EFFECT OF MIDGAP STATES IN D-WAVE SUPERCONDUCTORS ON THE FLUX-QUANTIZATION IN TRICRYSTAL RINGS

To determine whether a tricrystal ring [J. R. Kirtley et al., Phys. Re v. Lett. 76, 1336 (1996)] is a 0 ring or a pi ring, the following expr ession has been used for the critical current between two d-wave super conductors with misorientation angles theta(1) and theta(2): I-c=I(0)c os2 theta(1)cos2 theta(2). We show that the recently predicted midgap surface states lead to an additional component: I-c(midgap)=-I(MG)sin2 theta(1)sin2 theta(2) (I-MG>0). The midgap component may get enhanced at low temperatures resulting in the conversion of a 0 ring to a pi r ing (or vice versa) when the temperature is reduced. The observability of this effect in real structures is discussed.