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Quantum confinement effects in Pb nanocrystals grown on InAs

Tianzhen Zhang, Sergio Vlaic, Stéphane Pons, Alexandre Assouline, Alexandre Zimmers, Dimitri Roditchev, Hervé Aubin, Guy Allan, Christophe Delerue, Christophe David, Guillemin Rodary, and Jean-Christophe Girard
Phys. Rev. B 97, 214514 – Published 19 June 2018
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Abstract

In the recent work of Vlaic et al. [Nat. Commun. 8, 14549 (2017)], it has been shown that Pb nanocrystals grown on the electron accumulation layer at the (110) surface of InAs are in the regime of Coulomb blockade. This enabled a scanning tunneling spectroscopy study of the superconducting parity effect across the Anderson limit. The nature of the tunnel barrier between the nanocrystals and the substrate has been attributed to a quantum constriction of the electronic wave function at the interface due to the large Fermi wavelength of the electron accumulation layer in InAs. In this paper, we detail and review the arguments leading to this conclusion. Furthermore, we show that, thanks to this highly clean tunnel barrier, this system is remarkably suited for the study of discrete electronic levels induced by quantum confinement effects in the Pb nanocrystals. We identified three distinct regimes of quantum confinement. For the largest nanocrystals, quantum confinement effects appear through the formation of quantum well states regularly organized in energy and in space. For the smallest nanocrystals, only atomiclike electronic levels separated by a large energy scale are observed. Finally, in the intermediate size regime, discrete electronic levels associated to electronic wave functions with a random spatial structure are observed, as expected from random matrix theory.

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  • Received 16 April 2018
  • Revised 2 June 2018

DOI:https://doi.org/10.1103/PhysRevB.97.214514

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tianzhen Zhang, Sergio Vlaic, Stéphane Pons, Alexandre Assouline, Alexandre Zimmers, Dimitri Roditchev, and Hervé Aubin*

  • LPEM, ESPCI Paris, PSL Research University, CNRS, Sorbonne Université, 75005 Paris, France

Guy Allan and Christophe Delerue

  • Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520 - IEMN, F-59000 Lille, France

Christophe David, Guillemin Rodary, and Jean-Christophe Girard

  • Centre de Nanosciences et de Nanotechnologies, CNRS, Univ. Paris-Sud, Universités Paris-Saclay, C2N Marcoussis, 91460 Marcoussis, France

  • *herve.aubin@espci.fr

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Issue

Vol. 97, Iss. 21 — 1 June 2018

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