Transport and magnetotransport in three-dimensional Weyl semimetals

Navneeth Ramakrishnan, Mirco Milletari, and Shaffique Adam

Phys. Rev. B 92, 245120 – Published 14 December 2015

Abstract

We theoretically investigate the transport and magnetotransport properties of three-dimensional Weyl semimetals. Using the random phase approximation–Boltzmann transport scattering theory for electrons scattering off randomly distributed charged impurities, together with an effective medium theory to average over the resulting spatially inhomogeneous carrier density, we smoothly connect our results for the minimum conductivity near the Weyl point with known results for the conductivity at high carrier density. In the presence of a nonquantizing magnetic field, we predict that for both high and low carrier densities, Weyl semimetals show a transition from quadratic magnetoresistance (MR) at low magnetic fields to linear MR at high magnetic fields, and that the magnitude of the $MR ≳ 10$ for realistic parameters. Our results are in quantitative agreement with recent unexpected experimental observations on the mixed-chalcogenide compound TlBiSSe.

Received 18 February 2015

DOI:https://doi.org/10.1103/PhysRevB.92.245120

Authors & Affiliations

Navneeth Ramakrishnan¹, Mirco Milletari^1,*, and Shaffique Adam^1,2,†

¹Department of Physics and Center for Advanced 2D Materials, National University of Singapore, 117551, Singapore
²Yale-NUS College, 16 College Avenue West, 138527, Singapore

^*phymirc@nus.edu.sg
^†shaffique.adam@yale-nus.edu.sg

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Vol. 92, Iss. 24 — 15 December 2015

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Images

Figure 1
Conductivity as a function of carrier density. RPA-Drude theory (Ref. [22], blue curve), self-consistent Thomas-Fermi (Ref. [28], green curve), and the EMT approach (assuming uncorrelated impurities in both regimes) discussed in the main text (red curve). The EMT predicts a minimum conductivity close to the Weyl point and reproduces the Drude one $σ \sim n^{4 / 3} / n_{imp}$ far away from the Weyl point. In order to compare with the results of Ref. [22], we follow their parameters for this figure and use $α = 1.2, g = 2, n_{imp} = 10^{24} m^{- 3}$ , and ${\tilde{Π}}_{V} = 0$ . Inset: Close-up of the Weyl point.
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Figure 2
Comparison of $n^{*} / n_{imp}$ obtained using RPA and Thomas-Fermi approximations. The error introduced by using the Thomas-Fermi screening to calculate the effective minimum carrier density, $n^{*}$ , increases with an increase in the effective fine structure constant $α$ . We note that for materials such as ${Cd}_{3} {As}_{2}$ , this is a relatively small error but this is not the case for TlBiSSe. Here we use cutoff $δ = 10$ .
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Figure 3
Comparison with the experimental data of Ref. [26]. The experimentally determined mobility of TlBiSSe, $μ_{\exp}$ , decreases as a function of the measured carrier density $n_{\exp}$ , whereas the Drude theory with constant $n_{imp}$ (blue curve) would predict the opposite trend. In the main text, we propose two possible scenarios compatible with this behavior. The red curve assumes that the experiments are in the inhomogeneous regime with $n_{\exp} ≪ n_{rms}$ with correlated charged impurities. Alternatively, the green curve assumes that the experiments are in the homogeneous regime $n_{\exp} ≫ n_{rms}$ , with the charged impurities also responsible for doping. Here $n_{\exp} = n_{0} \approx 4 n_{imp}, α = 0.68$ , and $δ = 10$ .
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Figure 4
Magnetoresistance in TlBiSSe. Disordered 3D Weyl fermions can have large MR $> 10$ for realistic experimental parameters. The figure shows that both in the homogeneous and in the inhomogeneous regime, the magnetoresistance is quadratic at low fields (see inset) and linear at high fields in agreement with experimental observations. Notice that the MR in the inhomogeneous regime is much larger than that of the homogeneous regime, suggesting that increasing disorder is an easy way to enhance the MR.
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Figure 5
Disorder-averaged self-energy. Amputated diagrams defining the self-energy at the Gaussian level. The brackets represent disorder averaging, the “x” accounts for the impurity concentration, the dot for the impurity potential insertion, and the solid line is the clean propagator.
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