Friedel oscillations due to Fermi arcs in Weyl semimetals

Weyl semimetals harbor unusual surface states known as Fermi arcs, which are essentially disjoint segments of a two-dimensional Fermi surface. We describe a prescription for obtaining Fermi arcs of arbitrary shape and connectivity by stacking alternate two-dimensional electron and hole Fermi surfaces and adding suitable interlayer coupling. Using this prescription, we compute the local density of states—a quantity directly relevant to scanning tunneling microscopy—on a Weyl semimetal surface in the presence of a point scatterer and present results for a particular model that is expected to apply to pyrochlore iridate Weyl semimetals. For thin samples, Fermi arcs on opposite surfaces conspire to allow nested backscattering, resulting in strong Friedel oscillations on the surface. These oscillations die out as the sample thickness is increased and Fermi arcs from the opposite surface retreat and weak oscillations, due to scattering between the top surface Fermi arcs alone, survive. The surface spectral function, accessible to photoemission experiments, is also computed. In the thermodynamic limit, this calculation can be done analytically and separate contributions from the Fermi arcs and the bulk states can be seen.

Figure 1

Top: Layering prescription for obtaining FAs of arbitrary shape. Dotted (dashed) ellipses represent electron (hole) FSs, and solid red segments are the residual FAs on adding interlayer hoppings $t_{\mathbf{k}}$ and ${\Delta }_{\mathbf{k}}$. The horizontal black dashed line on the topmost layer separates regions with ${\Delta }_{\mathbf{k}}>t_{\mathbf{k}}$ and ${\Delta }_{\mathbf{k}}<t_{\mathbf{k}}$. An even (odd) number of total layers gives identical (nonidentical) FAs on the two surfaces, as shown on the left (right). Bottom: 1D systems at fixed $\mathbf{k}\in C$ under the influence of $\Delta$ and $t$ in the extreme cases where the smaller hopping vanishes, for even (left) and odd (right) $L$. Filled (empty) circles denote a state on an electron (a hole) Fermi surface in the limit of decoupled layers. The ellipses enclose the states that get mutually gapped out by the hoppings.

Figure 2

(a) FAs in the surface Brillouin zone on the 111 surface of iridate WSMs. Solid (dashed) lines denote FAs on the near (far) surface. Filled (empty) circles denote projections of Weyl nodes of positive (negative) chirality in all the figures above. (b) and (c) Surface LDOS in arbitrary units due to the six FAs near the $L$ point in the presence of a point scatterer on the surface (brown cross) for a thin sample (b) and a thick sample (c). Insets show the numerically computed surface spectral function at $E=0$ for the clean system, with darker colors representing larger values. The computation is done for the model, described in the text, which generates the six FAs near the $L$ point but not the remaining eighteen FAs near the Brillouin zone edges.