A minimal description of strange carriers

TL;DR

The paper proposes a universal quantum diffusion framework for strange metals, replacing the classical Drude picture when the thermal de Broglie length exceeds the mean free path. By enforcing a quantum diffusion bound $D^{(Q)}=\hbar/m$ and interpreting collisions as projective measurements, it derives a Planckian d.c. resistivity $\rho^{(Q)}(T)=\frac{m k_B}{n e^2 \hbar} T$ and a quantum optical response with a prefactor that yields a stretched Drude peak and $\omega/T$ scaling. The approach yields a quantum Drude formula that naturally explains experimental observations, including $B/T$ magnetotransport and extended Drude analyses, without requiring quantum criticality. The framework applies to cuprates and twisted-layer systems, emphasizing memory effects and diffusion-limited transport, while leaving open how strange carriers evolve with doping toward conventional metals.

Abstract

I explore a theory of transport and optical properties of strange metallic carriers in strongly correlated systems that follows from assuming that the diffusion constant has reached its quantum limit $D=\hbar/m$, and that such quantum carriers behave as distinguishable particles as they would in an electronic solid. These assumptions immediately lead to $T$-linear resistivities with apparent Planckian scattering rates and, extending to the frequency domain, to the stretched Drude peaks and $ω/T$ scaling commonly observed in optical absorption experiments in strange metals. This behavior can be rationalized by observing that when the thermal de Broglie length $λ_{dB}$ exceeds the mean-free-path, the carrier motion can no longer be described in terms of random collisions of classical particles as assumed by Drude-Boltzmann theory and should be viewed instead as a sequence of projective measurements collapsing the wavefunction.

Figures (4)

• Figure 1: Transport of strange carriers. (a) Diffusion of classical particles traveling ballistically with velocity $v$ and undergoing random collisions with a mean-free-path $\ell$, corresponding to a Drude-like behavior of the conductivity. (b) When the de Broglie length $\lambda_{dB}$ is larger than the mean-free-path, the classical picture breaks down due to the increasing quantum uncertainty. (c) Charge transport can be viewed as a series of projective measurements allowing the quantum particle to diffuse over a length $\lambda_{dB}$ over a Planckian time-scale $\tau^{(Q)}$, corresponding to a diffusion constant $D=(\lambda_{dB})^2/\tau^{(Q)}=\hbar/m$. (d) The resulting resistivity is linear in temperature, falling below the classical value set by the Mott-Ioffe-Regel limit. The numerical result for a weakly doped Mott insulator in the limit $U/t \to \infty$Planckian-tJ is reported as open circles. (e) The corresponding optical conductivity features a stretched Drude peak whose width is governed by the same Planckian scale $\tau^{(Q)}$ (dashed lines: see note [31]).
• Figure 2: Quantum Drude formula. (a) In good metals, $\hbar/\tau \ll k_BT$, the prefactor in Eq. (\ref{['eq:DrudeQ']}) is $\approx 1$ (green) and the Drude result is recovered with $\sigma^{(Q)} = \sigma_D$ (red). (b) In strange metals, where $k_BT \ll \hbar/\tau$, $\sigma^{(Q)} \gg \sigma_D$ and the optical absorption is entirely determined by the prefactor, with a power-law decay $1/\omega$ and a width set by the Planckian scale $1/\tau^{(Q)}$, cf. Eq. (\ref{['eq:DrudeQapp']}).
• Figure 3: Extended Drude analysis. (a) Optical scattering rate as a function of frequency at different temperatures as obtained from Eq. (\ref{['eq:DrudeQapp']}) and (b) the same quantity rescaled in Planckian units, shown together with the optical effective mass.
• Figure 4: Relaxation in the time domain. The numerical Fourier transform of Eq. (\ref{['eq:DrudeQ']}) for $k_BT/t=0.001$ is shown together with the the analytical expression Eq. (\ref{['eq:mystretch']}) and the KWW stretched exponential function with stretching exponent $b=0.32$. All three exhibit identical non-exponential decay in the time window $\hbar/t \lesssim \mathrm{t} \lesssim \tau^{(Q)}$.