Pauli susceptibility of nonadiabatic Fermi liquids

(received ; accepted) PACS. 63.20Kr – Phonon-electron and phonon-phonon interactions. PACS. 71.38+i – Polarons and electron-phonon interactions. PACS. 76.30−v – Electron paramagnetic resonance and relaxation. 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 …