Quantum oscillations from nodal bilayer magnetic breakdown in the   underdoped high temperature superconductor YBa2Cu3O6+x
  We report quantum oscillations in underdoped YBa2Cu3O6.56 over a significantly large range in magnetic field extending from 24 to 101 T, enabling three well-spaced low frequencies at 440 T, 532 T, and 620 T to be clearly resolved. We show that a small nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0 - {\Delta}F, F0, and F0 + {\Delta}F and accompanying beat pattern similar to that observed experimentally, on invoking magnetic breakdown tunneling at the nodes. The relative amplitudes of the multiple frequencies observed experimentally in quantum oscillation measurements are shown to be reproduced using a value of nodal bilayer gap quantitatively consistent with that measured in photoemission experiments in the underdoped regime. 
Suchitra E. Sebastian, N. Harrison, Ruixing Liang, D. A. Bonn, W. N.   Hardy, C. H. Mielke, and G. G. Lonzarich
cond-mat.supr-con cond-mat.str-el