Anomalous conductance scaling in strained Weyl semimetals

Magnetotransport provides key experimental signatures in Weyl semimetals. The longitudinal magnetoresistance is linked to the chiral anomaly and the transversal magnetoresistance to the dominant charge relaxation mechanism. Axial magnetic fields that act with opposite sign on opposite chiralities facilitate new transport experiments that probe the low-energy Weyl nodes. As recently realized, these axial fields can be achieved by straining samples or adding inhomogeneities to them. Here, we identify a robust signature of axial magnetic fields: an anomalous scaling of the conductance in the diffusive ultraquantum regime. In particular, we demonstrate that the longitudinal conductivity in the ultraquantum regime of a disordered Weyl semimetal subjected to an axial magnetic field increases with both the field strength and sample width due to a spatial separation of charge carriers. We contrast axial magnetic with real magnetic fields to clearly distinguish the different behavior of the conductance. Our results rely on numerical tight-binding simulations and are supported by analytical arguments. We argue that the spatial separation of charge carriers can be used for directed currents in microstructured electronic devices.

Figure 1

Fermi surface and dispersion of a Weyl semimetal, Eq. (2), subjected to a magnetic field $\mathbf{B}$, panels (a) and (b), and to an axial magnetic field ${\mathbf{B}}_5$, panels (c) and (d). The color denotes the real-space localization $\langle x\rangle$ of the states; cf. inset panel (c). We choose open boundary conditions with $L/a=100$ sites in the $x$ direction and a (pseudo-)magnetic length of ${\ell }_B={\ell }_5=7.07a$ with lattice constant $a$. (a) Fermi surface in presence of $\mathbf{B}=B\widehat{z}$. (b) Corresponding dispersion at $k_y=0.19/a$ [dashed lines in panels (a) and (c)]. The dashed lines in panels (b) and (d) show the Fermi energy ${\varepsilon }_F=0$ as a guide for the eyes. (c) Fermi surface in presence of bulk ${\mathbf{B}}_5=B_5\widehat{z}$ that results in pseudo-Landau levels with opposite position-momentum locking. (d) Corresponding dispersion at $k_y=0.19/a$.

Figure 2

Conductance of clean samples in the presence of (axial) magnetic fields. (a) Numerically obtained conductance (circles) as a function of the field strength $B$ (${\mathbf{B}}_5=0$) for transport along $\widehat{z}\parallel \mathbf{B}$. The conductance is independent of $L_{\parallel }$ and grows linearly with $B$ (linear fit indicated by solid lines). (b) Similarly, the conductance grows linearly with $B_5$ ($\mathbf{B}=0$) up to $a^2/{\ell }_5^2\lesssim 0.12$. (c) The slope of $\partial G/\partial B_{\left(5\right)}$ increases linearly with $L_{\perp }^2$, such that $G\propto B{L}_{\perp }^2$ ($G\propto B_5{L}_{\perp }^2$). The ratio of the slopes in panel (c) is 1.29.

Figure 3

Numerically obtained inverse conductance (a) in presence of $\mathbf{B}$ and (b) in presence of ${\mathbf{B}}_5$ as a function of $L_{\parallel }$, the system size in transport direction. The colors denote different values of the (pseudo-)magnetic length ${\ell }_B$ (${\ell }_5$). The slope from panels (a) and (b) is the inverse of the dimensionless conductivity $g$, shown in panels (c) and (d) as a function of the (axial) magnetic field strength for different disorder strengths $W/v$. While $g$ clearly increases with $B_5$, it stays almost constant in presence of $B$ and disorder $W/v\gtrsim 2.5$. The inset in panel (c) shows the slope $\partial g/\partial L_{\perp }$ for different disorder strengths and $B$ (dark gray) and $B_5$ (light gray). All results are averaged over twisted boundary conditions and 100 disorder configurations; the chemical potential in the leads is ${\mu }_{\mathrm{lead}}=1.5v$, and the transversal width $L_{\perp }=21a$.

Figure 4

Numerically obtained inverse conductance (a) in the presence of $\mathbf{B}$ and (b) in the presence of ${\mathbf{B}}_5$ as a function of $L_{\parallel }$. The colors denote different values of $L_{\perp }$. The slope from panels (a) and (b) is the inverse of the dimensionless conductivity $g$, shown in panels (c) and (d) as a function of $L_{\perp }$ for different disorder strengths $W/v$. While $g$ increases linearly with $L_{\perp }$ in the presence of axial fields, it stays, apart from finite-size effects, constant in presence of magnetic fields $B$, as evident from the inset in panel (c) that shows the slope $\partial g/\partial L_{\perp }$ for $B$ (dark gray) and $B_5$ (light gray). (Pseudo-)magnetic length ${\ell }_B=2.65a$ (${\ell }_5=2.65a$); other parameters as in Fig. 3.