Theory of a Planckian metal

Abstract

We present a lattice model of fermions with $N$ flavors and random interactions which describes a Planckian metal at low temperatures, $T\to 0$, in the solvable limit of large $N$. We begin with quasiparticles around a Fermi surface with effective mass $m^{\ast }$, and then include random interactions which lead to fermion spectral functions with frequency scaling with $k_{B}T/\hslash$. The resistivity, $\rho$, obeys the Drude formula $\rho =m^{\ast }/(n{e}^2{\tau }_{\text{tr}})$, where $n$ is the density of fermions, and the transport scattering rate is $1/{\tau }_{\text{tr}}=f{k}_{B}T/\hslash$; we find $f$ of order unity, and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes non-resonant in the bare quasiparticle energies only renormalize $m^{\ast }$, while resonant processes are shown to produce the Planckian behavior.

6 + 3 pages, 5 + 1 figures, minor textual updates