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We review the appearance of the Planckian time $tau_text{Pl} = hbar/(k_B T)$ in both conventional and unconventional metals. We give a pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize metals, emphasizing conditions under which these times are the same or different. Throughout, we have attempted to clear up aspects of the problem that had been confusing us, in the hope that this helps the reader as well. We discuss the possibility of a Planckian bound on dissipation from both a quasiparticle and a many-body perspective. Planckian quasiparticles can arise naturally from a combination of inelastic scattering and mass renormalization. Many-body dynamics, on the other hand, is constrained by the basic time- and length- scales of local thermalization.
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Could it be that the matter from the electrons in high Tc superconductors is of a radically new kind that may be called many body entangled compressible quantum matter? Much of this text is intended as an easy to read tutorial, explaining recent theoretical advances that have been unfolding at the cross roads of condensed matter- and string theory, black hole physics as well as quantum information theory. These developments suggest that the physics of such matter may be governed by surprisingly simple principles. My real objective is to present an experimental strategy to test critically whether these principles are actually at work, revolving around the famous linear resistivity characterizing the strange metal phase. The theory suggests a very simple explanation of this unreasonably simple behavior that is actually directly linked to remarkable results from the study of the quark gluon plasma formed at the heavy ion colliders: the fast hydrodynamization and the minimal viscosity. This leads to high quality predictions for experiment: the momentum relaxation rate governing the resistivity relates directly to the electronic entropy, while at low temperatures the electron fluid should become unviscous to a degree that turbulent flows can develop even on the nanometre scale.
The room temperature thermal diffusivity of high T$_c$ materials is dominated by phonons. This allows the scattering of phonons by electrons to be discerned. We argue that the measured strength of this scattering suggests a converse Planckian scattering of electrons by phonons across the room temperature phase diagram of these materials. Consistent with this conclusion, the temperature derivative of the resistivity of strongly overdoped cuprates is noted to show a kink at a little below 200 K that we argue should be understood as the onset of a high temperature Planckian $T$-linear scattering of electrons by classical phonons. This kink continuously disappears towards optimal doping, even while strong scattering of phonons by electrons remains visible in the thermal diffusivity, sharpening the long-standing puzzle of the lack of a feature in the $T$-linear resistivity at optimal doping associated to onset of phonon scattering.
We study the problem of disorder-free metals near a continuous Ising nematic quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory in the `Yukawa coupling between the electrons and undamped bosons (nematic order parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the `marginal Fermi liquid phenomenologycite{Varma}. We discuss a large N theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.
A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids are not amenable to the perturbative methods of Fermi liquid theory, but can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene, which possesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes of their band structure provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in stoichiometric Scandium (Sc) Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction and hence reflects the strength of the correlations, is enhanced by a factor of about 3.2 as compared to graphene, due to orbital hybridization. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put, for the first time, the turbulent flow regime described by holography within the reach of experiments.
Heavily oxygen deficient NdNiO$_3$ (NNO) films, which are insulating due to electron localization, contain pristine regions that undergo a hidden metal-insulator transition. Increasing oxygen content increases the connectivity of the metallic regions and the metal-insulator transition is first revealed, upon reaching the percolation threshold, by the presence of hysteresis. Only upon further oxygenation is the global metallic state (with a change in the resistivity slope) eventually achieved. It is shown that sufficient oxygenation leads to linear temperature dependence of resistivity in the metallic state, with a scattering rate directly proportional to temperature. Despite the known difficulties to establish the proportionality constant, the experiments are consistent with a relationship 1/$tau$= $alpha k_B T/hbar$, with $alpha$ not far from unity. These results could provide experimental support for recent theoretical predictions of disorder in a two-fluid model as a possible origin of Planckian dissipation.
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