Electronic Structure and Superconducting Gap of HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ Revealed by Laser-Based Angle-Resolved Photoemission Spectroscopy

Abstract

The spatially-resolved laser-based high resolution angle resolved photoemission spectroscopy (ARPES) measurements have been performed on the optimally-doped HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ (Hg1223) superconductor with a $T_c$ at 133 K. Two distinct regions are identified on the cleaved surface: the single Fermi surface region where only one Fermi surface is observed, and the double Fermi surface region where two Fermi surface sheets are resolved coming from both the inner (IP) and outer (OP) CuO$_2$ planes. The electronic structure and superconducting gap are measured on both of these two regions. In both cases, the observed electronic states are mainly concentrated near the nodal region. The momentum dependence of superconducting gap deviates from the standard d-wave form. These results indicate that the surface electronic structure of Hg1223 behaves more like that of underdoped cuprates.

Figures (5)

• Figure 1: Spatially resolved ARPES measurements on different cleavage surfaces of Hg1223. (a) Crystal structure of the trilayer cuprate Hg1223, consisting of three CuO$_2$ planes per unit cell. The inner CuO$_2$ plane (IP) is sandwiched between two outer planes (OPs) separated by Ca layers. The right panel illustrates several possible cleavage planes (HgO$_\delta$, BaO or CuO$_2$). (b) AC magnetic susceptibility measurement under a 10 Oe field showing a sharp superconducting transition at $T_c=133$ K with a transition width (10%-90%) of 2.5 K. (c) Real space photocurrent map acquired by point-by-point scanning the sample surface. Two kinds of regions with distinct Fermi surface topology are observed on the surface. (d) Fermi surface mapping obtained from Region 1 (red circle in c) where only a single Fermi surface near the nodal region is observed. To enhance the covered momentum space, we measurement was carried out by applying a bias voltage of -90 V on the sample. (e) Fermi surface mapping obtained from Region 2 (blue circle in c) where two Fermi surface sheets near the nodal region are observed. The measurement was also performed under a -90 V sample bias.
• Figure 2: Electronic structure of Hg1223 measured at 30 K from the single Fermi surface region. The measurement was performed under a sample bias of -30 V. (a) Fermi surface mapping of Hg1223 measured at 30 K in the superconducting state. The red open circles denote the experimentally determined Fermi momenta ($k_F$), and the black dashed curve represents guide to the eyes. (b) The corresponding constant energy contour at a binding energy of 30 meV. (c) Band structures measured along different momentum cuts. The location of the momentum cuts is shown by black lines in (b). All the momentum cuts cross the $(\pi,\pi)$ point when extrapolated. The vertical tick in each panel mark the determined Fermi momenta.
• Figure 3: Superconducting gap of Hg1223 measured in the single Fermi surface region at 30 K. (a) Energy distribution curves (EDCs) measured along the Fermi surface of the single Fermi surface region. The momentum locations of each spectrum (P1-P15) are indicated by black circles in (c). The spectra are vertically offset for clarity. (b) The corresponding symmetrized EDCs from (a). The vertical ticks mark the peak positions of the symmetrized EDCs from which the superconducting gap is extracted. (c) Schematic Fermi surface of Hg1223 in single Fermi surface region with the corresponding Fermi momentum points (P1-P15) labeled. (d) Angular dependence of the superconducting gap size $\Delta(\theta)$ (filled circles) extracted from (b). The open circles are obtained by flipping the filled circles along 45$^\circ$ by considering the nodal mirror plane. The angle $\theta$ is defined as shown in (c). The gap near the nodal region is fitted by a $d$-wave form, $\Delta(\theta) = \Delta_0 \cos(2\theta)$, with $\Delta_0 \approx 41$ meV (solid curve). (e) Momentum dependence of the superconducting gap plotted as a function of $|\cos(k_x a) - \cos(k_y a)|/2$. The gap near the nodal region is fitted by a linear line, $\Delta=\Delta_0\cdot |\cos(k_x a) - \cos(k_y a)|/2$, with $\Delta_0=37$ meV (solid line).
• Figure 4: Electronic structure of Hg1223 measured at 30 K from the double Fermi surface region. The measurement was performed under a sample bias of -30 V. (a) Fermi surface mapping of Hg1223 measured at 30 K in the superconducting state, showing two Fermi surface sheets corresponding to the outer (OP) and the inner (IP) CuO$_2$ planes. The blue (red) open circles denote the experimentally determined Fermi momenta of OP (IP). The two black dashed curves represent guide to the eyes. (b) The corresponding constant energy contour at a binding energy of 30 meV. (c) Band structures measured along different momentum cuts. The location of the momentum cuts is shown by black lines in (b). All the momentum cuts cross the $(\pi,\pi)$ point when extrapolated. The blue and red vertical ticks in each panel mark the Fermi momenta for OP and IP, respectively.
• Figure 5: Superconducting gap of Hg1223 measured in the double Fermi surface region at 30 K. (a) EDCs measured along the IP Fermi surface. The momentum locations of each spectrum (IP1-IP14) are indicated by red circles in (e). The spectra are vertically offset for clarity. (b) The corresponding symmetrized EDCs from (a). The vertical ticks mark the peak positions of the symmetrized EDCs from which the superconducting gap is extracted. (c) EDCs measured along the OP Fermi surface. The momentum locations of each spectrum (OP1-OP14) are indicated by blue circles in (e). (d) The corresponding symmetrized EDCs from (c). The vertical ticks mark the peak positions of the symmetrized EDCs from which the superconducting gap is extracted. (e) Schematic Fermi surfaces of Hg1223 in double Fermi surface region, showing the inner (IP) and outer (OP) Fermi surface sheets and the corresponding measurement points. (f) Angular dependence of the superconducting gap size $\Delta(\theta)$ for both IP (filled red circles) and OP (filled blue circles) extracted from (b) and (d), respectively. The open circles are obtained by flipping the filled circles along 45$^\circ$ by considering the nodal mirror plane. The angle $\theta$ is defined as shown in (e). The gap is fitted by a $d$-wave form, $\Delta(\theta) = \Delta_0 \cos(2\theta)$, with $\Delta_0 \approx 52$ meV for IP (red solid curve) and $\Delta_0 \approx 41$ meV for OP (blue solid curve). (g) Momentum dependence of the superconducting gap plotted as a function of $|\cos(k_x a) - \cos(k_y a)|/2$. The gap is fitted by a linear line, $\Delta=\Delta_0\cdot |\cos(k_x a) - \cos(k_y a)|/2$, with $\Delta_0=47$ meV for IP (red solid line) and $\Delta_0=35$ meV for OP (blue solid line).