Equivalence of Effective Medium and Random Resistor Network models for disorder-induced unsaturating linear magnetoresistance

Abstract

A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological Random Resistor Network model constructs a grid of four-terminal resistors, each with a varying random resistance. The Effective Medium Theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the Random Resistor Network is actually equivalent to the Effective Medium Theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e. the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile.

arXiv comment6 pages, 5 figures

References in corpus (19)

• Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd${}_3$As${}_2$
• Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP
• Non-saturating magnetoresistance in heavily disordered semiconductors
• Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals
• Classical magnetotransport of inhomogeneous conductors
• Transport in chemically doped graphene in the presence of adsorbed molecules
• Charge Transport and Inhomogeneity near the Charge Neutrality Point in Graphene
• Large linear magnetoresistance in the Dirac semimetal TlBiSSe
• Axial anomaly and longitudinal magnetoresistance of a generic three dimensional metal
• Non-saturating magnetoresistance of inhomogeneous conductors: comparison of experiment and simulation
• Linear magnetoresistance in metals: guiding center diffusion in a smooth random potential
• Model for a Macroscopically Disordered Conductor with an Exactly Linear High-Field Magnetoresistance
• Quantum transport and observation of Dyakonov-Perel spin-orbit scattering in monolayer MoS${}_2$
• Disorder induced magnetoresistance in a two dimensional electron system
• Magnetoresistance of compensated semimetals in confined geometries
• Large linear magnetoresistance in a new Dirac material BaMnBi2
• Transport and magnetotransport in 3D Weyl Semimetals
• Model for the magnetoresistance and Hall coefficient of inhomogeneous graphene
• Large linear magnetoresistance in a transition-metal stannide $\beta$-RhSn${}_4$

Cited by in corpus (14)

• Magnetotransport in a model of a disordered strange metal
• Room-temperature colossal magnetoresistance in terraced single-layer graphene
• Magnetoresistance scaling, disorder, `hot spots' and the origin of $T$-linear resistivity in BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$
• Signatures of long-range-correlated disorder in the magnetotransport of ultrathin topological insulators
• Signatures of dephasing by mirror-symmetry breaking in weak-antilocalization magnetoresistance across the topological transition in Pb${}_{1-x}$Sn${}_x$Se
• Single-parameter scaling in the magnetoresistance of optimally doped La${}_{2-x}$Sr${}_x$CuO${}_4$
• On the temperature scaling behaviour of the linear magnetoresistance observed in high-temperature superconductors
• Absence of strong localization at low conductivity in the topological surface state of low disorder Sb2Te3
• Impurity and dispersion effects on the linear magnetoresistance in the quantum limit
• Inhomogeneous superconductivity and quasilinear magnetoresistance at amorphous LaTiO3/SrTiO3 interfaces
• Electronic Transport and Fermi Surface Topology of Zintl Phase Compound SrZn2Ge2
• Giant and Linear Magnetoresistance in Liquid Metals at Ambient Temperature
• Theory of Linear Magnetoresistance in a Strange Metal
• $H$-linear magnetoresistance in NbSe${}_2$ due to impeded cyclotron motion