Dephasing induced steady state refrigeration in the Fibonacci chain

Understanding quantum transport in low dimensional systems has become of obvious relevance for the design of mesoscopic thermoelectrics. Quasiperiodic disorder, incommensurate with the underlying periodicity of the lattice, induces fractality in the energy spectra and non-trivial transport properties even in one dimension, which can be exploited in the context of quantum heat engines. As an example, the Fibonacci model exhibits critical states and anomalous diffusion, with a continuously varying dynamical exponent. When dephasing is introduced, it always renders transport standard diffusive, however, the competition with quasiperiodicity gives rise to a maximum in the diffusion constant at finite dephasing. We study electric and heat currents in the Fibonacci model at finite temperature in the Landauer-Büttiker framework, with dephasing incorporated through the action of Büttiker probes. We observe a remarkably different sensitivity of the position of the maxima of thermal and electric conductivities to the thermodynamic parameters of the set-up. We show that by tuning the strength of the dephasing we can enhance the performance of the device in regimes where it acts as refrigerator.