Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance

TL;DR

This paper establishes a duality between extraordinary magnetoresistance in semiconductor-metal hybrids and a generalized geometric gravity theory, providing a new theoretical framework to understand and potentially optimize EMR effects.

Contribution

It introduces a novel duality linking EMR phenomena with generalized complex geometry and gravity, offering a new theoretical approach to analyze and enhance EMR.

Findings

Derived covariant field equations for EMR

Revealed emergence of diffusive pseudo currents

Proposed geometrical deformations to optimize EMR

Abstract

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties.