Jian Wang group and collaborators report equally spaced quantum well states in van der Waals epitaxy-grown nanoislands

With increasing the well width, various properties can be periodically modulated by the quantum well states (QWSs), such as density of states, film thermodynamic stability, tunneling current, electron–phonon coupling, superconducting transition temperature, work function, and surface diffusion, etc. The QWS of parabolic-dispersion nonrelativistic electrons is the text-book content in quantum mechanics. The corresponding studies in experiments have inspired the invention of quantum cascade laser. By contrast, the quantum confinement of relativistic fermions with linear dispersion, e.g. Dirac/Weyl particles, would be of more fundamental interest with exotic physics and can in principle yield the quantum cascade laser in a single quantum well. However, the QWSs of relativistic fermions are rarely investigated systematically in systems beyond graphene. Along [111] direction, Pb shows isolated, approximately linear dispersions, thus providing a possible system for studying the [111] confinement of relativistic electrons. Nevertheless, the quantitative proof of the precisely equal interval of QWSs is still lacking as the evidence for confined linearly dispersive relativistic electrons.

Recently, Prof. Jian Wang at Peking University, in collaboration with Prof. Zhenyu Zhang at University of Science and Technology of China, Prof. Yu Jia at Zhengzhou University and others, reports strong UHV STM evidence for the equally spaced, strikingly sharp, and densely distributed QWSs in Pb(111) nano-islands, van-der-Waals epitaxially grown on graphitized 6H-SiC(0001). Fourier analysis of the normalized QWS spectrum reveals the sharp low-frequency peak, highlighting the well-defined periodicity of QWSs. For the nano-islands showing two discrete thicknesses, two sets of QWS peaks with different periods are consistently observed. The observations can be explained as the quantized energies of confined linearly dispersive [111] electrons, which essentially ‘simulate’ the out-of-plane relativistic quasiparticles. The equally spaced QWSs with an origin of confined relativistic electrons are supported by phenomenological simulations and Fabry–Pérot fittings based on the relativistic fermions. First-principles calculations further reveal that the spin–orbit coupling in Pb strengthens the relativistic nature (linear dispersion) of electrons near Fermi energy. Our finding of QWSs for relativistic particles in condensed matter systems not only is of fundamental value in elementary quantum mechanics, but also uncovers the unique equally spaced quantum states in intrinsic electronic systems beyond Landau levels. The work may inspire future studies on confined relativistic quasiparticles in quantum well structures with linear dispersions along specific directions and potential applications in structurally simpler quantum cascade laser.

The paper was published in Nano Letters on Oct. 22, 2021 (Nano Letters 2021, DOI: 10.1021/acs.nanolett.1c03423). Prof. Jian Wang at Peking University is the corresponding author, and Chaofei Liu (PhD graduate) at Peking University is the first author. This work was financially supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, Beijing Natural Science Foundation, and Strategic Priority Research Program of Chinese Academy of Sciences.

Paper link：https://pubs.acs.org/doi/10.1021/acs.nanolett.1c03423

Figures: Equally spaced quantum well states (a,b) in Pb nano-islands van der Waals epitaxy-grown on graphitized SiC (c). (d) Spin−orbit coupling-strengthened relativistic nature of linearly dispersive quantum well states. The Pb nanoisland is around 61 monolayer thick.