Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance

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.

13 pages and 6 figures. Revised/edited for clarity and purpose. Several references added. Updated title based on suggestions and comments received. Version accepted for publication in Phys.Rev.B

References in corpus (7)

• Hydrodynamics of electrons in graphene
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography
• Probing topological superconductors with emergent gravity
• High Temperature Superconductivity and Effective Gravity
• Sign of viscous magnetoresistance in electron fluids

Cited by in corpus (2)

• Classical Kalb-Ramond field theory in curved spacetimes
• Geometrodynamics of a 2D Curved Surface due to a Constrained Quantum Particle via its Gravitational Dual: ${\mathcal{S}}^2$ Analytical Model Calculations