Quantum confinement effects in Pb Nanocrystals grown on InAs

TL;DR

This paper reviews and demonstrates how quantum confinement effects manifest in Pb nanocrystals grown on InAs, revealing three regimes of electronic behavior due to size-dependent quantum effects, with implications for superconductivity studies.

Contribution

It provides a detailed analysis of quantum confinement regimes in Pb nanocrystals on InAs, highlighting their suitability for studying discrete electronic levels and quantum effects.

Findings

Identification of three quantum confinement regimes in Pb nanocrystals

Observation of quantum well states in large nanocrystals

Detection of atomic-like levels in smallest nanocrystals

Abstract

In the recent work of Ref.\cite{Vlaic2017-bs}, 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 the first 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 manuscript, 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 atomic-like 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.