Fermi-Arc Metals

We predict a novel metallic state of matter that emerges in a Weyl-semimetal superstructure with spatially varying Weyl-node positions. In the new state, the Weyl nodes are stretched into extended, anisotropic Fermi surfaces, which can be understood as being built from Fermi arclike states. This “Fermi-arc metal” exhibits the chiral anomaly of the parental Weyl semimetal. However, unlike in the parental Weyl semimetal, in the Fermi-arc metal the “ultraquantum state,” in which the anomalous chiral Landau level is the only state at the Fermi energy, is already reached for a finite energy window at zero magnetic field. The dominance of the ultraquantum state implies a universal low-field ballistic magnetoconductance and the absence of quantum oscillations, making the Fermi surface “invisible” to de Haas–van Alphen and Shubnikov–de Haas effects, although it signifies its presence in other response properties.

Figure 1

(a) Fermi-arc metal from a stack of WSMs with Weyl-node positions (dotted red or blue lines for Weyl-node of chirality $+$ or $-$) rotating discretely in form of a double helix, shown in a mixed real ($z$) and momentum ($k_x$, $k_y$) space. Interfaces host Fermi arcs (red and blue lines) that connect Weyl nodes of the same chirality at opposite sides of the interface. (b) An applied magnetic field ${\mathit{B}}_{\mathrm{ext}}$ along the stacking direction leading to particle flow along Fermi arcs on the interface and via anomalous chiral Landau levels of Weyl Fermions between interfaces. The propagation direction (parallel or antiparallel to ${\mathit{B}}_{\mathrm{ext}}$) depends on the chirality of the Weyl node. Higher Landau levels are finite-size-gapped due to reflections at interfaces. (c) Reduced bulk Brillouin zone with cylindrical chiral Fermi surfaces (red or blue for chirality $+$ or $-$).

Figure 2

Dispersion from numerical diagonalization of a lattice model, which at low energy corresponds to the continuum model with nodes at $\pm {\mathit{K}}_{\perp }(z)=\pm [\cos (Qz)\widehat{y}-\sin (Qz)\widehat{x}]$, $Q=2\pi /31$ [42] (a) as a function of $k_x$ at $k_y=0=k_z$ (left) and as a function of $k_z$ at $k_y=0$, $k_x=1$. Color encodes the expectation value of the chirality. The inset shows a close-up at the crossing at zero energy, where chirality conservation is violated for energies exponentially small in $K_{\perp }/Q$. The dispersion is rotation symmetric around $k_z$. (b) Same as (a) but with an applied magnetic field ${\mathit{B}}_{\mathrm{ext}}=\widehat{x}2\pi /(10\times 31)$ (left) and ${\mathit{B}}_{\mathrm{ext}}=\widehat{z}2\pi /30$ (right). (Normalization of the applied field is chosen such, that $|{\mathit{B}}_{\mathrm{ext}}|$ is the inverse square of the magnetic length in units of the lattice constant.) Note that the right panel shows a single Landau level per chirality, backfolded into the reduced Brillouin zone ($k_z\in [-Q/2,Q/2]$).