Field-dependence of interlayer tunnelling in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$

Micron-scale `mesa' structures fabricated on the surface of single crystals of strongly anisotropic high-temperature superconducting (HTS) compounds form stacks of `intrinsic Josephson junctions' connected in series. Studying the current-voltage (I-V) characteristics of HTS mesas is now an established technique for obtaining important information regarding the electronic density of states (DoS) in these compounds, such as the magnitude $\Delta$ of the superconducting energy gap, and its symmetry in $k$-space. We have fabricated mesas on the HTS compound Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ (Bi-2212) and studied these at a range of hole-doping levels, temperatures, and applied magnetic fields. Of particular interest is the field-dependent behaviour of the I-V characteristic at bias voltages much less than the sum-gap voltage 2$\Delta $/e, corresponding to quasiparticles near the gap nodes. We compare our results with predictions for the field-dependent DoS made by Volovik [1] in which the local energy is assumed to be Doppler shifted by the local superfluid velocity. We also discuss features seen in our tunnelling characteristics at voltages above 2$\Delta $/e, which may correspond to strong-coupling effects in Bi-2212. [1] G. E. Volovik, JETP Lett., 58: 469-473, 1993.