## Weyl semimetals

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Weyl semimetals are peculiar 3D materials defined by "accidental" intersections between bulk bands and "Fermi arc" surface states that resemble broken segments of a 2D Fermi surface. Near the bulk intersections or Weyl nodes, electrons mimic relativistic Weyl fermions -- hence the name Weyl semimetal -- and carry robust topological protection, thus rendering the semimetal a gapless topological phase of matter. We are broadly interested in the physics of Weyl semimetals and related phases and explore their signatures in transport, interplay with superconductivity and potential for device applications.

## Surface superconductivity but metallic bulk

According to Landau’s mean-field theory, interacting particles can evade spontaneous ordering far more effectively in lower dimensions. This is why the surface of an ice cube is often watery; the lower dimensionality of the surface impedes the crystallization of H2O molecules, leaving them liquid. We proposed a strange scenario where the opposite seems to occur: the 2D surface of 3D Weyl semimetals enters an ordered phase – a superconductor – while the 3D bulk remains a non-superconducting metal. This picture is consistent with surface-only superconductivity recently seen in t-PtBi2. Learn even more.

Illustration of the parametric regime, shaded gray, where the surface is superconducting while the bulk is in the normal phase. Temperatures above the bulk Tc but below the surface Tc will show surface-only superconductivity.

Left: Rotating a chiral fluid drives an axial current. Right: Devices in which carriers travel in curved paths can harness vortical effects.

## Vortical effects in chiral band structures

We introduce a new type of response theory – a “vortical response theory” – that describes rotating electrons in a crystal. Applying it to chiral band structures reveals a novel phenomenon, the “gyrotropic vortical effect”, besides yielding the chiral vortical effect that is well-established for Weyl fermions in particle physics but has proven controversial in condensed matter. Our approach helps resolve these controversies and helps us to conceive circuit building blocks that harness the vortical effects. Learn even more

## SUSY and non-local Majorana fermions in superconductor vortices

Superconductor vortices host discrete energy levels that carry critical information about the parent metal. Weyl semimetals have two distinct types of metallic states in their spectrum -- Weyl fermions in the bulk and Fermi arcs on the surface -- that are intricately coupled and cannot be captured by standard Hamiltonians. We ask, "what is the vortex spectrum of a superconductor that descends from a Weyl semimetal?'' We find that the spectrum is determined by semiclassical quantization of cyclotron-like closed orbits consisting of Fermi arcs on opposite surfaces connected by one-way bulk conduits. Miraculously, merely tilting the vortices can transmute them between bosonic, fermionic and supersymmetric, with the last class hosting a pair of non-local Majorana fermions. Thus, we propose a tabletop and tunable realization of a long sought-after system that displays supersymmetry, namely, an equivalence between bosons and fermions. At tilts that we dub "magic angles", the vortex spectrum becomes independent of the slab thickness. In many models and materials, non-local Majorana fermions and supersymmetry exist precisely at these tilts. Learn even more

Closed semiclassical orbits govern the vortex spectrum and endow it with characteristic dependences on the Berry phases and penetration depths of the Fermi arcs, bulk Weyl node locations, vortex orientation and sample thickness.

When the surface Fermi arcs (red curves) plus the projections (black solid lines) of the geodesics between bulk Weyl nodes in the same kz-plane (black dashed lines) form M closed loops, the vortex is gapped and has (lacks) end Majorana modes if M is odd (even). If the Fermi-arc + geodesic-projections form open contours, the vortex is gapless.

## New route to Majorana fermions

The search for Majorana fermions - particles that are their own anti-particles that were first proposed but never found in high-energy physics - has driven fierce activity in condensed matter, where they occur as zero energy states in topological defects such as vortex cores of type-II superconductors. Among 3D materials, criteria for finding Majorana fermions at the ends of superconducting vortices in time-reversal symmetric insulators and metals are well-known. We derive analogous criteria for the third and last generic type of 3D band structure, namely, time-reversal symmetric Weyl semimetals. The criteria we find depend only on the bulk and surface band structure of the semimetal, which are outcomes of routine photoemission experiments and first-principles simulations, and allow tuning the Majorana fermions in and out of existence by merely tilting an external magnetic field. Learn even more

## Surface Luttinger arcs

Besides the well-known Fermi arcs, we show that the surface of a Weyl semimetal is also endowed with a feature normally associated with strongly interacting systems -- Luttinger arcs, defined as zeros of the electron Green's function. We find that the Luttinger and Fermi arcs form closed loops when the Weyl nodes are undoped. Remarkably, unlike Luttinger contours in strongly interacting systems, the precise shape of the Luttinger arcs here can be determined experimentally by simply peeling off a surface layer. Learn even more

Fermi and Luttinger arcs in the first Brillouin zone for different surface terminations in Co3Sn2S2. For a given termination, the two types of arcs form a closed loop since the Brillouin zone is periodic.

## Anomalous surface conductivity

We discover an anomalous contribution to the surface dc conductivity of Weyl semimetals in addition to a normal Drude contribution from the Fermi arc. The anomalous part is independent of the surface scattering time, but involves an effective lifetime due to the non-perturbative coupling of the surface to the bulk. Remarkably, the temperature dependence of the surface conductivity at low temperatures is dominated by the anomalous response which can be probed experimentally. Learn even more

Figure shows that the anomalous conductivity is non-zero when the scattering time (tau) vanishes, while the normal, Drude conductivity shown inset is linear in tau.

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