SO(5) Theory of Antiferromagnetism and Superconductivity

We construct a microscopic model of electron interactions which gives rise to both superconductivity and antiferromagnetism, and which admits an approximate SO(5) symmetry that relates these two phases. The symmetry can be exact, or it may exist only in the long-wavelength limit, depending on the detailed form of the interactions. We compute the macroscopic Landau-Ginzburg free energy for this model as a function of temperature and doping, by explicitly integrating out the fe...

We present an SU(4) model of high-temperature superconductivity having many similarities to dynamical symmetries known to play an important role in microscopic nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU(2) X SO(3) limit that may be interpreted as a d-wave pairing condensate; and an SO(5) limit that may be interpreted...

S.C. Zhang has put forward the idea that high-temperature-superconductors can be described in the framework of an SO(5)-symmetric theory in which the three components of the antiferromagnetic order-parameter and the two components of the two-particle condensate form a five-component order-parameter with SO(5) symmetry. Interactions small in comparison to this strong interaction introduce anisotropies into the SO(5)-space and determine whether it is favorable for the system to...

Recent angle resolved photoemission data, which found evidence for a d-wave-like modulation of the antiferromagnetic gap, suggest an intimate interrelation between the antiferromagnetic insulator and the superconductor with its d-wave gap. It is shown here that a projected SO(5) theory, which explicitly takes the Mott-Hubbard gap into account, correctly describes the observed gap characteristics. Specifically, it accounts for the order of magnitude difference between the anti...

We report on the basis of Cu-NQR measurements that superconductivity (SC) and antiferromagnetism (AF) coexist on a microscopic level in CeCu_{2}(Si_{1-x}Ge_{x})_{2}, once a tiny amount of 1%Ge (x = 0.01) is substituted for Si. This coexistence arises because Ge substitution expands the unit-cell volume in nearly homogeneous CeCu2Si2 where the SC coexists with slowly fluctuating magnetic waves. We propose that the underlying exotic phases of SC and AF in either nearly homogene...

The present approach takes into account thermal fluctuations both in the rotation of SO(5) superspins between the AF and SC subspaces, and in the phase variables of SC order parameters. Temperature vs. g-field phase diagrams for null external magnetic field are presented, where the g field is conjugate with the quadratic order parameters and breaks the SO(5) symmetry. The normal(N)/AF and N/SC phase boundaries merge tangentially at the bicritical point into the AF/SC phase bo...

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we propose in the present note three toy models, namely, one based on $SO_{q}(3)$ the other two constructed with the $SO_{q}(4)$ and $SO_{q}(5)$ quantum groups. Possible motivations and rationale for these choices are outlined. One of the prime motivations underlying our proposal is the experimental observation of stripe structure [phase] in high ...

We study an SO(5) model unifying p-wave superconductivity and ferromagnetism. If only a single p-wave pairing wavefunction is involved, the p-wave superconducting (pSC) and ferromagnetic (F) states can be unified to form 10-dimensional multiplet of SO(5). The collective modes in pSC and F states are studied from this viewpoint in terms of a non-linear sigma model.

Recent angle resolved photoemission (ARPES) data, which found evidence for a d-wave-like modulation of the antiferromagnetic gap, suggest an intimate interrelation between the antiferromagnetic insulator and the superconductor with its d-wave gap. This poses a new challenge to microscopic descriptions, which should account for this correlation between, at first sight, very different states of matter. Here, we propose a microscopic mechanism which provides a definite correlati...

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we propose in the present note three toy models, namely, one based on SO_{q}(3) the other two constructed with the SO_{q}(4) and SO_{q}(5) quantum groups. Possible motivations and rationale for these choices are outlined. One of the prime motivations underlying our proposal is the experimental observation of stripe structure [phase] in high T_c supe...