Quantum transport in Dirac materials: Signatures of tilted and anisotropic Dirac and Weyl cones

We calculate conductance and noise for quantum transport at the nodal point for arbitrarily tilted and anisotropic Dirac or Weyl cones. Tilted and anisotropic dispersions are generic in the absence of certain discrete symmetries, such as particle-hole and lattice point group symmetries. Whereas anisotropy affects the conductance $g$, but leaves the Fano factor $F$ (the ratio of shot noise power and current) unchanged, a tilt affects both $g$ and $F$. Since $F$ is a universal number in many other situations, this finding is remarkable. We apply our general considerations to specific lattice models of strained graphene and a pyrochlore Weyl semimetal.

Figure 1

A tilted Dirac cone in two dimensions. The momentum coordinates are labeled $k_x$ and $k_y$; the third dimension represents energy. Transparent planes indicate zero-energy plane (violet) and tilt $\mathbf{a}=(-0.5,0)$ (green plane), respectively.

Figure 2

Dimensionless conductance $g$ and Fano factor $F$ for a tilted two-dimensional Dirac cone, as a function of the angle $\phi$ between transport and tilt direction. The tilt strength $a$ is given in the legend.

Figure 3

Same as in Fig. 2, but for a three-dimensional Weyl cone.

Figure 4

Dimensionless conductance $g$ of a strained graphene sheet as a function of the strain $\epsilon$ for different orientations $\phi$ (the angle between transport direction and $\vec{s}$) and summed over both Dirac cones and spin. The inset shows a hexagon of the graphene lattice for $\epsilon =0.2$.

Figure 5

Dimensionless conductance $g$ (solid line) and Fano factor $F$ (dashed line) for a pyrochlore slab as a function of the in-plane next-nearest-neighbor hopping amplitude $t_2$ (left panel). Transport direction is parallel to the crystal axis $\vec{s}$ (as shown in the upper right panel). Hopping parameters are indicated in the lower right panel.