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arXiv:2306.05489

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

Mengxing Ye, Andrey V. Chubukov

Published Jun 8, 2023• 0 citations
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Abstract

It is generally believed that in a 2D metal, whose ground state is antiferromagnetically ordered with ${\bf Q} = (π,π)$, thermal (static) magnetic fluctuations give rise to precursor behavior above $T_N$, in which the spectral function of a hot fermion (the one for which ${\bf k}$ and ${\bf k} + {\bf Q}$ are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of $T >T_N$ and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following [Y.M. Vilk and A.-M. S. Tremblay, J. Phys. I France ${\bf 7}$ 1309 (1997)] that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion, but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, like, e.g., Eliashberg theory for magnetically-mediated superconductivity. We also analyze the potential pseudogap behavior at $T=0$. We argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.

DOI
10.48550/arxiv.2306.05489

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We analyze several almost exactly solvable models of the electronic spectrum of two-dimensional systems with well-developed short-range-order dielectric (e.g., antiferromagnetic) or superconducting fluctuations that give rise to an anisotropic pseudogap state in certain segments of the Fermi surface. We develop a recurrence procedure for calculating the one-electron Green’s function that is equivalent to summing all Feynman diagrams. The procedure is based on an approximate ansatz for higher order terms in the perturbation series. We do detailed calculations of the spectral densities and the one-electron density of states. Finally, we analyze the limits of the adopted approximations and some important points concerning the substantiation of these approximations.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation n T and temperature is calculated. At low temperatures, the susceptibility presents a peak for n T ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above n T ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).
Spectral functions within the generalized $t\ensuremath{-}J$ model as relevant to cuprates are analyzed using the method of equations of motion for projected fermion operators. In the evaluation of the self-energy a decoupling of spin and single-particle fluctuations is performed. It is shown that in an undoped antiferromagnet the method reproduces the self-consistent Born approximation. For finite doping with short-range antiferromagnetic order the approximation evolves into a paramagnon contribution which retains a large incoherent contribution in the hole part of the spectral function as well as the hole-pocket-like Fermi surface at low doping. On the other hand, the contribution of longer-range spin fluctuations, with the coupling mostly determined predominantly by J and next-neighbor hopping ${t}^{\ensuremath{'}},$ is essential for the emergence of the pseudogap. The latter shows, at low doping in the effective truncation of the large Fermi surface, a reduced electron density of states and at the same time a quasiparticle density of states at the Fermi level.