  There is strong experimental evidence that the superconductor Sr2RuO4 has a
chiral p-wave order parameter. This symmetry does not require that the
associated gap has nodes, yet specific heat, ultrasound and thermal
conductivity measurements indicate the presence of nodes in the superconducting
gap structure of Sr2RuO4. Theoretical scenarios have been proposed to account
for the existence of accidental nodes or deep accidental minima within a p-wave
state. To elucidate the nodal structure of the gap, it is essential to know
whether the lines of nodes (or minima) are vertical (parallel to the tetragonal
c axis) or horizontal (perpendicular to the c axis). Here, we report thermal
conductivity measurements on single crystals of Sr2RuO4 down to 50 mK for
currents parallel and perpendicular to the c axis. We find that there is
substantial quasiparticle transport in the T = 0 limit for both current
directions. A magnetic field H immediately excites quasiparticles with
velocities both in the basal plane and in the c direction. Our data down to
Tc/30 and down to Hc/100 show no evidence that the nodes are in fact deep
minima. Relative to the normal state, the thermal conductivity of the
superconducting state is found to be very similar for the two current
directions, from H = 0 to H = Hc2. These findings show that the gap structure
of Sr2RuO4 consists of vertical line nodes. Given that the c-axis dispersion
(warping) of the Fermi surface in Sr2RuO4 varies strongly from surface to
surface, the small a-c anisotropy suggests that the line nodes are present on
all three sheets of the Fermi surface. If imposed by symmetry, vertical line
nodes would be inconsistent with a p-wave order parameter for Sr2RuO4. To
reconcile the gap structure revealed by our data with a p-wave state, a
mechanism must be found that produces accidental line nodes in Sr2RuO4.
