Doping and magnetic field dependence of in-plane tunneling into YBa₂Cu₃O_7−x: Possible evidence for the existence of a quantum critical point

We present tunneling measurements into (1,1,0)YBa₂Cu₃O_7−x films at various doping levels around the optimum. We find that, above a certain doping level near optimum doping, a spontaneous zero bias conductance peak splitting, δ, appears. It increases with doping. It also increases with magnetic field applied along the c axis, for both underdoped and overdoped films. The low field susceptibility χ = dδ/dH | H→0 is maximum, possibly diverging when the spontaneous value of δ goes to zero. These results suggest a transition from a pure d_{x² − y²} to a d + id_xy or d + is order parameter.