A unified description of cuprate and iron arsenide superconductors

Abstract

We propose a unified description of cuprate and iron-based superconductivity. Consistency with magnetic structure inferred from neutron scattering implies significant constraints on the symmetry of the pairing gap for the iron-based superconductors. We find that this unification requires the orbital pairing formfactors for the iron arsenides to differ fundamentally from those for cuprates at the microscopic level. 71.27.+a, A. IntroductionIn a 2004 paper [1] we proposed that an SU(4) dynamical symmetry introduced in Ref.[2] had two properties important for understanding high-temperature superconductivity (SC). The first was that the SU(4) algebra imposed no double occupancy by symmetry, not projection. Thus superconductivity emerges naturally from an antiferromagnetic (AF) Mott insulator state at half filling. The second was that SU(4) symmetry alone is sufficient to guarantee many essential features of cuprate superconductivity, irrespective of microscopic details such as pairing formfactors (except to the extent that these are broadly consistent with an emergent SU(4) symmetry).This led us to propose that cuprate superconductivity was a new kind of superconductivity characterized by more complex behavior than normal BCS superconductivity because the symmetry structure associated with the superconductivity was non-abelian. The physical content of this mathematical statement is that the non-abelian algebra imposes dynamical constraints on the interaction of collective degrees of freedom such as magnetism and charge with superconductivity. Because of the key dynamical role played by the commutators, we termed this behavior non-abelian superconductivity.We demonstrated in Ref.[1], and amplified in more recent papers [3,4,5,6,7,8], that any microscopic structure consistent with an algebra having non-abelian subalgebras can lead to the complex behavior observed for cuprate superconductors. In Ref.[1] we predicted that there could be other compounds rather different from cuprate superconductors in microscopic details that could exhibit properties analogous to cuprate superconductors, provided that they realized in their emergent properties a symmetry, such as SU(4), having nonabelian subgroups and thus non-trivial commutators between pairing and other degrees of freedom.In early 2008 a series of experiments initiated in Japan and China demonstrated a surprising new class of hightemperature superconductors based on iron arsenides [9,10,11,12,13,14,15,16,17,18]. These compounds have achieved critical temperatures T c ∼ 55 K that are surpassed only by cuprates. These Fe-based superconductors have an atomic structure differing from that of the cuprates in significant details, yet there are many similarities when compared with the cuprates. This has led to a flurry of effort to determine whether these two classes of superconductors share a similar origin. At stake is the mechanism for Fe-based superconductivity, but perhaps a deeper understanding of that for cuprate superconductivity as well.In understanding the cuprate...

Inhomogeneity, dynamical symmetry, and complexity in high-temperature superconductors: Reconciling a universal phase diagram with rich local disorder

“…In particular, similar phenomena may be possible in the new iron-based high-temperature superconductors [31], because we have proposed that they may also exhibit SU(4) dynamical symmetry [32]. Thus, the existence of complex inhomogeneities for compounds having (paradoxically) universal phase diagrams suggests that (1) properties of superconductors in the pseudogap state, and near magnetic vortices and impurities, are largely determined by critical dynamical symmetry, and (2) inhomogeneity provides a strong diagnostic tool in detailing the mechanism of hightemperature superconductivity but it is only consequential, not causative.…”

Superconductivity and superfluidity as universal emergent phenomena

“…The most powerful means of implementing this space truncation is to identify dynamical symmetries expressed through Lie algebras and associated Lie groups [16][17][18][19][20][21][22][23][24][25][26][27]. Such methods have been applied extensively in nuclear [16,24], elementary particle [25], molecular [26], and condensed matter physics [18].…”

“…Adding up, we require minimally 15 generators for condensed matter and 21 for nuclear physics applications. An upper limit may be estimated by noting that previous applications to topics as complex as high-T c SC and the structure of heavy nuclei required no more than 28 generators [16,18,21].…”

“…4 illustrates for the condensed matter case. The essential point is not whether SC is conventional or unconventional, since that influences only the pairing formfactor and dynamical symmetries are often compatible with a variety of formfactors [19,21]. It is the symmetry of the truncated Hilbert space that is central to understanding superconductivity and superfluidity, not the pairing geometry.…”

Generalizing the Cooper-pair instability to doped Mott insulators

“…The SC in these materials seems unconventional, competes with AF [26], and has many other similarities with the cuprates [27,28]. The normal states are (poor) metals, though nearness to a Mott transition can be debated.…”