Excess equilibrium noise in a topological SNS junction between chiral Majorana liquids

We consider a Josephson contact mediated by 1D chiral modes on a surface of a 3D topological insulator with superimposed superconducting and magnetic layers. The system represents an interferometer in which 1D chiral Majorana modes on the boundaries of superconducting electrodes are linked by ballistic chiral Dirac channels. This model may be realized also in recently fabricated heterostructures based on quantum anomalous Hall insulators. We investigate the noise of the Josephson current as a function of the dc phase bias and the Aharonov-Bohm flux. Starting from the scattering formalism, a Majorana representation of the Keldysh generating action for cumulants of the transmitted charge is found. At temperatures higher than the Thouless energy E_Th, we obtain the usual Johnson-Nyquist noise, 4 G₀k_BT , characteristic for a single-channel wire with G₀≡e²/(2 π ℏ ) . At lower temperatures, the behavior is much richer. In particular, the equilibrium noise is strongly enhanced to a temperature-independent value ∼G₀E_Th if the Aharonov-Bohm and superconducting phases are both close to 2 π n , which are points of emergent degeneracy in the ground state of the junction. The equilibrium noise is related to the Josephson junction's impedance via the fluctuation-dissipation theorem. In a striking contrast to usual Josephson junctions (tunnel junctions between two s -wave superconductors), the real part of the impedance does not vanish, reflecting the gapless character of Majorana modes in the leads.