Surface States in Holographic Weyl Semimetals

We study the surface states of a strongly coupled Weyl semimetal within holography. By explicit numerical computation of an inhomogeneous holographic Weyl semimetal, we observe the appearance of an electric current restricted to the surface in the presence of an electric chemical potential. The integrated current is universal in the sense that it only depends on the topology of the phases showing that the bulk-boundary correspondence holds even at strong coupling. The implications of this result are subtle and may shed some light on anomalous transport at weak coupling.

Figure 1

Horizon values of scalar and axial gauge field (dashed, solid) along the sample for temperatures $\pi \overline{T}≔\pi T/M=100,1/16$ (red, blue). The black dotted line corresponds to the profile of $a(x)/M$.

Figure 2

Current profile along the $x$ direction for different interface widths $l=0.1$, 0.5, 1, 4 (blue, green, yellow, red) and low temperature $\pi \overline{T}=1/16$.

Figure 3

Integrated current as a function of ${\overline{a}}_R$ for ${\overline{a}}_L<{\overline{a}}_c$ (blue) and ${\overline{a}}_c<{\overline{a}}_L\in \{4,10\}$ (green, red). Solid lines correspond to low temperature $\pi \overline{T}=1/16$ and dashed lines to high temperature $\pi \overline{T}=1$.

Figure 4

Integrated current as a function of ${\overline{a}}_R$ and ${\overline{a}}_L$ at low temperature $\pi \overline{T}=1/16$. Contour lines shown in black.