Scanning gate microscopy probing of anisotropic electron flow in a two dimensional electron gas at the (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interface: A theoretical investigation

TL;DR

This theoretical study models the anisotropic electron flow at the (110) LaAlO3/SrTiO3 interface, revealing how Fermi surface anisotropy influences electron trajectories and interference patterns in scanning gate microscopy.

Contribution

Develops an efficient tight-binding model to analyze anisotropic dispersion and electron flow at the (110) LaAlO3/SrTiO3 interface, highlighting orientation-dependent effects.

Findings

Fermi surface anisotropy causes direction-dependent electron flux.

Electron trajectories are skewed when gates are misaligned with lattice vectors.

Different orbitals are separated in wide quantum wells due to Fermi velocity distribution.

Abstract

We theoretically investigate the anisotropic dispersion features of a two dimensional electron gas at the (110) oriented $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interfaces, as revealed by scanning gate microscopy of electronic flow from a quantum point contact. The dispersion relation of the (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interface is characterized by a highly non-circular Fermi surface. Here, we develop an efficient tight-binding model for the electron gas at the interface. We show that the anisotropy of the Fermi surface causes both the direction of the electron flux from the quantum point contact and the periodicity of the self-interference conductance fringes to depend strongly on the orientation of the constriction relative to the crystal lattice. We show that the radially non-uniform distribution of the Fermi velocity on the Fermi surface results in skewing of electron trajectories when the quantum point contact gates are not aligned with the in-plane primitive vectors. We show that this effect results in the separation of electrons belonging to different orbitals for wide (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ quantum wells.