We obtain an exact expression for the conductivity of a disordered, non-Galilean-invariant Fermi liquid by solving the kinetic equation with both screened Coulomb and $z=3$ Pomeranchuk critical interactions. While consistent with previous asymptotic results, our solution shows that electron-electron interactions enter the conductivity solely via the quasiparticle scattering time, $τ_\mathrm{ee}$ . Accordingly, the crossovers between the collisionless and hydrodynamic regimes occur when $1/τ_\mathrm{ee}$ becomes comparable to the larger of the impurity scattering rate and the probe frequency, $Ω$ . In addition, the exact solution yields the optical response in the hydrodynamic regime, $Ω\ll 1/τ_\mathrm{ee}$ , which is inaccessible within perturbation theory. Near a $z=3$ Pomeranchuk quantum critical point, consistency between the kinetic-equation and Kubo approaches requires proper inclusion of mass renormalization within the Eliashberg approximation, which also ensures that the crossover between the collisionless and hydrodynamic regimes in the optical conductivity occurs at the Planckian scale $Ω\sim T$ .We obtain an exact expression for the conductivity of a disordered, non-Galilean-invariant Fermi liquid by solving the kinetic equation with both screened Coulomb and $z=3$ Pomeranchuk critical interactions. While consistent with previous asymptotic results, our solution shows that electron-electron interactions enter the conductivity solely via the quasiparticle scattering time, $τ_\mathrm{ee}$. Accordingly, the crossovers between the collisionless and hydrodynamic regimes occur when $1/τ_\mathrm{ee}$ becomes comparable to the larger of the impurity scattering rate and the probe frequency, $Ω$. In addition, the exact solution yields the optical response in the hydrodynamic regime, $Ω\ll 1/τ_\mathrm{ee}$, which is inaccessible within perturbation theory. Near a $z=3$ Pomeranchuk quantum critical point, consistency between the kinetic-equation and Kubo approaches requires proper inclusion of mass renormalization within the Eliashberg approximation, which also ensures that the crossover between the collisionless and hydrodynamic regimes in the optical conductivity occurs at the Planckian scale $Ω\sim T$.

arXiv:2605.21774Physical review. B./Physical review. BOct 14, 20260 citations

Superconductivity and fermionic quantum criticality

Jian-Huang She, Jan Zaanen

Physica C SuperconductivityApr 22, 20131 citation

Nematic order and non-Fermi liquid behavior from a Pomeranchuk instability in a two-dimensional electron system

Walter Metzner, Luca Dell’Anna, Hiroyuki Yamase

Interactions in Fermi systems can induce a "Pomeranchuk instability" leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We discuss electrons on a square lattice near a Pomeranchuk instability with d-wave symmetry. The strong response of such a system to a small orthorhombic perturbation can explain naturally the large in-plane anisotropy of electronic and magnetic properties observed in detwinned YBCO crystals. Fluctuations in a quantum critical regime near the instability provide a mechanism for non-Fermi liquid behavior. They lead to a singular forward scattering interaction, which destroys fermionic quasi-particles on the whole Fermi surface except at "cold spots" on the Brillouin zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots, where conventional Fermi liquid behavior survives. In clean systems this gives rise to a T 3/2 temperature dependence of the DC resistivity, as observed in some overdoped cuprates. In the presence of disorder, the resistivity is linear in T at low temperatures.Interactions in Fermi systems can induce a "Pomeranchuk instability" leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We discuss electrons on a square lattice near a Pomeranchuk instability with d-wave symmetry. The strong response of such a system to a small orthorhombic perturbation can explain naturally the large in-plane anisotropy of electronic and magnetic properties observed in detwinned YBCO crystals. Fluctuations in a quantum critical regime near the instability provide a mechanism for non-Fermi liquid behavior. They lead to a singular forward scattering interaction, which destroys fermionic quasi-particles on the whole Fermi surface except at "cold spots" on the Brillouin zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots, where conventional Fermi liquid behavior survives. In clean systems this gives rise to a T 3/2 temperature dependence of the DC resistivity, as observed in some overdoped cuprates. In the presence of disorder, the resistivity is linear in T at low temperatures.

Journal of Physics Conference SeriesFeb 1, 20090 citations

We obtain an exact expression for the conductivity of a disordered, non-Galilean-invariant Fermi liquid by solving the kinetic equation with both screened Coulomb and

z=3

Pomeranchuk critical interactions. While consistent with previous asymptotic results, our solution shows that electron-electron interactions enter the conductivity solely via the quasiparticle scattering time,

τ_\mathrm{ee}

. Accordingly, the crossovers between the collisionless and hydrodynamic regimes occur when

1/τ_\mathrm{ee}

becomes comparable to the larger of the impurity scattering rate and the probe frequency,

Ω

. In addition, the exact solution yields the optical response in the hydrodynamic regime,

Ω\ll 1/τ_\mathrm{ee}

, which is inaccessible within perturbation theory. Near a

z=3

Pomeranchuk quantum critical point, consistency between the kinetic-equation and Kubo approaches requires proper inclusion of mass renormalization within the Eliashberg approximation, which also ensures that the crossover between the collisionless and hydrodynamic regimes in the optical conductivity occurs at the Planckian scale

Ω\sim T