In-plane magnetotransport phenomena in tilted Weyl semimetals

The nontrivial Berry curvature and chiral anomaly result in plenty of interesting magnetotransport and magneto-thermoelectric transport phenomena in Weyl semimetals, two of which are the planar Hall effect and planar Nernst effect. Based on the semi-classical Boltzmann theory, we theoretically study the in-plane magnetotransport coefficients (including electric conductivity, thermoelectric conductivity and Nernst thermopower) for both type-I and type-II Weyl semimetals using a linearized low-energy Hamiltonian. We find that for tilt-coplanar setup where the electric field (or temperature gradient) is applied along the tilted direction of the Weyl nodes, the planar Hall conductivity (or planar Nernst thermopower) shows a magnetic field linear dependence. And these linear responses do no obey the reportedcosθsinθdependence on the angleθbetween the magnetic and electric field for planar Hall effect. For tilt-perpendicular setup where the applied field (Eor∇T) and magnetic field are perpendicular to the tilted direction, the planar Hall conductivity (or planar Nernst thermopower) mainly follows a magnetic field quadratic dependence, and it satisfies thecosθsinθcharacteristic. There are also anomalous Hall effect and anomalous Nernst effect in the plane perpendicular to the tilted direction of the two oppositely tilted Weyl nodes. These findings can be verified experimentally by changing the direction and magnitude of the in-plane magnetic field.