Thermal Signature of Majorana Fermion in a Josephson Junction

Experimental attempts for the detection of Majorana bound state(MBS) are primarily based on two theoretical predictions: (1) 2e²/h resonant conductance peak at zero bias and (2) the 4π Josephson Effect, both of which rely heavily on the subgap physics of topological superconductors. In a complementary approach, we look for non-trivial signatures of MBS in heat transport across a Josephson Junction (JJ). Specifically, we consider a thermally biased JJ hosting a pair of MBS in a helical edge state of a2D topological insulator. We show that the presence of Majorana endstates in a three-terminal JJ setup results in two sets of testable relations⁽¹⁾:

(i) The ratios between the various multiterminal thermal conductances are independent of the Josephson phase bias.

(ii) The ratios of ‘ratios of the phase derivative of multiterminal thermal conductance and the corresponding Josephson current’ are also independent of the Josephson phase bias.

These results owe their existence to the fact that the hybridization of an odd number of Majoranas always leaves a zero mode in the subgap spectrum of the junction. We establish that these results are unique to the presence of Majorana fermions and cannot be mimicked in a Josephson junction setup composed of a 1D topological superconductor hosting “Andreev type end states”⁽²⁾.

We have recently extended our work to the thermoelectric conductance of a JJ. We have shown that a finite length JJ can induce a finite thermal-bias-induced charge current across the junction without breaking explicit particle-hole symmetry, even in the presence of disorder averaging⁽³⁾.

Ref: (1) Phys. Rev. B 103, 144502

(2) Phys. Rev. B 100, 220502(R)

(3) Phys. Rev. B 106, 075421