Controlled calculation of the thermal conductivity for a spinon Fermi surface coupled to a U(1)U(1) gauge field

Motivated by recent transport measurements on the candidate spin-liquid phase of the organic triangular lattice insulator EtMe3Sb[Pd(dmit)2]2, we perform a controlled calculation of the thermal conductivity at intermediate temperatures in a spin liquid system where a spinon Fermi surface is coupled to a U(1)U(1) gauge field. The present computation builds upon the double expansion approach developed by Mross et al. (2010) for small ϵ=zb−2ϵ=zb−2 (where zbzb is the dynamical critical exponent of the gauge field) and large number of fermionic species NN. Using the so-called memory matrix formalism that most crucially does not assume the existence of well-defined quasiparticles at low energies in the system, we calculate the temperature dependence of the thermal conductivity κκ of this model due to non-critical Umklapp scattering of the spinons for a finite NN and small ϵϵ. Then we discuss the physical implications of such theoretical result in connection with the experimental data available in the literature.