Some remarks on pseudogap behavior of nearly antiferromagnetic metals

Abstract

In the antiferromagnetically ordered phase of a metal, gaps open on parts of the Fermi surface if the Fermi volume is sufficiently large. We discuss simple qualitative and heuristic arguments under what conditions precursor effects, i.e. pseudo gaps, are expected in the paramagnetic phase of a metal close to an antiferromagnetic quantum phase transition. At least for weak interactions, we do not expect the formation of pseudo gaps in a three dimensional material. According to our arguments, the upper critical dimension dc for the formation of pseudo gaps is dc = 2. However, at the present stage we cannot rule out a higher upper critical dimension, 2 ≤ dc ≤ 3. We also discuss briefly the role of statistical interactions in pseudo gap phases. 71.10.Hf,75.40.Gb Experiments on metals close to an antiferromagnetic quantum critical point (QCP) show clearly that these systems cannot be described by standard Fermi liquid theory. This is not very surprising, as at the QCP magnetic fluctuations dominate and electronic quasi particles scatter from spin-fluctuations characterized by a diverging correlation length. Indeed, a theory of quantum critical fluctuations interacting weakly with Fermi liquid quasi particles 1,2 can explain a substantial part of the experiments at least if effects like weak impurity scattering are properly taken into account 3 . However, a number of experiments seems to contradict the standard spin-fluctuation scenario, presently the best studied example for this is probably CeCu 6−x Au x 4-6 . It has been speculated that this might be due to anomalous twodimensional spin fluctuation 5 or a partial breakdown of the Kondo effect 6 . In this paper we discuss a different route which can lead to a breakdown of the theory of weakly interacting spin fluctuations, first proposed by Hertz 1,2 . The general idea 7 is the following: close to the QCP, the behavior of the system is dominated by large antiferromagnetic domains of size ξ, slowly fluctuating on the time scale τ ξ ∼ ξ zop where z op is the dynamical critical exponent of the order parameter. As ξ is diverging when the QCP is approached, it is suggestive to assume that the electrons will adjust their wave functions adiabatically to the local antiferromagnetic background and will therefore show a similar behavior as in the antiferromagnetically ordered phase. If the Fermi surface is sufficiently large, the (staggered) order parameter of the antiferromagnetic phase induces gaps in parts of the Fermi surface with ǫ k ≈ ǫ k±Q ≈ 0, where ǫ k is the dispersion of the quasi particles measured from the Fermi energy and Q the ordering wave-vector of the antiferromagnet. Will precursors of this effect show up and induce pseudo gaps in the paramagnetic phase for sufficiently large ξ? Pseudo gaps play an important role in the physics of underdoped cuprates [8][9][10][11][12][13][14][15] and it has been speculated that they are indeed precursors of gaps in either superconducting, antiferromagnetic, flux or striped phases. In this report we want to investigate q...

Quantum critical transport at a semimetal-to-insulator transition on the honeycomb lattice

“…(37) for the function g. The following discussion closely follows the presentation given in Ref. 25.…”

“…The question is whether the conductivity can still show signatures of a pseudogap in the conductivity which diverges as temperature is lowered. The role of a finite temperature pseudogap in scaling functions has been analyzed before in the context of the Hertz-Millis theory in two dimensional systems 37 . In our qualitative consideration, however, we go along the lines of Lee et al 38 , who considered fluctuation effects at the Peierls transition in one dimensional systems.…”

Quantum phase transitions

“…Consequently, the critical theory should be characterized by two dynamic critical exponents [23]. A proper RG analysis of such a theory, keeping both low-energy degrees of freedom, has so far only been carried out for the ferromagnetic transition [24].…”

Pseudogaps in an Incoherent Metal

“…A plausible explanation for it involves the effect of finite ranged fluctuating antiferromagnetic or superconducting domains leading to a distribution of local spin gaps [6]. We will show below that there is a different source of pseudogaps arising through nearest neighbor exchange coupling and retardation effects in the presence of strong magnetic fluctuations.…”