Pauli susceptibility of nonadiabatic Fermi liquids

Abstract

Abstract. -The nonadiabatic regime of the electron-phonon interaction leads to behaviors of some physical measurable quantities qualitatively different from those expected from the Migdal-Eliashberg theory. Here we identify in the Pauli paramagnetic susceptibility χ one of such quantities and show that the nonadiabatic corrections reduce χ with respect to its adiabatic limit. We show also that the nonadiabatic regime induces an isotope dependence of χ, which in principle could be measured.When the Fermi energy E F is anomalously small, as in high-T c cuprates [1] and in the fullerene compounds [2], the Migdal-Eliashberg (ME) approach [3,4] may result inadeguate in describing the interplay between charge carriers and phonons. For example, the alkali-doped fullerenes (A 3 C 60 ) have Fermi energies of order 0.25 eV [2] and intramolecular phonon modes with frequencies ω 0 in the range between 20 meV and 0.2 eV [5]. In this case, the adiabatic parameter ω 0 /E F lies somewhere between 0.1 and 0.9, depending on which phonon modes most couple to the electrons. The main consequence is that the electron-phonon vertex corrections may no longer be negligible, as assumed in the ME framework, and a generalization of the theory is required to include the nonadiabatic contributions [6].This generalization In terms of the electron-phonon coupling λ and the adiabatic parameter ω 0 /E F , the ME regime applies for λ < ∼ 1 and ω 0 /E F ≪ 1. Therefore, a generalization beyond the ME framework is required when λ > ∼ 1 and/or ω 0 /E F is no longer negligible. However, when λ is larger than some critical value λ c (which is of order one or larger), the system evolves toward a polaronic regime characterized by strong electron-lattice correlations. This holds true even in the adiabatic case in which the charge carriers aquire large effective masses. On the other hand, a region in the λ-ω 0 /E F plane different from the one leading to polaronic states is defined by λ < ∼ 1 and ω 0 /E F finite. Within this region, where the charge carriers are weakly interacting nonadiabatically with phonons, the nature of quasiparticles is different from both the ME and the polaronic ones. In such a nonadiabatic regime we shall speak of nonadiabatic Fermi liquids (or nonadiabatic fermions), to stress the difference from the ME and Typeset using EURO-L a T E X

Nonadiabatic Channels in the Superconducting Pairing of Fullerides

“…This situation unavoidably leads to the opening of nonadiabatic channels in the electron-phonon pairing which we argue to play the primary role for the high values of T c in fullerene compounds. Finally, we stress the importance of peculiar nonadiabatic effects in both superconducting [11] and normal state properties [18,19] of fullerene compounds. Experiments in this direction are, therefore, of great interest.…”

“…Indeed, characteristic effects of the nonadiabatic vertex corrections are predicted to be observable in several quantities, such as T c and its isotope coefficient [9,10], the reduction rate of T c itself upon disorder [11], the effective electronic mass m ‫ء‬ [18], and the Pauli susceptibility [19]. A peculiar feature of the nonadiabatic processes is to produce, under some conditions, constructive electron-phonon interference in the particle-particle channel leading to an enhancement of T c [9,10].…”

Nonadiabatic breakdown and pairing in high-Tc compounds

“…Hence, any evidence of electron-phonon effects on the Pauli spin susceptibility would be a direct proof of a nonadiabatic electron-phonon coupling [63,69]. The proper inclusion of the electron-phonon interaction in Eq.…”

“…where m B is the Bohr magneton and G c is the total spin vertex function. It can be shown that the electron-phonon interaction in the Green's functions G and in the spin vertex G c cancels out in the adiabatic limit since the electron-phonon self-energy S ep in the presence of a magnetic field H has nonzero contributions only at a nonadiabatic level [67][68][69]:…”

Nonadiabatic Pauli susceptibility in fullerene compounds

“…Therefore, following the same procedure reported in Ref. 11, we replace the electron-phonon interaction |g(k − k ′ )| 2 by its average over the Fermi surface:…”