Homogeneous superconducting gap in $\mathrm{Dy}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ synthesized by oxide molecular beam epitaxy

Much of what is known about high-temperature cuprate superconductors stems from studies based on two surface analytical tools, angle-resolved photoemission spectroscopy (ARPES) and spectroscopic imaging scanning tunneling microscopy (SI-STM). A question of general interest is whether and when the surface properties probed by ARPES and SI-STM are representative of the intrinsic properties of bulk materials. We find this question is prominent in thin films of a rarely studied cuprate $\mathrm{Dy}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (DBCO). We synthesize DBCO films by oxide molecular beam epitaxy and study them by in situ ARPES and SI-STM. Both ARPES and SI-STM show that the surface DBCO layer is different from the bulk of the film—it is heavily underdoped, while the doping level in the bulk is close to optimal doping evidenced by bulk-sensitive mutual inductance measurements. ARPES shows the typical electronic structure of a heavily underdoped $\mathrm{Cu}{\mathrm{O}}_2$ plane and two sets of one-dimensional bands originating from the CuO chains with one of them gapped. SI-STM reveals two different energy scales in the local density of states, with one (at $\sim 18\mathrm{meV}$) corresponding to the superconductivity and the other one (at $\sim 90\mathrm{meV}$) to the pseudogap. While the pseudogap shows large variations over the length scale of a few nanometers, the superconducting gap is very homogeneous. This indicates that the pseudogap and superconductivity are of different origins.

Figure 1

Structure of a $\mathrm{Dy}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (DBCO) film. (a) The unit cell of DBCO ($\delta =0$ in this model). (b) A LEED pattern of the DBCO film after the synthesis, taken at electron beam energy of 67 eV. (c) Atomic models of CuO chains ordering with different oxygen deficiency $\delta$ in the CuO-chain plane. (d)–(f) RHEED patterns captured at electron beam energy of 30 keV: (d) after the synthesis before cooling down; (e) in the middle of cooling down around 400 °C; (f) after cooling down and with ozone shut off. (g) A cross-section profile of the DBCO film by aberration corrected STEM. The inset shows the zoomed-in image of the area marked with the red rectangle, with the unit cell model placed on top as a guide for atom identification. The interface between the Nb-doped $\mathrm{SrTi}{\mathrm{O}}_3$ substrate and the DBCO film is marked by the yellow dashed line.

Figure 2

Superconductivity and determination of $T_c$ of the DBCO film by mutual-inductance measurements. (a) The real component of pick-up signal $V_p$, the voltage across the pickup coil, showing diamagnetic screening (the Meissner effect) when the film becomes superconducting. Inset is the schematic of the experimental setup, where the driving coil is under the substrate and the pick-up coil is above the film. (b) The imaginary part of $V_p$, indicating that $T_c\approx 79\mathrm{K}$, with the transition HWHM of $\sim 0.5\mathrm{K}$. The metallic Nb-STO substrate has a slight diamagnetic screening effect, which causes the slow ramp of $\mathrm{Im}{V}_p$ above the superconducting phase transition of the DBCO film.

Figure 3

Fermi surface and band dispersions of the DBCO film. (a) Fermi surface map showing both $\mathrm{Cu}{\mathrm{O}}_2$-plane and CuO-chain features (the map is symmetrized with respect to $k_y=0$). The first Brillouin zone is marked with the dotted square. The intensity bar shown at the right bottom applies to all panels. (b) Iso-energy surface at $E=E_F–65\mathrm{meV}$, showing the two sets of CuO-chain states originating from the subsurface (green arrows) and the surface (blue arrows). (c) and (d) Energy-momentum dispersions along the momentum cuts 1 and 2 in (a), respectively, taken at $T=35\mathrm{K}$. Fermi level is set to 0 eV for (c)–(h). (e) and (f) Energy distribution curves (EDCs) corresponding to cuts 1 and 2, below and above $T_c$ as indicated. EDCs corresponding to cut 2 shows suppression of intensity near the Fermi level due to the pseudogap of $\mathrm{Cu}{\mathrm{O}}_2$ planes. (g) and (h) Energy-momentum dispersions along momentum cuts 3 and 4, respectively, showing dispersions of two sets of orthogonal CuO-chain bands. The set of chains states indicated by blue arrows shows a gaplike feature with the suppression of intensity near the Fermi level.

Figure 4

Spectroscopic imaging of the DBCO film. (a) Topography of a $20\times 20\mathrm{n}{\mathrm{m}}^2$ field of view, where a differential conductance spectrum is measured within ±150 meV at each location on a 200 × 200 pixels grid. (b) Spatially averaged LDOS spectra for both low $\left(\left|E\right|<30\mathrm{meV}\right)$ and high energies $\left(\left|E\right|<150\mathrm{meV}\right)$. (c) and (d) Spatial variations of the gaps at low-energy and high-energy scales, with insets showing the corresponding distribution histograms. (e) LDOS spectra taken along the line cut in (a), showing spatially uniform low-energy states and heterogeneous high-energy states.