Abstract
Using a microscopic theory for the magnetoconductivity at low magnetic fields we show how the Hall and longitudinal conductivity can be calculated in the low scattering rate limit. In the lowest order of the scattering rate, we recover the result of the semiclassical Boltzmann transport theory. At higher order, we get corrections containing the Berry curvature and the orbital magnetic moment. We use this formalism to study the linear longitudinal magnetoconductivity in tilted Weyl semimetals. We discuss how our result is related to the semiclassical Boltzmann approach and show the differences that arise compared to previous studies related to the orbital magnetic moment.
Highlights
Electric transport in a magnetic field is an extensively studied topic of great importance in solid-state physics with a long history
At finite low magnetic fields the magnetoconductivity can be discussed with the Boltzmann theory [2,7,8,9], and if the anomalous velocity is included, the magnetoconductivity was shown to have a contribution coming from the Berry curvature [10,11,12,13,14,15,16,17,18,19,20]
To show the validity of our formula, we study the magnetoconductivity of a tilted Weyl node and compare our results with those obtained using the semiclassical Boltzmann theory
Summary
Electric transport in a magnetic field is an extensively studied topic of great importance in solid-state physics with a long history. At finite low magnetic fields the magnetoconductivity can be discussed with the Boltzmann theory [2,7,8,9], and if the anomalous velocity is included, the magnetoconductivity was shown to have a contribution coming from the Berry curvature [10,11,12,13,14,15,16,17,18,19,20]. For small magnetic fields a microscopic theory for the Hall conductivity was developed by Fukuyama [36,37] In this theory the magnetoconductivity in the linear order of the magnetic field is given as a formula containing velocity operators and Green’s functions. This complete formalism is analogous to our problem, but a big difference is that in the case of orbital susceptibility the scattering rate can be ignored, while in the case of magnetoconductivity it is essential to have finite results
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