Tunneling between parallel one-dimensional Wigner crystals

Abstract

Vertically aligned arrays are a frequent outcome in the nanowires synthesis by self-assembly techniques or in its subsequent processing. When these nanowires are close enough, quantum electron tunneling is expected between them. Then, because extended or localized electronic states can be established in the wires by tuning its electron density, the tunneling configuration between adjacent wires could be conveniently adjusted by an external gate. In this contribution, by considering the collective nature of electrons using a Yukawa-like effective potential, we explore the electron interaction between closely spaced, parallel nanowires while varying the electron density and geometrical parameters. We find that, at a low-density Wigner crystal regime, the tunneling can take place between adjacent localized states along and transversal to the wires axis, which in turn allows to create two- and three-dimensional electronic distributions with valuable potential applications.

Asymmetric Wigner molecules in nanowire Y-junctions

“…5 c–d the ground and first excited states, respectively, of a Y-J with a very small 3 nm are presented. Electronic tunneling can be observed for this small separation between the lower branches of the Y, quite similar to the recently reported tunneling between parallel NWs 49 . Due to the symmetric charge distributions along the z axis of the Y-J, the overlap of electron wavefunctions only happens between adjacent electronic distributions (along the x -axis), being stronger where the distribution is denser.…”

“…In this section, we follow the numerical solution of the Schrödinger equation for two electrons interacting via a Yukawa-like effective potential 46 , which was originally used to study individual semiconductor NWs. We also consider the modifications required to incorporate an external electric field 48 and arrays of multiple parallel NWs 49 . In the following, we outline the key steps to understand the adaptation we made to the reported models to tailor the Y-J geometry: (1) the derivation of the effective potential, as in reference 49 , for arrays of (the bottom part of the Y) and (the top part of the Y) of parallel NWs, (2) the incorporation of a longitudinal EEF 48 and, (3) the way we manage the coupling of the three NWs.…”

“…The use of this kind of Yukawa-like potentials to address many-body problems has been extensively used in other branches of physics, such as soft matter and nuclear physics 44 . Applied to electron distributions in nanostructures, this approach has been able to correctly describe experimental results related to the Wigner molecule formation in micron-long NWs with electrons/ 45 , 46 , as well as to describe the effect of an external electric field (EEF) applied along the NW axis 47 , 48 and the tunneling between parallel NWs 49 . In this contribution, we adapt such model to tailor the Y geometry via three interconnected NWs.…”

Solution to the Thomson Problem for Clifford Tori with an Application to Wigner Crystals

“…Wigner crystals have also been observed in one dimension. − The properties of Wigner crystals have been studied extensively in condensed-matter physics and have important implications for understanding the behavior of electrons in low-dimensional systems. Closely related to Wigner crystals are Wigner molecules, which are confined few-electron systems in which the electrons form a stable bound state due to their mutual repulsion. ,− Experimental observations of Wigner molecules have been reported in various physical systems, including carbon nanotubes, nanowires, , and quantum dots . Since the Thomson problem is a classical problem, we will focus here on classical Wigner crystals, i.e., we are interested in the relative positions of the localized electrons.…”

“…Closely related to Wigner crystals are Wigner molecules, which are confined few-electron systems in which the electrons form a stable bound state due to their mutual repulsion. 20,39−48 Experimental observations of Wigner molecules have been reported in various physical systems, including carbon nanotubes, 49 nanowires, 50,51 and quantum dots. 52 Since the Thomson problem is a classical problem, we will focus here on classical Wigner crystals, i.e., we are interested in the relative positions of the localized electrons.…”