Origin of dissipative Fermi arc transport in Weyl semimetals

By making use of a low-energy effective model of Weyl semimetals, we show that the Fermi arc transport is dissipative. The origin of the dissipation is the scattering of the surface Fermi arc states into the bulk of the semimetal. It is noticeable that the corresponding scattering rate is nonzero and can be estimated even in a perturbative theory, although in general the reliable calculations of transport properties necessitate a nonperturbative approach. Nondecoupling of the surface and bulk sectors in the low-energy theory of Weyl semimetals invalidates the usual argument of a nondissipative transport due to one-dimensional arc states. This property of Weyl semimetals is in drastic contrast to that of topological insulators, where the decoupling is protected by a gap in the bulk. Within the framework of the linear response theory, we obtain an approximate result for the conductivity due to the Fermi arc states and analyze its dependence on chemical potential, temperature, and other parameters of the model.

Figure 1

The bulk (blue) and Fermi arc (red) states in the model of Weyl semimetal at $y>0$ given by Eq. (1) with $k_y=0$ (left panel). The green plane represents the Fermi energy $E_F/\left(\gamma m\right)=0.9$. The corresponding Fermi surface is plotted in the right panel.

Figure 2

The upper component of the surface part of scattered wave ${\psi }_s^{\left(1\right)}$, defined by Eq. (41), as a function of $x/a$ (left panel), $y/a$ (middle panel), and $z/c$ (right panel). The numerical values of the model parameters are $u_0=0.1\text{eV}{\text{Å}}^3, \omega =0.5\text{eV}, \mathbf{q}=(0,0,0), {\mathbf{r}}_j=\left(\omega /v_F,0,0\right)$, and $a$ and $c$ are defined in Eq. (6). The wave function is shown for $\mathbf{r}=\left(x,5a,5c\right)$ in the left panel, $\mathbf{r}=\left(5a,y,5c\right)$ in the middle panel, and $\mathbf{r}=\left(5a,5a,z\right)$ in the right panel.

Figure 3

The upper component of the bulk part of scattered wave ${\psi }_b^{\left(1\right)}$, given by Eq. (43), as a function of $x/a$ (left panel), $y/a$ (middle panel), and $z/c$ (right panel). The numerical values of the model parameters are $u_0=0.1\text{eV}{\text{Å}}^3, \omega =0.5\text{eV}, \mathbf{q}=(\omega /v_F,0,0), {\mathbf{r}}_j=\left(0,0,0\right)$. The wave function is shown for $\mathbf{r}=\left(x,5a,5c\right)$ in the left panel, $\mathbf{r}=\left(5a,y,5c\right)$ in the middle panel, and $\mathbf{r}=\left(5a,5a,z\right)$ in the right panel.

Figure 4

The lower component of the bulk part of scattered wave ${\psi }_b^{\left(1\right)}$, given by Eq. (43), as a function of $x/a$ (left panel), $y/a$ (middle panel), and $z/c$ (right panel). The numerical values of the model parameters are $u_0=0.1\text{eV}{\text{Å}}^3, \omega =0.5\text{eV}, \mathbf{q}=(\omega /v_F,0,0), {\mathbf{r}}_j=\left(0,0,0\right)$. The wave function is shown for $\mathbf{r}=\left(x,5a,5c\right)$ in the left panel, $\mathbf{r}=\left(5a,y,5c\right)$ in the middle panel, and $\mathbf{r}=\left(5a,5a,z\right)$ in the right panel.

Figure 5

The real part of the upper component of the bulk part of scattered wave ${\psi }_b^{\left(1\right)}$, given by Eq. (43), as a function of $x/a$ (left panel) and as a function of $z/c$ (right panel) for large values of arguments. The numerical values of the model parameters are $u_0=0.1\text{eV}{\text{Å}}^3, \omega =0.5\text{eV}, \mathbf{q}=(\omega /v_F,0,0), {\mathbf{r}}_j=\left(0,0,0\right)$. For plotting the results, we used $\mathbf{r}=\left(x,5a,5c\right)$ in the left panel and $\mathbf{r}=\left(5a,5a,z\right)$ in the right panel.

Figure 6

The real part of the surface conductivity at $T=0$ as a function of distance from the surface $y$ (left panel), the parameter $m$ (middle panel), and the chemical potential $\mu$ (right panel). In the left and middle panels $\mu =0.05\text{eV}$, in the middle and right panels $y=0$. The other model parameters are $u_0=0.1\text{eV}\text{Å}{}^3$ and $n_{\mathrm{imp}}={10}^{-3}\AA {}^{-3}$.

Figure 7

The real part of the surface conductivity as a function of temperature $T$ at $\mu =0.05\text{eV}$ (left panel), $\mu =0.1\text{eV}$ (middle panel), as well as as a function of the chemical potential $\mu$ at several different temperatures (right panel). The other model parameters are $u_0=0.1\text{eV}{\text{Å}}^3$ and $n_{\mathrm{imp}}={10}^{-3}{\AA }^{-3}$.