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We study the conductance $g$ of an electron interferometer created in a twodimensional electron gas between a nanostructured contact and the depletionregion induced by the charged tip of a scanning gate microscope. Usingnon-interacting models, we study the beating pattern of interference fringesexhibited by the images giving $g$ as a function of the tip position when aparallel magnetic field is applied. The analytical solution of a simplifiedmodel allows us to distinguish between two cases: (i) If the field is appliedeverywhere, the beating of Fabry-P\'erot oscillations of opposite spins givesrise to interference rings which can be observed at low temperatures when thecontact is open between spin-split transmission resonances. (ii) If the fieldacts only upon the contact, the interference rings cannot be observed at lowtemperatures, but only at temperatures of the order of the Zeeman energy. For acontact made of two sites in series, a model often used for describing aninversion-symmetric double-dot setup, a pseudo-spin degeneracy is broken by theinter-dot coupling and a similar beating effect can be observed withoutmagnetic field at temperatures of the order of the interdot coupling.Eventually, numerical studies of a quantum point contact with quantizedconductance plateaus confirm that a parallel magnetic field applied everywhereor only upon the contact gives rises to similar beating effects betweenspin-split channel openings.

physical review. b, condensed matter and materials physics

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