Aspects of the topological Kondo effect - Temaismithi, J (2017)
We investigate theoretically the topological Kondo effect (TKE) and related non-Fermi-liquid (NFL) phenomena in correlated mesoscopic devices containing Majorana fermions. Using the numerical renormalisation group (NRG), we confirm and extend results obtained by conformal field theory (CFT) and we calculate numerically exact conductance curves for several different devices over large temperature ranges, which could be compared directly to future experiments. Our calculations uncover a wide range of physics in these mesoscopic devices and we derive several effective models to explain this behaviour. We first consider the prototypical model proposed by Béri and Cooper [B. Béri and N. R. Cooper. Phys. Rev. Lett., 109, 156803 (2012).] in which a non-local spin-1/2 is coupled to spin-1 conduction electrons. This model was proposed as the minimal model for the TKE, arising as the low-energy effective model of a superconducting grain connected to three leads containing Majorana fermions at the ends. We study the model in detail, confirming asymptotic CFT results and calculating the full conductance curves. We show that the NFL physics is robust to asymmetric Majorana–lead couplings, and uncover a duality between weak- and strong-coupling regimes using Abelian bosonisation. We also show how inter-Majorana couplings destabilise the NFL behaviour. We next consider the device beyond the effective spin-1/2 model, working instead with an Anderson-type model where charge fluctuations can be taken into account. We consider various possibilities for the energy levels on the superconducting grain and calculate and compare the behaviour in each case. We show that the NFL physics is robust to charge fluctuations, and is not restricted only to the regime of a non-degenerate ground state on the superconductor with large charging energy. We also derive various low-energy effective models for the different charging states. Finally, we investigate the device with a fourth lead attached. This gives rise to an effective two-channel Kondo model, but the device geometry means that the conductance is distinct from that studied previously. We also consider the full Anderson model, showing again that the conductance results are robust to charge fluctuations.