Electronic self-energy and triplet pairing fluctuations in the vicinity of a ferromagnetic instability in two-dimensional systems: Quasistatic approach

Abstract

The self-energy, spectral functions and susceptibilities of 2D systems with strong ferromagnetic fluctuations are considered within the quasistatic approach. The self-energy at low temperatures T has a non-Fermi liquid form in the energy window |ω| ∆0 near the Fermi level, where ∆0 is the groundstate spin splitting for magnetically ordered ground state, and ∆0 ∝ T 1/2 ln 1/2 (vF /T ) in the quantum critical regime (vF is the Fermi velocity). Spectral functions have a two-peak structure at finite T above the magnetically ordered ground state, which implies quasi-splitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations. The triplet pairing amplitude in the quasistatic approximation increases with increasing correlation length; at low temperatures T ≪ ∆0 the vertex corrections become important and the Eliashberg approach is not justified. The results for the spectral properties and susceptibilities in the quantum critical regime near charge-(spin-) instabilities with large enough correlation length ξ ≫ (T /vF ) −1/3 are obtained.

Spectral functions of two-dimensional systems with coupling of electrons to collective or localized spin degrees of freedom

“…Although the spectral functions have one-peak structure at small enough I, one can observe that the quasiparticle picture is in fact invalid at arbitrarily small I since the real part of the self-energy has positive slope and |ImΣ ν | is maximum at the Fermi level. These features are very similar to those observed earlier in the spin-fermion model in the presence of strong magnetic correlations [24], although their physical origin in the present case is different. Above a critical value I > I c = 0.5D both the real and imaginary parts of the self-energy diverge at the Fermi level and the spectral functions have the two-peak structure.…”

“…[17,24], the finite gap in the spectral function in this case is however an artifact of the first-order approximation in 1/M , since the actual spectral function in the atomic limit has a behavior at small frequencies A(ν) ∼ |ν| M−1 which is non-analytic in 1/M (see Refs. [21,24]). However, as it will be shown below, the gap disappears quickly at finite ξ, making the situation in this case more favorable for the application of 1/M expansion.…”

“…The result for the spectral weight A(k F , ν) ∼ ν 2 in the zero-bandwidth limit of the spinfermion model [21,24] shows that the spectral weight vanishes at ν = 0 only, and a true metal-insulator transition is not expected to occur. Such a transition is however expected to be described by the s-d model [25,26,27].…”

“…Although this model was originally proposed as a phenomenological model for systems with strong antiferromagnetic (AFM) fluctuations, the systems with strong ferromagnetic (FM) fluctuations can be treated within this model as well [23,24].…”

“…The spectral properties of the 2D systems with strong magnetic fluctuations were investigated previously within the spin-fermion model in the Eliashberg approximation [22,23] which neglects vertex corrections and in the quasistatic approach, performing summation of all the types of diagrams, but neglecting the effect of dynamic spin fluctuations [21,24]. The latter approach yields the two-peak structure of the spectral function for both strong FM and AFM correlations with a finite spectral weight at the Fermi level at finite ξ.…”