Edge States of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ Detected by In-Plane Tunneling Spectroscopy

Tunneling spectroscopy has been performed on ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ searching for the edge states peculiar to topological superconductivity. Conductance spectra exhibit broad humps with three types of peak shape: domelike peak, split peak, and two-step peak. By comparing the experiments with predictions for unconventional superconductivity, these varieties are shown to originate from multiband chiral $p$-wave symmetry with weak anisotropy of pair amplitude. The broad hump in the conductance spectrum is a direct manifestation of the edge state due to chiral $p$-wave superconductivity.

Figure 1

(a) Schematic of in-plane and out-of-plane junctions. (b) Scanning ion microscopy image ($300\times 300\mu {\mathrm{m}}^2$) of a ${\mathrm{Sr}}_2{\mathrm{RuO}}_4/\mathrm{Au}$ junction fabricated on a ${\mathrm{SiO}}_2$ substrate and a schematic of the junction structure. The four terminal Au contacts are patterned by a focused ion beam, and the crystal axes are characterized by x-ray analysis. (c) Temperature dependence of resistance of a ${\mathrm{Sr}}_2{\mathrm{RuO}}_4/\mathrm{Au}$ junction. The inset shows the enlarged plot near $T_c$ ($\sim 1.5\mathrm{K}$). (d) Schematic of quasiparticle injection to an unconventional superconductor.

Figure 2

Conductance spectra obtained on the same ${\mathrm{Sr}}_2{\mathrm{RuO}}_4/\mathrm{Au}$ junction as in Fig. 1c. Each successive curve is vertically shifted by 0.001 for clarity. (a) A series of spectra obtained in the magnetic field range between 0 and 1000 Oe at 0.6 K. (b) A series of spectra obtained in the temperature range between 0.6 and 1.8 K in the absence of the magnetic field.

Figure 3

Comparison between experimental conductance spectra obtained on ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ (SRO) junctions at 0.55 K (solid lines) and theoretical spectra (dotted lines). The vertical axes are normalized by their normal-state background values and the horizontal axes are normalized by (a),(b) 0.7 mV and (c) 0.93 mV; the broken lines mark the gap amplitude as guides to the eyes. The dotted lines are calculated for (a) isotropic chiral $p$-wave symmetry with the barrier parameter $Z=3$ (domelike peak), (b) the chiral $p$-wave symmetry with a small gap amplitude modulation with $Z=3$ (split peak), and (c) two-band superconductivity with isotropic chiral $p$-wave symmetry with $Z=2$ (two-step peak). (d) Experimental spectra obtained on an ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (YBCO) junction at 3 K cited from Ref. 19. We normalize the vertical axis by the normal-state value and the horizontal axis by 18 mV.

Figure 4

Angle-resolved conductance spectra for (a) $d_{xy}$-wave superconductors and (b) chiral $p$-wave superconductors with the barrier parameter $Z=4$. The vertical axis is the quasiparticle energy normalized by ${\Delta }_0$. The brightness represents the magnitude of conductance of the junction. Bright regions correspond to the conductance peak originating from Andreev bound states formed at the edge. Conductance spectra for (c) $d_{xy}$-wave superconductors and (d) chiral $p$-wave superconductors. The solid line, broken line, and dotted line represent the in-plane junction, out-of-plane junction, and in-plane junction with the anisotropic pair amplitude (see text), respectively.