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Superconducting order parameters that change phase around the Fermi surfacemodify Josephson tunneling behavior, as in the phase-sensitive measurementsthat confirmed $d$ order in the cuprates. This paper studies Josephson couplingwhen the individual grains break time-reversal symmetry; the specific casesconsidered are $p \pm ip$ and $d \pm id$, which may appear in Sr$_2$RuO$_4$ andNa$_x$CoO$_2 \cdot $(H$_2$O)$_y$ respectively. $T$-breaking order parameterslead to frustrating phases when not all grains have the same sign oftime-reversal symmetry breaking, and the effects of these frustrating phasesdepend sensitively on geometry for 2D arrays of coupled grains. These systemscan show perfect superconducting order with or without macroscopic$T$-breaking. The honeycomb lattice of superconducting grains has asuperconducting phase with no spontaneous breaking of $T$ but instead power-lawcorrelations. The superconducting transition in this case is driven by bindingof fractional vortices, and the zero-temperature criticality realizes ageneralization of Baxter's three-color model.Comment: 8 page

physical review. b, condensed matter and materials physics

Geometric effects on<i>T</i>-breaking in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>p</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>d</mml:mi></mml:math>superconducting arrays

Geometric effects onT-breaking inp+ipandd+idsuperconducting arrays