/PhysRevLett.112.146404	journal	April 2014
Quantum Dot Systems: a versatile platform for quantum simulations Barthelemy, Pierre; Vandersypen, Lieven M. K. Annalen der Physik, Vol. 525, Issue 10-11 https://doi.org/10.1002/andp.201300124	journal	September 2013
Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure Hunt, B.; Sanchez-Yamagishi, J. D.; Young, A. F. Science, Vol. 340, Issue 6139 https://doi.org/10.1126/science.1237240	journal	May 2013
Magnetotransport through an antidot lattice in GaAs- ${Al}_{x}$ ${Ga}_{1 - x}$ As heterostructures Ensslin, K.; Petroff, P. M. Physical Review B, Vol. 41, Issue 17 https://doi.org/10.1103/PhysRevB.41.12307	journal	June 1990
Detection of a Landau Band-Coupling-Induced Rearrangement of the Hofstadter Butterfly Geisler, M. C.; Smet, J. H.; Umansky, V. Physical Review Letters, Vol. 92, Issue 25 https://doi.org/10.1103/PhysRevLett.92.256801	journal	June 2004
Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays Byrnes, Tim; Kim, Na Young; Kusudo, Kenichiro Physical Review B, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevB.78.075320	journal	August 2008
Goals and opportunities in quantum simulation Cirac, J. Ignacio; Zoller, Peter Nature Physics, Vol. 8, Issue 4 https://doi.org/10.1038/nphys2275	journal	April 2012
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields Hofstadter, Douglas R. Physical Review B, Vol. 14, Issue 6 https://doi.org/10.1103/PhysRevB.14.2239	journal	September 1976
Theory of Oscillatory g Factor in an MOS Inversion Layer under Strong Magnetic Fields Ando, Tsuneya; Uemura, Yasutada Journal of the Physical Society of Japan, Vol. 37, Issue 4 https://doi.org/10.1143/JPSJ.37.1044	journal	October 1974
High-resolution spectroscopy of two-dimensional electron systems Dial, O. E.; Ashoori, R. C.; Pfeiffer, L. N. Nature, Vol. 448, Issue 7150 https://doi.org/10.1038/nature05982	journal	July 2007
Evidence of Hofstadter's fractal energy spectrum in the quantized Hall conductance Albrecht, C.; Smet, J. H.; von Klitzing, K. Physica E: Low-dimensional Systems and Nanostructures, Vol. 20, Issue 1-2 https://doi.org/10.1016/j.physe.2003.09.031	journal	December 2003
Metal-insulator transitions Paesler, Michael Journal of Non-Crystalline Solids, Vol. 130, Issue 1 https://doi.org/10.1016/0022-3093(91)90162-y	journal	June 1991
Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy Kim, Sungmin; Schwenk, Johannes; Walkup, Daniel Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-22886-7	journal	May 2021
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan SPIE NanoScience + Engineering, SPIE Proceedings https://doi.org/10.1117/12.2023842	conference	September 2013
Evidence of Hofstadter's Fractal Energy Spectrum in the Quantized Hall Conductance Albrecht, C.; Smet, J.; Klitzing, K. Universität Regensburg https://doi.org/10.5283/epub.7911	text	January 2001
High Resolution Spectroscopy of Two-Dimensional Electron Systems Dial, O. E.; Ashoori, R. C.; Pfeiffer, L. N. arXiv https://doi.org/10.48550/arxiv.0707.1686	text	January 2007
Quantum simulation of Fermi-Hubbard models in semiconductor quantum dot arrays Byrnes, Tim; Kim, Na Young; Kusudo, Kenichiro arXiv https://doi.org/10.48550/arxiv.0711.2841	text	January 2007
Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice Singha, A.; Gibertini, M.; Karmakar, B. arXiv https://doi.org/10.48550/arxiv.1106.3215	text	January 2011
Photonic Floquet Topological Insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan arXiv https://doi.org/10.48550/arxiv.1212.3146	text	January 2012
Cloning of Dirac fermions in graphene superlattices Ponomarenko, L. A.; Gorbachev, R. V.; Yu, G. L. arXiv https://doi.org/10.48550/arxiv.1212.5012	text	January 2012
Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices Yu, G. L.; Gorbachev, R. V.; Tu, J. S. arXiv https://doi.org/10.48550/arxiv.1404.3856	text	January 2014
Sharp Tunneling Resonance from the Vibrations of an Electronic Wigner Crystal Jang, Joonho; Hunt, Benjamin; Pfeiffer, Loren N. arXiv https://doi.org/10.48550/arxiv.1604.06220	text	January 2016

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