Theories of Planckian dissipation in strongly correlated systems

The apparently universal value, 2π k_BT/h, of the transport scattering rate observed experimentally in a wide variety of non-Fermi liquid metals with T-linear resistivity has been a longstanding mystery in condensed matter physics; this phenomenon is called 'Planckian dissipation'. We present a lattice model of fermions with N flavors and random interactions that describes a non-Fermi liquid metal at low temperatures T → 0, in the solvable limit of large N. We begin with quasiparticles around a Fermi surface with effective mass m*, and then include random interactions that lead to fermion spectral functions with frequency scaling with 2π k_BT/h. The resistivity ρ obeys the Drude formula ρ = m*/(ne²τ_tr), where n is the density of fermions, and the transport scattering rate is 1/τ_tr = f 2π k_BT/h; we find f to be of order unity and essentially independent of the strength and form of the interactions, hence 'universal'. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes nonresonant in the bare quasiparticle energies only renormalize m*, while resonant processes are shown to produce Planckian dissipation. We point out some predictions of this theory that are, in principle, testable in photoemission experiments. We further present some other large N models that can also give rise to Planckian dissipation under certain conditions.

Reference: A. A. Patel and S. Sachdev, Phys. Rev. Lett. 123, 066601 (2019)