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It is known that the contribution of torsion to the equation for the chiral Weyl fermions can be equivalently considered in terms of the axial $U(1)$ gauge field. In this scenario the gravitational field transforms to the $U(1)$ gauge field. Here we show that in chiral superconductors the opposite scenario takes place: the electromagnetic $U(1)$ field serves as the spin connection for the Bogoliubov fermionic quasiparticles. As a result the electromagnetic field gives rise to the gravitational anomaly, which contains the extra factor $1/3$ in the corresponding Adler-Bell-Jackiw equation as compared with the conventional chiral anomaly. We also consider the gravitational anomaly produced in neutral Weyl superfluids by the analog of the gravitational instanton, the process of creation and annihilation of the 3D topological objects -- hopfions. The gravitational instanton leads to creation of the chiral charge.
Momentum transport is anomalous in chiral $p+ip$ superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent
Optical control of chirality in chiral superconductors bears potential for future topological quantum computing applications. When a chiral domain is written and erased by a laser spot, the Majorana modes around the domain can be manipulated on ultra
Majorana fermions exist on the boundaries of two-dimensional topological superconductors (TSCs) as charge-neutral quasi-particles. The neutrality makes the detection of such states challenging from both experimental and theoretical points of view. Cu
We propose the existence of an electric-field induced nonlinear magnetization in a weakly coupled granular superconductor due to time-parity violation. As the field increases the induced magnetization passes from para- to dia-magnetic behavior. We di
We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, assoc