Magnetic Induction of ${\mathit{d}}_{{\mathit{x}}^2-{\mathit{y}}^2}+{\mathrm{id}}_{\mathrm{xy}}$ Order in High- $T_c$ Superconductors

I propose that the phase transition in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ recently observed by Krishana et al. [Science 277, 83 (1997)] is the development of a small $d_{\mathrm{xy}}$ superconducting order parameter phased by $\pi /2$ with respect to the principal $d_{x^2{-y}^2}$ one to produce a minimum energy gap $\Delta$. The violation of both parity and time-reversal symmetry allows the development of a magnetic moment, the key to explaining the experiment. The origin of this moment is a quantized boundary current of $I_B=2e\Delta /h$ at zero temperature.