Dissipationless Counterflow Currents above Tc in Bilayer Superconductors

We report the existence of dissipationless currents in bilayer superconductors above the critical temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mi>c</a:mi></a:msub></a:math>, assuming that the superconducting phase transition is dominated by phase fluctuations. Using a semiclassical U(1) lattice gauge theory, we show that thermal fluctuations cause a transition from the superconducting state at low temperature to a resistive state above <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mi>c</c:mi></c:msub></c:math>, accompanied by the proliferation of unbound vortices. Remarkably, while the proliferation of vortex excitations causes dissipation of homogeneous in-plane currents, we find that counterflow currents, flowing in the opposite direction within a bilayer, remain dissipationless. The presence of a dissipationless current channel above <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>T</e:mi><e:mi>c</e:mi></e:msub></e:math> is attributed to the inhibition of vortex motion by local superconducting coherence within a single bilayer, in the presence of counterflow currents. Our theory presents a possible scenario for the pseudogap phase in bilayer cuprates.