Quantum Phase Fluctuations Dominate Unconventional Superconductivity

Unconventional superconductivity has remained one of the most important mysteries in condensed matter physics since its discovery several decades ago. In contrast to conventional gapped s-wave BCS theory, early experiments indicated T-linear superfluid density at low temperature and more recent experiments with ever-higher accuracy frequently find superlinear dependence at low temperature, casting doubt on conventional theory categorically. We examine many well-known prototypical unconventional superconductors from several families and discover systematic T³ depletion of the 3D superfluid density at low temperature. To explain this novel behavior, we study the many-body current-current response of bosons in a lattice and find generic T³ depletion of the superfluid density. In contrast to the universality found in the vicinity of phase transitions, such stable low-temperature behavior is highly sensitive to the underlying quantum many-body theory and can be used to distinguish between possible theories. The success of our bosonic model at low temperature implies that phase-fluctuation dominated superfluidity underlies the quantum nature of the superconductivity in many of these materials.