Mott insulators, no double occupancy, and non-Abelian superconductivity

2009

Front. Phys. China

Self Cite

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...

Section: A Introductionmentioning

confidence: 99%

Section: B Cuprate and Fe-based Phenomenologymentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

“…In 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).…”

Section: A Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A unified description of cuprate and iron arsenide superconductors

Guidry¹,

2009

Front. Phys. China

Self Cite

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

Guidry

2011

Chin. Sci. Bull.

Self Cite

A model for high-temperature superconductors incorporating antiferromagnetism, d-wave superconductivity, and no double latticesite occupancy can give energy surfaces delicately balanced between antiferromagnetic and superconducting order for specific ranges of doping and temperature. The resulting properties can reconcile a universal cuprate phase diagram with rich inhomogeneity, relate that inhomogeneity to pseudogaps, give a fundamental rationale for giant proximity effects and other emergent behavior, and provide an objective framework to separate essential from peripheral in the superconducting mechanism.high-temperature superconductivity, pseudogap, critical dynamical symmetry, inhomogeneity, complexity, emergent behavior High-temperature superconductivity was discovered more than two decades ago [1], but its interpretation remains controversial [2,3]. We believe that this lack of theoretical consensus may be attributed to two fundamental, and related, issues: (1) Most models emphasize a limited aspect of the (complex) problem; as a result, there are few solvable models that capture a sufficient range of essential physics. (2) The complex behavior of these compounds obscures the superconducting mechanism because, in the absence of solvable models incorporating a sufficiently wide range of the physics, it is difficult to separate essential from secondary features using only data. For example, high-temperature superconductors exhibit a variety of spatial inhomogeneities such as stripes or checkerboards, particularly in the hole-underdoped region and near magnetic vortex cores [4][5][6][7][8]. The relationship of these inhomogeneities to the unusual properties of these systems has yet to be settled. Does it lead to superconductivity (SC)?

Generalizing the Cooper-pair instability to doped Mott insulators

Guidry¹,

2010

Front. Phys. China

Self Cite

Copper oxides become superconductors rapidly upon doping with electron holes, suggesting a fundamental pairing instability. The Cooper mechanism explains normal superconductivity as an instability of a fermi-liquid state, but high-temperature superconductors derive from a Mott-insulator normal state, not a fermi liquid. We show that precocity to pair condensation with doping is a natural property of competing antiferromagnetism and d-wave superconductivity on a singly-occupied lattice, thus generalizing the Cooper instability to doped Mott insulators, with significant implications for the high-temperature superconducting mechanism.Keywords Cooper-pair instability, high-temperature superconductivity, SU(4) model PACS numbers 74.72.Kf, 74.20.Mn Understanding cuprate high-temperature superconductors is complicated by unusual properties of the normal state and how this state becomes superconducting with doping [1]. Band theory suggests that cuprates at half lattice filling should be metals, but they are instead insulators with antiferromagnetic (AF) properties. This behavior is thought to result from a Mott-insulator normal state, where the insulator properties follow from strong on-site Coulomb repulsion rather than band-filling properties. Upon doping the normal states with electron holes, there is a rapid transition to a superconducting (SC) state, with evidence for a pairing gap at zero temperature typically appearing for about 3%-5% hole density per copper site in the copper-oxygen plane. In addition, there is strong evidence at low to intermediate doping for a partial energy gap at temperatures above the SC transition temperature T c that is termed a pseudogap (PG), with the size of the SC gap and PG having opposite doping dependence at low doping [2,3].Parent states of normal superconductors are fermi liquids (strongly interacting systems having excitations in one-to-one correspondence with the excitations of a non-interacting fermi gas). Normal superconductors are described by Bardeen-Cooper-Schrieffer (BCS) theory [4], and result from condensation of zero-spin, zeromomentum fermion pairs into a new collective state with long-range coherence of the wavefunction. The key to understanding normal superconductivity was the demonstration by Cooper [5] that normal fermi liquids possess a fundamental instability: an electron pair above a filled fermi sea can form a bound state for vanishingly small attractive interaction. In normal superconductors, the attraction is provided by interactions with lattice phonons, which bind weakly over a limited frequency range because electrons and the lattice have different response times. However, it is the Cooper instability, not the microscopic origin of the attractive interaction, that is most fundamental: a weak electron-electron interaction alone cannot produce a superconducting state, but the Cooper instability can (in principle) produce a superconducting state for any weakly attractive interaction.The rapid onset of superconductivity in high-T c compounds with hole dopi...