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Register a new userFermion condensation, $T$-linear resistivity and Planckian limit
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We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition (FCQPT). We emphasize that so - called Planckian limit, widely used to explain the above universal scattering rate, may occur accidentally as in conventional metals its experimental manifestations (e.g. scattering rate at room and higher temperatures) are indistinguishable from those generated by the well-know phonons being the classic lattice excitations. Our results are in good agreement with experimental data and show convincingly that the topological FCQPT can be viewed as the universal agent explaining the very unusual physics of strongly correlated Fermi systems.
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The perfectly linear temperature dependence of the electrical resistivity observed as $T rightarrow$ 0 in a variety of metals close to a quantum critical point is a major puzzle of condensed matter physics . Here we show that $T$-linear resistivity as $T rightarrow$ 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bi-layer cuprate Bi2212 and found that it exhibits a $T$-linear dependence with the same slope as in the single-layer cuprates Bi2201, Nd-LSCO and LSCO, despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the $T$-linear coefficient (per CuO$_2$ plane), $A_1$, is given by the universal relation $A_1 T_F = h / 2e^2$, where $e$ is the electron charge, $h$ is the Planck constant and $T_F$ is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1 / $tau$ of charge carriers reaches the Planckian limit whereby $hbar / tau = k_B T$, works not only for hole-doped cuprates but also for electron-doped cuprates despite the different nature of their quantum critical point and strength of their electron correlations.
A variety of strange metals exhibit resistivity that decreases linearly with temperature as $Trightarrow 0$, in contrast with conventional metals where resistivity decreases as $T^2$. This $T$-linear resistivity has been attributed to charge carriers scattering at a rate given by $hbar/tau=alpha k_{rm B} T$, where $alpha$ is a constant of order unity. This simple relationship between the scattering rate and temperature is observed across a wide variety of materials, suggesting a fundamental upper limit on scattering---the Planckian limit---but little is known about the underlying origins of this limit. Here we report a measurement of the angle-dependent magnetoresistance (ADMR) of Nd-LSCO---a hole-doped cuprate that displays $T$-linear resistivity down to the lowest measured temperatures. The ADMR unveils a well-defined Fermi surface that agrees quantitatively with angle-resolved photoemission spectroscopy (ARPES) measurements and reveals a $T$-linear scattering rate that saturates the Planckian limit, namely $alpha = 1.2 pm 0.4$. Remarkably, we find that this Planckian scattering rate is isotropic, i.e. it is independent of direction, in contrast with expectations from hot-spot models. Our findings suggest that $T$-linear resistivity in strange metals emerges from a momentum-independent inelastic scattering rate that reaches the Planckian limit.
Recent experimental results: (i) the measurement of the $T ln T$ specific heat in cuprates and the earlier such results in some heavy fermion compounds, (ii) the measurement of the single-particle scattering rates, (iii) the density fluctuation spectrum in cuprates and (iv) the long standing results on the linear temperature dependence of the resistivity, show that a theory of the quantum-criticality in these compounds based on the solution of the dissipative 2D - XY model gives the temperature and frequency dependence of each of them, and the magnitudes of all four with one dimensionless coupling parameter. These low frequency or temperature dependences persist to an upper cut-off which is measured to be about the same from the singularity in the specific heat or the saturation of the single-particle self-energy. The same two parameters are deduced in the analysis of results of photoemission experiments to give d-wave superconductivity and its transition temperature. The coupling parameter and the cut-off had been estimated in the microscopic theory to within a factor of 2. The simplicity of the results depends on the discovery that orthogonal topological excitations in space and in time determine the fluctuations near criticality such that the space and time metrics are free of each other. The interacting fermions then form a marginal Fermi-liquid.
The description of dynamics of strongly correlated quantum matter is a challenge, particularly in physical situations where a quasiparticle description is absent. In such situations, however, the many-body Kubo formula from linear response theory, involving matrix elements of the current operator computed with many-body wavefunctions, remains valid. Working directly in the many-body Hilbert space and not making any reference to quasiparticles (or lack thereof), we address the puzzle of linear in temperature ($T$-linear) resistivity seen in non-Fermi liquid phases that occur in several strongly correlated condensed matter systems. We derive a simple criterion for the occurrence of $T$-linear resistivity based on an analysis of the contributions to the many-body Kubo formula, determined by an energy invariant $f$-function involving current matrix elements and energy eigenvalues that describes the DC conductivity of the system in the microcanonical ensemble. Using full diagonalization, we test this criterion for the $f$-function in the spinless nearest neighbor Hubbard model, and in a system of Sachdev-Ye-Kitaev dots coupled by weak single particle hopping. We also study the $f$-function for the spin conductivity in the 2D Heisenberg model with similar conclusions. Our work suggests that a general principle, formulated in terms of many-body Hilbert space concepts, is at the core of the occurrence of $T$-linear resistivity in a wide range of systems, and precisely translates $T$-linear resistivity into a notion of energy scale invariance far beyond what is typically associated with quantum critical points.
A theoretical understanding of the enigmatic linear-in-temperature ($T$) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust $T$-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub slope invariance. Recently, several solvable models with $T$-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate $T$-linearity: a lattice of coupled Sachdev-Ye-Kitaev (SYK) models and the Hubbard model in single-site dynamical mean-field theory (DMFT). We find that the two models achieve $T$-linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit slope invariance across the two temperature regimes. We thus not only reveal some of the diversity in the theoretical inner workings that can lead to $T$-linear resistivity, but we also establish that different mechanisms can result in slope invarance.
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