Chiral Meissner state in time-reversal invariant Weyl superconductors

Weyl semimetals have nodes in their electronic structure at which electrons attain a definite chirality. Due to the chiral anomaly, the nonconservation of charges with given chirality, the axion term appears in their effective electromagnetic action. We determine how this affects the properties of time-reversal invariant Weyl superconductors (SCs) in the London regime. For type II SCs the axion coupling generates magnetic $B$ fields transverse to vortices, which become unstable at a critical coupling so that a transition into type I SC ensues. In this regime an applied $B$ field not only decays inside the SC within the London penetration depth, but the axion coupling generates an additional perpendicular field. Consequently, when penetrating into the bulk the $B$ field starts to steadily rotate away from the applied field. At a critical coupling the screening of the magnetic field breaks down. The novel chiral superconducting state that emerges has a periodically divergent susceptibility that separates onsets of chiral Meissner regimes. The chiral anomaly thus leaves very crisp experimental signatures in structurally chiral Weyl SCs with an axion response.

Figure 1

Magnetic induction profiles for different values of the axion coupling $a$ [(a) and (b) for the field components $B_{\phi }$ and $B_z$, respectively]. Fields are plotted in units of $M^2{\mathrm{\Phi }}_0/\left(2\pi \right)$ against the radial coordinate $r$ in units of $M$. (c) and (d) correspond to a situation where $a$ is very close to the critical value $a_c=2M$ for which the vortex solution ceases to exist. We note that as $a$ approaches $a_c$ from below the field profiles start to become more oscillatory. The onset of these spatial oscillations is illustrated by the three-dimensional plots for $B_z$ in (e) and (f).

Figure 2

(a) and (b) Magnetic field components of a semi-infinite superconductor located at $x>0$ and in the presence of an applied magnetic field, ${\mathit{B}}_{\mathrm{ap}}=B_{\mathrm{ap}}\widehat{\mathit{y}}$. The chiral magnetic screening occurs for $a<a_c$ (a) and is absent for $a\ge a_c$ (b). (c)–(f) Magnetic field profiles in a finite TRI Weyl SC. At (c)–(e) we have $a<a_c$, corresponding to $a=0.4a_c, a=0.75a_c$, and $a=0.95a_c$, respectively. We can see once more the onset of spatial oscillations in the magnetic induction as $a$ increases. In (f) $a=1.1a_c$ leading to the case where the axion coupling completely dominates over Meissner screening.