Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

Norman J M Horing

doi:10.1063/1.4986221

Abstract

This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x)-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x)-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

Highlights

Starting with the discovery of the exceptional electronic transport and detection properties of graphene, there has grown up an extremely broad and powerful research effort directed at understanding and developing the basic science, engineering and production as such Dirac-like materials, having a relativistic-type energy spectrum
It facilitates the analysis of the role of a quantum wire, modeled here by a one-dimensional δ(x)-potential profile, enabling the explicit determination of the wire Green’s function and its Landau quantized Dirac-like spectrum
This section is focused on Green’s function dynamics of a quantum wire modelled by a 1D Dirac delta function δ(x)-potential well profile superposed on carriers in a 2D group-VI dichalcogenide material subject to a normal quantizing magnetic field

Summary

INTRODUCTION

Starting with the discovery of the exceptional electronic transport and detection properties of graphene, there has grown up an extremely broad and powerful research effort directed at understanding and developing the basic science, engineering and production as such Dirac-like materials, having a relativistic-type energy spectrum. As an agent for probing the properties and inducing new physical features, the magnetic field has always had an important role Such studies of the effects of the magnetic field in nonrelativistic carrier propagation and collective modes date back to the 1960’s and 1970’s for three and two-dimensional quantum plasmas.[1,2] The relativistic Green’s function in a magnetic field was most elegantly first determined by Schwinger,[3] and interesting variants for particular Dirac-like materials have been advanced by Rusin and Zawadski,[4] as well as the author.[5] This paper is focused on yet another important representation for the Landau-quantized Green’s function for the group-VI dichalcogenides, in direct time representation, whose behavior is more transparent in the low field limit in comparison with that of the eigenfunction expansion. Integration and the dispersion relation are included in three appendices

LANDAU QUANTIZED GREEN’S FUNCTION

QUANTUM WIRE

SPECTRAL WEIGHT AND THERMODYNAMIC GREEN’S FUNCTION

SUMMARY