Fractionalization: superconductivity and stable hc/e vortices

Doping the quantum paramagnets with deconfined spinon excitations leads to states with unusual properties. Apart from a possible Wigner crystalline state at very low doping, the ground state can be a superconductor. The S=1/2 spinons are expected to survive as neutral excitations in the superconductor, but such excitations are no longer exotic: the familiar Bogoliubov excitations of a BCS superconductor also have S=1/2 and can be considered neutral. However, the presence of a parent insulating state with spin-charge separation does lead to some exotic properties in the superconductor. It was argued in paper 3 (and reviewed in paper 4) that such a superconductor should support stable hc/e vortices in the underdoped region. There has been renewed interest in these issues in recent years: the work of Senthil and Fisher (T. Senthil and Matthew P. A. Fisher Physical Review B 62, 7850 (2000)) has made the connection to deconfined insulating states, as described by a Z2 gauge theory, especially clear. The online version of paper 4 contains a brief discussion of the relationship of the recent work to the earlier ideas. These authors have also proposed an interesting flux-memory effect which is intimately related to the effects leading to stable hc/e vortices, as discussed in the on-line version of paper 5.


  1. Large N expansion for frustrated and doped quantum antiferromagnets, S. Sachdev and N. Read, International Journal of Modern Physics B 5, 219 (1991); cond-mat/0402109.
  2. Superconducting, metallic, and insulating phases in a model of CuO2 layers, J. Ye and S. Sachdev, Physical Review B 44, 10173 (1991).
  3. Stable hc/e vortices in a gauge theory of superconductivity in strongly correlated electronic systems, S. Sachdev, Physical Review B 45, 389 (1992).
  4. Stable hc/e vortices in superconductors with spin-charge separation, S. Sachdev, International Journal of Modern Physics B 6, 509 (1992).
  5. Quantum criticality: competing ground states in low dimensions, S. Sachdev, Science 288, 475 (2000); cond-mat/0009456.
  6. Fractionalized Fermi liquids, T. Senthil, S. Sachdev, and M. Vojta, Physical Review Letters 90, 216403 (2003); cond-mat/0209144.
  7. Understanding correlated electron systems by a classification of Mott insulators, S. Sachdev, Annals of Physics 303, 226 (2003); cond-mat/0211027.