Scanning Gate Microscopy of Quantum Contacts Under Parallel Magnetic Field: Beating Patterns Between Spin-Split Transmission Peaks or Channel Openings

TL;DR

This study investigates how parallel magnetic fields influence interference patterns in a two-dimensional electron gas, revealing beating effects between spin-split transmission peaks through analytical and numerical models.

Contribution

It provides a detailed analysis of beating patterns in conductance interference fringes caused by spin splitting under different magnetic field applications, using non-interacting models.

Findings

Beating patterns depend on whether the magnetic field is applied everywhere or only at the contact.

Interference rings are observable at low temperatures when the contact is open between spin-split resonances with a uniform field.

Similar beating effects occur in double-dot models without magnetic fields at temperatures related to inter-dot coupling.

Abstract

We study the conductance $g$ of an electron interferometer created in a two dimensional electron gas between a nanostructured contact and the depletion region induced by the charged tip of a scanning gate microscope. Using non-interacting models, we study the beating pattern of interference fringes exhibited by the images giving $g$ as a function of the tip position when a parallel magnetic field is applied. The analytical solution of a simplified model allows us to distinguish between two cases: (i) If the field is applied everywhere, the beating of Fabry-P\'erot oscillations of opposite spins gives rise to interference rings which can be observed at low temperatures when the contact is open between spin-split transmission resonances. (ii) If the field acts only upon the contact, the interference rings cannot be observed at low temperatures, but only at temperatures of the order of the Zeeman energy. For a contact made of two sites in series, a model often used for describing an inversion-symmetric double-dot setup, a pseudo-spin degeneracy is broken by the inter-dot coupling and a similar beating effect can be observed without magnetic field at temperatures of the order of the interdot coupling. Eventually, numerical studies of a quantum point contact with quantized conductance plateaus confirm that a parallel magnetic field applied everywhere or only upon the contact gives rises to similar beating effects between spin-split channel openings.