Jan’s Publications

@article{WOS:000272310900106,

title = {BCS superconductivity in quantum critical metals},

author = {Jian-Huang She and Jan Zaanen},

doi = {10.1103/PhysRevB.80.184518},

issn = {2469-9950},

year  = {2009},

date = {2009-11-01},

journal = {PHYSICAL REVIEW B},

volume = {80},

number = {18},

publisher = {AMER PHYSICAL SOC},

address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA},

abstract = {We present a simple phenomenological scaling theory for the pairing 

 instability of a quantum critical metal. It can be viewed as a minimal 

 generalization of the classical Bardeen-Cooper-Schrieffer (BCS) theory 

 of superconductivity (SC) for normal Fermi-liquid metals. We assume that 

 attractive interactions are induced in the fermion system by an external 

 ``bosonic glue'' that is strongly retarded. Resting on the small 

 Migdal parameter, all the required information from the fermion system 

 needed to address the superconductivity enters through the pairing 

 susceptibility. Asserting that the normal state is a strongly 

 interacting quantum critical state of fermions, the form of this 

 susceptibility is governed by conformal invariance and one only has the 

 scaling dimension of the pair operator as free parameter. Within this 

 scaling framework, conventional BCS theory appears as the ``marginal'' 

 case but it is now easily generalized to the (ir)relevant scaling 

 regimes. In the relevant regime an algebraic singularity takes over from 

 the BCS logarithm with the obvious effect that the pairing instability 

 becomes stronger. However, it is more surprising that this effect is 

 strongest for small couplings and small Migdal parameters, highlighting 

 an unanticipated important role of retardation. Using exact forms for 

 the finite-temperature pair susceptibility from 1+1D conformal field 

 theory as models, we study the transition temperatures, finding that the 

 gap to transition temperature ratios is generically large compared to 

 the BCS case, showing, however, an opposite trend as a function of the 

 coupling strength compared to the conventional Migdal-Eliashberg theory. 

 We show that our scaling theory naturally produces the superconducting 

 ``domes'' surrounding the quantum critical points (QCPs), even when 

 the coupling to the glue itself is not changing at all. We argue that 

 hidden relations will exist between the location of the crossover lines 

 to the Fermi liquids away from the quantum critical points and the 

 detailed form of the dome when the glue strength is independent of the 

 zero-temperature control parameter. Finally, we discuss the behavior of 

 the orbital-limited upper critical magnetic field as a function of the 

 zero-temperature coupling constant. Compared to the variation in the 

 transition temperature, the critical field might show a much stronger 

 variation pending the value of the dynamical critical exponent.},

keywords = {BCS theory; critical exponents; critical points; fermion systems;   superconducting critical field; superconducting transition temperature},

pubstate = {published},

tppubtype = {article}

}