Universal linear-temperature resistivity: possible quantum diffusion transport in strongly correlated superconductors

Abstract

The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature (T) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation. As cooling down, those electron fluids lose the resistivity and condense into the superfluid. However, the origin of the linear-T resistivity behavior and its relationship to the strongly correlated superconductivity remain a mystery. Here we report a universal relation , which bridges the slope of the linear-T-dependent resistivity (dρ/dT) to the London penetration depth λ L at zero temperature among cuprate superconductor Bi2Sr2CaCu2O8+δ and heavy fermion superconductors CeCoIn5, where μ 0 is vacuum permeability, k B is the Boltzmann constant and ħ is the reduced Planck constant. We extend this scaling relation to different systems and found that it holds for other cuprate, pnictide and heavy fermion superconductors as well, regardless of the significant differences in the strength of electronic correlations, transport directions, and doping levels. Our analysis suggests that the scaling relation in strongly correlated superconductors could be described as a hydrodynamic diffusive transport, with the diffusion coefficient (D) approaching the quantum limit D ~ ħ/m*, where m* is the quasi-particle effective mass.

Flat bands and strongly correlated Fermi systems

“…The best way to calculate I(V ) is to use the method of Harrison [20,21], in which the tunneling current is proportional to the particle transition probability, introduced by Bardeen [23]. Namely, Bardeen considers a probability P 12 of a particle (say electron) transition from a state 1 on one side of the tunneling layer to a state 2 on the other side P 12 ∼ |t 12…”

“…Another experimental result [12] providing insight deals with the universal scaling relation, which can also be explained using the flat band concept. The authors [12] measured dρ/dT (ρ is a resistivity) for a large number of HTSC substances (with LSCO and well-known HF compound CeCoIn 5 among them, see Table I of Ref. [12]) for T > T c and discovered the remarkable result.…”

“…(ρ is the resistivity and λ 0 is the zero temperature London penetration depth) for large number of strongly correlated HTSC's [12]. The scaling spans several orders of magnitude in λ, signifying the robustness of the law (1).…”

“…The difference is that fermions to condense, the Fermi surface should change its topology [1-4], leading to violation of time-reversal (T) and particle-hole (C) symmetries. Thus, the famous Landau theory of Fermi liquids does not work for the systems with fermion condensate (FC) so that several experimentally observable anomalies have not been explained so far.Here we use FC approach to explain recent observations of the asymmetric tunneling conductivity in heavy-fermion compounds and graphene [5][6][7] and its restoration in magnetic fields, as well as the violation of Leggett theorem [8,9], recently observed experimentally [10,11] in overdoped cuprates, and recent observation of the challenging universal scaling connecting linear-T -dependent resistivity to the superconducting superfluid density [12].…”

Quantum diffusion regime of charge transport in GdB6 caused by electron and lattice instability

“…A short time after the discovery of high-temperature superconductivity in cuprates, it became clear that the highest critical temperatures T c were observed in materials with a linear temperature dependence of resistivity ρ(T) (see, for example, [1][2][3][4][5]), which could be extended to very high temperatures (~ 1000 K [1]) leading to violation of the Mott-Ioffe-Regel limit [6]. Later, a similar behavior of ρ(T) was found in pnictides [7][8] and organic superconductors [9][10] as well as in many heavy fermionic metals and superconductors [11][12] including those located in the vicinity of quantum critical point (QCP) [13]. Many different mechanisms were proposed to explain this effect, including quantum critical theories [13] and more exotic approaches, but its nature is the subject of active debate so far.…”