A. Auerbach: "Quantum Tunneling of vortices in underdoped cuprates: theory and experiment"

Assa Auerbach (Technion, Israel) told us about a new experiment performed by the group of G. Koren also at the Technion (cond-mat/0707.284) where variable range hopping (VRH) of vortices was observed in a special YBCO film. The film was 1m long and 14 um wide wire arranged in the form of a meander. This allowed the experimentalist to perform magneto-resistance (MR) measurements at low currents
(1uA) and low fields (up to 6T) where most of the contribution to the MR comes from single vortex tunneling.
The major finding in the experiment is a VRH type temperature dependence of the MR at low T, namely,

1) MR~exp[-(T_0/T)^1/3] .

Assa argued that VRH is not expected in a conventional BCS type superconductor, with large coherence length.
However, for underdoped cuprate superconductors, where the ratio of carrier density n_s to pinning site density n_pin can be low, Auerbach, Arovas Ghosh (PRB 74 2006) have predicted Eq. 1 based on a interacting boson model, and have calculated that

T0~(n_s/n_pin)^2(1/n_lay)*dV,

where n_lay is the layer density and dV is the fluctuations of the pinning potential. Reasonable values of the parameters agree with the measured T_0.

In the context of tunneling vortices, Assa also described recent studies of vortices in a model of half filled, hard core, lattice bosons (Lindner et. el. cond-mat/0701571).
He reported numerical estimates which found the vortex mass to be quite low (~3 times the boson mass), and hence the critical melting density of the vortex lattice was estimated to be of order 10^{-3} vortices per lattice site. This implies that quantum vortex liquid phases could be achieved by relatively weak rotations (in an optical lattice) or magnetic field (in e.g. cuprates), much lower than Hc_2.