Superconductivity in a strange metal
In a gas of charged particles with the density n, mass m, and charge e, the electrical conductivity σ is given by the Drude formula: σ = ne2 /mΓ, where Γ is the scattering rate. Standard metals are well described by Landau's Fermi Liquid (FL) theory, in which the electric current is carried by quasi-particles, low-energy excitations of the FL that resemble electrons with some effective mass m*. The scattering rate Γ= 1/τ= vF/l, where t is the (momentum) relaxation) time, l is the mean-free path, and vF is the Fermi velocity, can be expressed ("Matthiessen's Rule") as a sum of contributions from various scattering channels: Γ = Γ0 + Γel-el + Γel-ph + …, where Γ0 describes scattering on lattice imperfections, Γel-el the electron-electron scattering, Γel-ph the electron-phonon scattering, etc. Of these, Γ0 = vF/l0, where l0 is the average distance between the defects, is temperature-independent. Γel-el should scale as T2 because of Fermi statistics; for two electrons to scatter on one another, both must come from the "Debye shell" of the width kBT/EF, where kB is the Boltzmann constant and EF is the Fermi energy. Γel-ph typically grows as T5, so we expect this to overwhelm the other channels at a high enough T. However, since l cannot be shorter than the distance between the atoms, the total Γ saturates at Mott-Ioffe-Regel (MIR) limit, roughly vF/a0, where vF is the Fermi velocity and a0 is the lattice constant. The resistivity should also saturate at low T, at ρ0 = m*vF/ne2l0 T. FL theory also describes other electronic properties; e.g., it predicts that in the magnetic field B, the resistivity of the metal should increase with B2, because σ(B) = σ(B=0)/(1 + (ωc/Γ)2), where ωc= eB/m*.
- Research Organization:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)
- Grant/Contract Number:
- SC0012704
- OSTI ID:
- 1971481
- Report Number(s):
- BNL-224251-2023-JAAM; TRN: US2313571
- Journal Information:
- Science Bulletin, Vol. 68, Issue 9; ISSN 2095-9273
- Publisher:
- Elsevier; Science China PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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