Zeno blocking of interplanar tunneling by intraplane inelastic scattering in layered superconductors: a generalized spin-boson analysis

Abstract

Following an earlier proposal that the observed temperature dependence of the normal-state c-axis resistivity of oxide superconductors can be understood as arising from the inhibition of electron transport along the c axis due to in-plane incoherent inelastic scatterings suffered by the tagged electron, we consider a specific form for the interaction Hamiltonian. In this, the tagged electron is coupled to bosonic baths at adjacent planes (the baths at any two planes being uncorrelated) and is coupled also to the intraplane momentum-flip degree of freedom via the bath degrees of freedom. Thus our model Hamiltonian incorporates the earlier proposed picture that each in-plane inelastic scattering event is like a measurement of which plane the electron is in, and this, as in the quantum Zeno effect, leads to the suppression of interplane tunneling. In the present scenario it is the baths which bring about a coupling between the intraplane and interplane degrees of freedom. For simplicity we confine ourselves to dynamics in two adjacent planes and allow for two states only, as far as momentum flips due to scattering are concerned. In the case when the intraplane dynamics is absent, our model reduces effectively to the usual spin-boson model. We solve for the reduced tunneling dynamics of the electron using a non-Markovian master equation approach. Our numerical results on the survival probability of the electron in the initial plane show that the intraplane momentum flips lead to further inhibition of the interplane tunneling over and above the inhibition effected by pure spin-boson dynamics.