Effective action and electromagnetic response of topological superconductors and Majorana-mass Weyl fermions

Abstract

Motivated by an apparent paradox in [X-L. Qi, E. Witten, S-C. Zhang, Phys. Rev. B 87 134519 (2013)] we use the method of gauged Wess-Zumino-Witten functionals to construct an effective action for a Weyl fermion with a Majorana mass that arises from coupling to a charged condensate.We obtain expressions for the current induced by an external gauge field and observe that the topological part of the current is only one-third of that that might have been expected from the gauge anomaly. The anomaly is not changed by the induced mass gap however. The topological current is supplemented by a conventional supercurrent that provides the remaining two-thirds of the anomaly once the equation of motion for the Goldstone mode is satisfied. We apply our formula for the current to resolve the apparent paradox, and also to the chiral magnetic effect (CME) where it predicts a reduction of the CME current to one third of its value for a free Weyl gas in thermal equilibrium. We attribute this reduction to a partial cancelation of the CME by a chiral vortical effect (CVE) current arising from the persistent rotation of the fluid induced by the external magnetic field.

Superconductivity Provides Access to the Chiral Magnetic Effect of an Unpaired Weyl Cone

“…The predicted size of the induced current is the same as that of the nonequilibrium CME, up to a charge renormalization of order unity, and since that dynamical effect has been observed [9][10][11][12][13], the static counterpart should be observable as well-perhaps even more easily because decoherence and relaxation play no role. In closing, we note that the chiral anomaly in a crystal was originally proposed [6] as a condensed matter realization of an effect from relativistic quantum mechanics and has since been an inspiration in particle physics and cosmology [57][58][59][60]. The doorway to single-cone physics that we have opened here might well play a similar role.…”

Topological Phase Transitions in Multicomponent Superconductors

“…In 3D, the half quantum vortex line binds a propagating chiral Majorana mode [64,67]. Furthermore, we find that the dispersion = (k z ) of such a chiral Majorana mode exhibit both slow and fast components.…”

“…Since ∆ s and ∆ p differs by a phase π/2, this s + ip state spontaneously breaks time-reversal symmetry [44][45][46]. Such state in three dimensions has unconventional thermal response described by a axion topological field theory [48,60,[64][65][66][67], hence can be called an "axion superconductor".…”

Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics

“…[102] to the 4-group. It is also possible to apply our framework to a low-energy effective theory of topological superconductors in (3 + 1) dimensions, since they can be described by the massive photon and axions with topological couplings between them [44][45][46]. metry generators by using conserved currents j 3 ,..., j 0 as follows, Here, N is the normalization factor so that 1 = 1, and the symbol "D[φ, a, b, c]" stands for the integral measure DφDaDbDc.…”