Quantum Linear Magnetoresistance: A Modern Perspective

TL;DR

This paper surveys the quantum-origin linear magnetoresistance (LMR) and clarifies how a unified quantum transport framework, via the Kubo-formalism, distinguishes quantum LMR from classical and semiclassical pictures. It explains the role of Landau quantization, impurity potentials, and the quantum limit in producing a linear field dependence, and discusses how band structure (linear vs parabolic) and scattering models (Born vs T-matrix) as well as dimensionality (2D vs 3D) govern the linear response in the quantum limit. It emphasizes that no single theory spans all regimes and highlights observable signatures like Onsager symmetry and the relation between transverse and longitudinal MR, as well as the need for rigorous experimental validation. Finally, it provides practical guidelines for experimental identification of quantum LMR, including sample quality, geometry, temperature and field range, and analysis such as $dR/dB$ plots and multi-parameter transport.

Abstract

Magnetoresistance is a powerful probe for characterizing the intrinsic physics embedded in materials. Among its various manifestations, linear magnetoresistance has a long history and continues attracting research interest. In contemporary studies, a clear understanding of the magnetoresistance character of quantum origin is more crucial than ever for the study of emerging materials. In this perspective, we examine the linear magnetoresistance of quantum mechanism, from its theoretical basis to experimental studies, and discuss open questions and promising future research directions in this field.

Figures (1)

• Figure 1: Sketches for the LMR of (a) classical, (b) semiclassical, and (c) quantum mechanisms. In (b) and (c), the green color denotes unoccupied states and the orange color denotes occupied states. In the classical theory, the Lorentz force governs the motion of charged particles. In semiclassical case, energy dispersion is considered, but the Landau levels are squeezing together. In the quantum theory, with a fully quantum mechanical description, the Landau levels are clearly resolved, and the quantum limit is considered. (d) and (e) are sketches of the experimental setups used to measure the transverse MR and longitudinal MR, respectively. (f) LMR observed in$\mathrm{Cd_3As_2}$Zhao_PRX_2015. The MR not only exhibits a linear behavior in the quantum limit regime but also has a linear background in the SdH oscillation regime. (g) Spectral density of the 3D electron gas under a z-directional magnetic field. The lightness (color gradient from red to orange to white) denotes the carrier occupation. Parameters used in the plot are: the effective mass of 0.1 times the free electron mass, magnetic field strength of 50 T, Fermi energy of 20 meV, and temperature of 300 K. (h) Plot of Fermi-Dirac distribution function at 300 K.