Competing order and the asymmetric tunneling spectrum in high temperature cuprate superconductors

We show that the asymmetric tunneling spectrum observed in the cuprate superconductors stems from the existence of a competing order. The competition between the competing order and superconductivity can create a charge depletion region near the surface. The asymmetric response of the depletion region as the function of the external voltage causes the asymmetric tunneling spectrum. The effect is very general in a system which is near the phase boundary of two competing states favoring different carrier densities. The asymmetry which has recently been observed in the point-contact spectroscopy of the heavy fermion superconductor $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_5$ is another example of this effect.

Figure 1

Schematic picture of the carrier distribution and electrostatic field distribution along the $c$ axis in a double layer structure. The solid and darker solid lines represent the $A\text{−}\mathrm{O}$ and Cu–O planes, respectively, and the dash arrows represent the electrostatic field. (a) and (b) represent the distributions in the bulk and close to the surface, respectively.

Figure 2

The doping concentration near the surface. The average doping concentration inside the bulk is chosen to be 0.2.

Figure 3

The configurations of (a) the competing and (b) superconducting order parameters when the voltage is applied. $V$ is the voltage dropped near the surface. The curves are calculated at $V=100$, 0, and $-100\mathrm{meV}$, respectively. The absolute value of $V$ is expected to be less than the bias voltage of the sample with respect to the tip.

Figure 4

The length of the charge depletion region as the function of the voltage bias. The doping concentration at bulk is set to be optimal.

Figure 5

(Color online) The tunneling spectrum calculated by adding the effect of the depletion region in cuprates in superconductring states. The solid line in the inset shows the difference between the spectrum in negative voltage and one in positive voltage. The dashed dots are extracted experimental values from Ref. 14.