Fundamental properties, localization threshold, and the Tomonaga--Luttinger behavior of electrons in nanochains

TL;DR

This paper investigates the electronic properties of nanochains, revealing their transition from metallic to insulating states, analyzing Tomonaga-Luttinger behavior, and deriving a universal electron dispersion relation through a combined EDABI approach.

Contribution

It introduces a comprehensive method combining Exact Diagonalization and Ab Initio calculations to analyze nanochain properties, including electron correlations and phase transitions.

Findings

Observation of Tomonaga-Luttinger scaling in electron momentum distribution

Identification of mixed metallic and insulating features at half-filling

Derivation of a universal renormalized electron dispersion relation

Abstract

We provide a fairly complete discussion of electronic properties of nanochains modelling the simplest quantum nanowires, within the recently proposed approach combining Exact Diagonalization in the Fock space with an Ab Initio calculations (EDABI method). In particular, the microscopic parameters of the second-quantized Hamiltonian are determined and the evolution of the system properties is traced in a systematic manner as a function of the interatomic distance (the lattice parameter, R). Both the many-particle ground state and the dynamical correlation functions are discussed within a single scheme. The principal physical results are: (i) the evolution of the electron momentum distribution and its analysis in terms of the Tomonaga-Luttinger scaling, (ii) the appearance of mixed metallic and insulating features partial localization) for the half-filled band case, (iii) the appearence of a universal renormalized dispersion relation of electron energy, which incorporates both the band-structure and the Hubbard-splitting features in the presence of electron interactions, and (iv) the transformation from a highly-conducting nanometalic state to the charge-ordered nanoinsulator in the quarter-filled case. The analysis is performed using an adjustable Gaussian 1s-like basis set composing the Wannier functions, as well as includes the long-range Coulomb interaction.