Gate control of positive and negative carriers in graphene is used to guide current in a manner analogous to the guiding of light by an optical fibre.

Gate-controlled guiding of electrons in graphene.

By analogy of optical waveguides, we investigate the guided modes in graphene waveguides, which is made of symmetric quantum well. The unique properties of the graphene waveguide are discussed based on the two different dispersion relations, which correspond to classical motion and Klein tunneling, respectively. It is shown that the third-order mode is absent in the classical motion, while the fundamental mode is absent in the Klein tunneling case. We hope these phenomena can lead to the potential applications in graphene-based quantum devices.

Guided modes in graphene waveguides

The analogies between optical and electronic Goos–Hanchen effects are established based on electron wave optics in semiconductor or graphene-based nanostructures. In this paper, we give a brief overview of the progress achieved so far in the field of electronic Goos–Hanchen shifts, and show the relevant optical analogies. In particular, we present several theoretical results on the giant positive and negative Goos–Hanchen shifts in various semiconductor or graphene-based nanostructures, their controllability, and potential applications in electronic devices, e.g. spin (or valley) beam splitters.

https://iopscience.iop.org/article/10.1088/2040-8978/15/3/033001/pdf

Electronic analogy of the Goos–Hänchen effect: a review*

Novel displacement in transmission through a two-dimensional semiconductor barrier

We theoretically investigate Goos-Hanchen (GH) displacement by modelling the spin transport in an archetypal device structure-a magnetically confined GaAs/Al x Ga1-x As nanostructure modulated by spin-orbit coupling (SOC). Both Rashba and Dresselhaus SOCs are taken into account. The degree of spin-polarized GH displacement can be tuned by Rashba or Dresselhaus SOC, i.e. interfacial confining electric field or strain engineering. Based on such a semiconductor nanostructure, a controllable spatial spin splitter can be proposed for spintronics applications.

Calculations of spin-polarized Goos-Hänchen displacement in magnetically confined GaAs/Al x Ga1-x As nanostructure modulated by spin-orbit couplings.

Semiconductor slab electron waveguides with and without spatially varying effective mass are analyzed using the single-band effective-mass equation. Starting with ballistic electron incidence on a potential energy/effective mass interface, expressions for the phase shift, the lateral shift, and the time delay upon total internal reflection are found. It is shown that heterostructure wells, homostructure voltage-induced wells, and heterostructure barriers can act as waveguides for ballistic electrons, and that the waveguiding is described by a single dispersion relation. The guided mode wave functions, dispersion curves, cutoffs, group velocity. effective mass, density of states, and ballistic guided current density are determined. >

D.W. Wilson

Papers

Electron waveguiding characteristics and ballistic current capacity of semiconductor quantum slabs