Quantum phase transitions in d-wave superconductors: damping of nodal quasiparticles

The low energy excitations of a d-wave superconductor are the fermionic S=1/2 "nodal" quasiparticles in the vicinity of the wavevectors (K,K), (K,-K), (-K,-K), (-K,K), with K around 0.4 p. Because these low energy excitations reside only at four points in the Brillouin zone, their phase space for low energy scattering is very restricted, and the theoretical expectation is that these quasiparticles should have a long lifetime. Indeed, even strong fluctuations of "stripe" order cannot easily scatter the nodal quasiparticles: unless the stripe wavevector is very close to the wavevector separating two nodal points, the stripe/quasiparticle coupling will only lead to virtual processes which renormalizes their dispersion spectrums, but does not lead to on-shell damping. It is therefore surprising that photoemission and transport experiments (T. Valla et al., Science 285, 2110 (1999), J. Corson et al., Physical Review Letters 85, 2569 (2000)) have observed a rather short lifetime for the nodal quasiparticles.

In the papers below we explore the possibility that this short quasiparticle lifetime is due to the proximity to a quantum critical point between a d-wave superconductor and some other superconducting state. Because of the strong requirements imposed by wavevector matching, it is not expected that this new state is characterized by an order parameter at a non-zero wavevector (e.g. stripe or magnetic order). Motivated by these considerations, we undertook a group-theoretical classification of all possible order parameters with zero wavevector (described in paper 4). We identified the appropriate quantum field theory for each case, and analyzed its properties under renormalization group transformations (paper 5). Quite surprisingly we found that only two candidates possessed stable fixed points which could describe a second-order quantum critical point with strong damping of nodal quasiparticles: these fixed points described a transition between a d-wave superconductor and a (d+is)-wave superconductor or between a d-wave superconductor and a (d+id)-wave superconductor


  1. Charge order, superconductivity, and a global phase diagram of doped antiferromagnets, M. Vojta and S. Sachdev, Physical Review Letters 83, 3916 (1999); cond-mat/9906104.
  2. Competing orders and quantum criticality in doped antiferromagnets, M. Vojta, Y. Zhang, and S. Sachdev, Physical Review B 62, 6721 (2000); cond-mat/0003163.
  3. Damping of collective modes and quasiparticles in d-wave superconductors, S. Sachdev and M. Vojta, New Theoretical Approaches to Strongly Correlated Systems, NATO Science Series II, vol 23, Kluwer Academic, Dordrecht (2001); cond-mat/0005250.
  4. Quantum phase transitions in d-wave superconductors, M. Vojta, Y. Zhang, and S. Sachdev, Physical Review Letters 85, 4940 (2000); 100, 089904(E) (2008); cond-mat/0007170.
  5. Renormalization group analysis of quantum critical points in d-wave superconductors, M. Vojta, Y. Zhang, and S. Sachdev, International Journal of Modern Physics B 14, 3719 (2000); cond-mat/0008048.
  6. Quantum phase transitions and collective modes in d-wave superconductors, M. Vojta and S. Sachdev, Advances in Solid State Physics 41, 329 (2001), Proceedings of the 2001 DPG Meeting, Hamburg; cond-mat/0104176.
  7. Quantum phase transitions of correlated electrons in two dimensions, S. Sachdev, Lectures at the International Summer School on Fundamental Problems in Statistical Physics X, August-September 2001, Altenberg, Germany, Physica A 313, 252 (2002); cond-mat/0109419.
  8. Finite temperature dynamics near quantum phase transitions, S. Sachdev, keynote talk at the 11th International Conference on Recent Progress in Many-Body Theories, UMIST, Manchester UK, 9-13 July, 2001, edited by Raymond F. Bishop, Tobias Brandes, Klaus A. Gernoth, Niels R. Walet and Yang Xian, World Scientific, Singapore (2002); cond-mat/0110161.
  9. Order and quantum phase transitions in the cuprate superconductors, S. Sachdev, Reviews of Modern Physics 75, 913 (2003); cond-mat/0211005.
  10. Order and quantum phase transitions in the cuprate superconductors (summary), S. Sachdev, Solid State Communications 127, 169 (2003), Proceedings of the Euroconference on Quantum Phases at the Nanoscale, Erice, Italy, 15-20 July 2002.
  11. Nodal quasiparticles and the onset of spin density wave order in the cuprates, A. Pelissetto, S. Sachdev and E. Vicari, Physical Review Letters 101, 027005 (2008); arXiv:0802.0199.
  12. Theory of the nodal nematic quantum phase transition in superconductors, E.-A. Kim, M. J. Lawler, P. Oreto, S. Sachdev, E. Fradkin, and S. A. Kivelson, Physical Review B 77, 184514 (2008); arXiv:0705.4099.
  13. Renormalization group theory of nematic ordering in d-wave superconductors, Y. Huh and S. Sachdev, Physical Review B 78, 064512 (2008); arXiv:0806.0002.
  14. Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors, C. Xu, Y. Qi, and S. Sachdev, Physical Review B 78, 134507 (2008); arXiv:0807.1542.
  15. Low temperature quasiparticle transport in a d-wave superconductor with coexisting charge order, A. C. Durst and S. Sachdev, Physical Review B 80, 054518 (2009); arXiv:0810.3914.
  16. Signatures of the nematic ordering transition in the thermal conductivity of d-wave superconductors, L. Fritz and S. Sachdev, Physical Review B 80, 144503 (2009); arXiv:0901.3530.