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A clean ballistic quantum point contact in strontium titanate

Nature Electronics volume 6, pages 417–424 (2023)Cite this article

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Abstract

The perovskite oxide strontium titanate (SrTiO3) combines electrostatic tunability, superconductivity and spin–orbit coupling, and is of potential use in the development of quantum devices. However, exploring quantum effects in SrTiO3 nanostructures is challenging because of the presence of disorder. Here we report high-mobility, gate-tunable devices in SrTiO3 that have ballistic constrictions and clean normal-state conductance quantization. Our devices are based on SrTiO3 two-dimensional electron gas channels that have a thin hafnium oxide barrier layer between the channel and an ionic liquid gate. Conductance plateaus show twofold degeneracy that persists for magnetic fields of at least 5 T. This is above what is expected from the g factors extracted at high fields and could be a signature of electron pairing extending outside the superconducting regime.

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Fig. 1: Clean and nanopatternable 2DEG in SrTiO3.
Fig. 2: Data for d.c. bias spectroscopy of the QPC.
Fig. 3: Sub-band evolution in a magnetic field.
Fig. 4: Understanding constriction conductance.

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Data availability

The data that support the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.5590921.

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Acknowledgements

This work greatly benefited from discussions with P. Sriram, C. Hsueh, M. Andersen, J. Finney, J. Williams, J. Yue, B. Jalan, J. Ruhman, K. Moler, J. Sau and E. Mansfield. Experimental work (fabrication and measurement) by E.M. was primarily supported the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515, and by the Gordon and Betty Moore Foundation through grant GBMF9460. Early experimental development by E.M. was supported by the Air Force Office of Scientific Research through grant no. FA9550-16-1-0126. E.M. was also supported by the Nano- and Quantum Science and Engineering Postdoctoral Fellowship at Stanford University and by internal Stanford University funds. Measurement contribution by I.T.R. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515, and by the ARCS foundation. Engagement by M.A.K and D.G.-G. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. Measurement infrastructure was funded in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF3429 and grant GBMF9460. Part of this work was performed at the Stanford Nano Shared Facilities (SNSF)/Stanford Nanofabrication Facility (SNF), supported by the National Science Foundation under award ECCS-1542152. Work at the University of Strathclyde was supported by the EPSRC Programme Grant DesOEQ (EP/P009565/1).

Author information

Authors and Affiliations

  1. Department of Physics, Stanford University, Stanford, CA, USA

    Evgeny Mikheev, Marc A. Kastner & David Goldhaber-Gordon

  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Evgeny Mikheev, Ilan T. Rosen, Marc A. Kastner & David Goldhaber-Gordon

  3. Department of Physics, University of Cincinnati, Cincinnati, OH, USA

    Evgeny Mikheev

  4. Department of Applied Physics, Stanford University, Stanford, CA, USA

    Ilan T. Rosen

  5. Department of Physics and SUPA, University of Strathclyde, Glasgow, UK

    Johannes Kombe

  6. Institut de Physique Nucléaire, Atomique et de Spectroscopie, CESAM, University of Liège, Liège, Belgium

    François Damanet

  7. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Marc A. Kastner

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Contributions

E.M. and D.G.-G. designed the experiment. E.M. fabricated the devices. E.M. and I.T.R. performed the measurements. E.M. carried out the data analysis. J.K. and F.D. performed the theoretical simulations. All authors discussed the results and wrote the manuscript.

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Correspondence to Evgeny Mikheev or David Goldhaber-Gordon.

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Extended data

Extended Data Fig. 1 Quantum oscillations in the 2DEG.

(a) Temperature dependence of Shubnikov-de Haas oscillations in the 2DEG sheet resistance RXX. Same data are shown as background-subtracted resistance (δRXX) and its second derivative with B (d2RXX/dB2). Markers indicate indexed maxima and minima. (b) Landau level index RLL plotted against peak positions in 1/B. (c) Spacing between individual oscillations, converted to local frequency and implied carrier density. Solid line in (b, c) is a constant-frequency fit for B > 7 T. Dotted line in (c) is half of fitted value. (d) Temperature dependence of oscillation amplitude at B = 7.9 and 8.9 T, dashed lines are fits to Lifshitz-Kosevich model with m* = 3.

Extended Data Fig. 2 Absence of long range superconducting order.

Connected symbols show superconducting Tc for the same device with Hall density (NH) tuned by ionic liquid (IL) gate voltage. Lateral shading for SrTiO3/HfOx+IL data represents the NH region explored by VGIL modulation with frozen ionic liquid. SrTiO3+IL data are from26, SrTiO3/hBN+IL data are from14, the blue dashed line is the typical location of the superconducting dome in SrTiO3/LaAlO3, drawn consistent with62,63. The solid black line is a guide to the eye for NH = 0.

Extended Data Fig. 3 Subband packets and Pascal sequence.

Parametric plot of transconductance against conductance at B = 0. Markers are a line cut from data shown in Fig. 3c at zero field. The dips in transconductance follow the Pascal sequence G/(2e2/h) = 0, 1, 3, 6, 10, 15, 21, … (blue vertical lines). Shaded regions indicate the extent of subband packets with same ny + nz that are quasi-degenerate, within broadening. Black line is the model of transconductance generated by Eq. (2) with broadening by ℏωx = 0.11 meV, see supplementary sections S2B,C for details.

Supplementary information

Supplementary Information

Supplementary Sections 1–4, Figs. 1–35 and references.

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Mikheev, E., Rosen, I.T., Kombe, J. et al. A clean ballistic quantum point contact in strontium titanate. Nat Electron 6, 417–424 (2023). https://doi.org/10.1038/s41928-023-00981-5

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