In class Professor claimed that 1D superconductivity does not exist even at zero temperature. I did a preliminary search and found papers on 1D superconductors. Did I or the Prof make a mistake or could somebody point to me a proof to this claim published somewhere?
Many thanks!
In 1-d you can find BCS and charge density wave ground states at the mean field level, but these states are destroyed by quantum fluctuations and the correct ground state is a disordered phase called the Luttinger liquid, see, for example, http://arxiv.org/abs/cond-mat/9510014 .
Q: Why no 1D superconductivity?
A: By quantum fluctuation long-range order (LRO) does not exist. But power law decay of correlation functions is allowed as can be calculated by Luttinger liquid model.
Q: Why quasi-1D superconductivity?
A: LRO isn't required for superconductivity. There is still a critical temperature below which one can tell the difference between an exponential decay and a power law decay for the correlation function.
Sorry for the confusion (1D vs. quasi-1D)!