Abstract
The ratio between the shear viscosity and the entropy $\ensuremath{\eta}/s$ is considered a universal measure of the strength of interactions in quantum systems. This quantity was conjectured to have a universal lower bound $(1/4\ensuremath{\pi})\ensuremath{\hbar}/{k}_{B}$, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that $\ensuremath{\eta}/s\ensuremath{\propto}T$ violates the universal lower bound, scaling toward zero with decreasing temperature $T$ in the perturbative limit. We find that the hydrodynamic scattering time between collisions is nearly temperature independent, up to logarithmic scaling corrections, and can be extremely short for large nodal lines, near the Mott-Ragel-Ioffe limit. Our finding suggests that nodal-line semimetals can be very strongly correlated quantum systems.
Highlights
Hydrodynamics describes the behavior of quantum fluids in the regime where the relaxation of electrons is dominated by collision among the quasiparticles
The very low viscosity compared to the amount of entropy production, in violation of the conjectured lower bound, is highly suggestive that nodalline semimetals (NLSMs) may exhibit quantum turbulence [7,11,52]
Signatures of hydrodynamic behavior can be detected in the collisiondominated regime through optical and transport measurements when kBT εF, with εF being the energy of the Fermi surface and being the gap induced by spin-orbit coupling effects or possible many-body instabilities [53,54], including excitonic phases [55]
Summary
Hydrodynamics describes the behavior of quantum fluids in the regime where the relaxation of electrons is dominated by collision among the quasiparticles. The shear viscosity measures the longitudinal resistivity to transverse gradients in the velocity of a fluid It has been conjectured by Kovtun et al [10] that quantum systems have a universal lower bound for the ratio between the sheer viscosity and the entropy, η s (1/4π )h/kB. We show that in nodal systems where the density of states vanishes along a Fermi line, such as in nodalline semimetals (NLSMs) [25,26,27,28,29,30,31,32,33,34,35,36,37], the ratio between the shear viscosity and the entropy strongly violates the conjectured lower bound, scaling toward zero with decreasing temperature in the perturbative regime, η ∝ hkBT ∼ T τ, s kB α2vF kF (2).
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