Transport properties of a spinon Fermi surface coupled to a U(1) gauge field

Abstract

With the organic compound $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}\text{\ensuremath{-}}{\mathrm{Cu}}_{2}{(\mathrm{C}\mathrm{N})}_{3}$ in mind, we consider a spin liquid system where a spinon Fermi surface is coupled to a U(1) gauge field. Using the nonequilibrium Green's function formalism, we derive the quantum Boltzmann equation for this system. In this system, however, one cannot a priori assume the existence of Landau quasiparticles. We show that even without this assumption, one can still derive a linearized equation for a generalized distribution function. We show that the divergence of the effective mass and of the finite temperature self-energy do not enter these transport coefficients and thus they are well defined. Moreover, using a variational method, we calculate the temperature dependence of the spin resistivity and thermal conductivity of this system.