Quantum phase transitions in dwave superconductors: damping of nodal
quasiparticles
The low energy excitations of a dwave 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 onshell 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 dwave
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 nonzero wavevector (e.g.
stripe or magnetic order). Motivated by these considerations, we undertook a
grouptheoretical 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 secondorder quantum
critical point with strong damping of nodal quasiparticles: these fixed points
described a transition between a dwave superconductor and a (d+is)wave
superconductor or between a dwave superconductor and a (d+id)wave
superconductor
PAPERS
 Charge
order, superconductivity, and a global phase diagram of doped
antiferromagnets, M. Vojta and S. Sachdev, Physical Review Letters 83,
3916 (1999); condmat/9906104.
 Competing
orders and quantum criticality in doped antiferromagnets, M. Vojta, Y.
Zhang, and S. Sachdev, Physical Review B 62, 6721 (2000); condmat/0003163.
 Damping of collective modes and
quasiparticles in dwave superconductors, S. Sachdev and M.
Vojta, New Theoretical Approaches to Strongly Correlated Systems,
NATO Science Series II, vol 23, Kluwer Academic, Dordrecht (2001); condmat/0005250.
 Quantum
phase transitions in dwave superconductors, M. Vojta, Y.
Zhang, and S. Sachdev, Physical Review Letters 85, 4940 (2000); 100, 089904(E)
(2008); condmat/0007170.
 Renormalization group analysis of
quantum critical points in dwave superconductors, M. Vojta, Y.
Zhang, and S. Sachdev, International Journal of Modern Physics B 14,
3719 (2000); condmat/0008048.
 Quantum phase transitions and
collective modes in dwave superconductors, M. Vojta and S.
Sachdev, Advances in Solid State Physics 41, 329 (2001),
Proceedings of the 2001 DPG Meeting, Hamburg; condmat/0104176.
 Quantum phase transitions of
correlated electrons in two dimensions, S. Sachdev, Lectures at the International
Summer School on Fundamental Problems in Statistical Physics X,
AugustSeptember 2001, Altenberg, Germany, Physica A 313, 252 (2002); condmat/0109419.
 Finite temperature dynamics near quantum phase transitions, S. Sachdev, keynote talk at the 11th International Conference on Recent
Progress in ManyBody Theories, UMIST, Manchester UK, 913 July,
2001, edited by Raymond F. Bishop, Tobias Brandes, Klaus A. Gernoth,
Niels R. Walet and Yang Xian, World Scientific,
Singapore (2002); condmat/0110161.

Order and quantum phase transitions in the cuprate superconductors, S. Sachdev, Reviews of Modern Physics 75, 913 (2003); condmat/0211005.

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, 1520 July 2002.
 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.
 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.
 Renormalization group theory of nematic ordering in dwave superconductors, Y. Huh and S. Sachdev,
Physical Review B 78, 064512 (2008);
arXiv:0806.0002.
 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.
 Low temperature quasiparticle transport in a dwave superconductor with coexisting charge order, A. C. Durst
and S. Sachdev, Physical Review B 80, 054518 (2009);
arXiv:0810.3914.
 Signatures of the nematic ordering transition in the thermal conductivity of dwave
superconductors, L. Fritz and S. Sachdev, Physical Review B 80, 144503 (2009); arXiv:0901.3530.
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