For a dx2-y2-wave superconductor, the presence of nodes on the Fermi surface means that the supercurrent response to a weak applied magnetic field will be nonlinear even at . This is clearly seen in Fig. 2.4, where, due to the nodes, quasiparticle excitations will result from even a small displacement of the Fermi cylinder. For a given shift, the precise number of quasiparticle excitations will depend on the slope of the energy gap function at the nodes and the direction of . The excited quasiparticles located in a narrow wedge at the nodes produce a current density which flows in a direction opposite to that of the superfluid.
For the case in which is directed along a node, as shown in Fig. 2.4(a), the supercurrent-velocity relation is
As the temperature is increased, there is eventually a crossover to a situation in which thermal excitation of quasiparticles also occurs away from the nodes. Below this crossover temperature T*(H), is linear in H but quadratic in T, whereas above T*(H), is quadratic in H and linear in T . The first evidence for a linear H-dependence accompanied with a T2-dependence in a high-Tc material, was obtained by Maeda et al.  for measurements of the in-plane magnetic penetration depth in Bi2Sr2CaCu2Oy. Similar results have since been reported in YBa2Cu3O and Tl2Ba2CaCu2Oy . However, the results of these experiments are suspect because of the large demagnetization effect (associated with the shape of the sample) which arises from applying a magnetic field perpendicular to the flat - plane. Early measurements of in a single crystal of YBa2Cu3O6.95 found a large H2 term , but the sample had a reduced Tc indicating there may have been extrinsic effects due to impurities.