Demonstrating the model nature of the high-temperature superconductor ${\text{HgBa}}_2{\text{CuO}}_{4+\delta }$

The compound ${\text{HgBa}}_2{\text{CuO}}_{4+\delta }$ (Hg1201) exhibits a simple tetragonal crystal structure and the highest superconducting transition temperature $\left(T_c\right)$ among all single Cu-O layer cuprates, with $T_c=97\text{K}$ (onset) at optimal doping. Due to a lack of sizable single crystals, experimental work on this very attractive system has been significantly limited. Thanks to a recent breakthrough in crystal growth, such crystals have now become available. Here we demonstrate that it is possible to identify suitable heat treatment conditions to systematically and uniformly tune the hole concentration of Hg1201 crystals over a wide range, from very underdoped ($T_c=47\text{K}$, hole concentration $p\approx 0.08$) to overdoped $\left(T_c=64\text{K},p\approx 0.22\right)$. We then present quantitative magnetic susceptibility and dc charge transport results that reveal the very high-quality nature of the studied crystals. Using x-ray photoemission spectroscopy on cleaved samples, we furthermore demonstrate that it is possible to obtain large surfaces of good quality. These characterization measurements demonstrate that Hg1201 should be viewed as a model high-temperature superconductor.

Figure 1

(Color online) (a) Tetragonal crystal structure of ${\text{HgBa}}_2{\text{CuO}}_{4+\delta }$, including the position O(3) of the oxygen dopant [red (light gray) circle]. The Cu atoms reside at the center of ${\text{CuO}}_6$ octahedra. (b) ZFC (measured in 10 Oe; blue (dark gray)] and FC [cooled in 10 Oe and measured in 10 Oe; red (light gray)] susceptibility curves as a function of temperature for a sample with $T_c=79\left(2\right)\text{K}$ (midpoint). The FC to ZFC susceptibility ratio is very high, suggesting an unusually small density of vortex pinning centers. The data shown here were obtained for a sample of $\approx 0.3\text{mg}$ mass which was annealed for 1 month at $500°\text{C}$ in air.

Figure 2

(Color online) (a) The REM measurement (cooled in 5 Oe, with the field applied perpendicular to the ab planes) is used as a bulk probe of the superconducting state during annealing studies. For as-grown samples and for samples that were not annealed sufficiently long, the superconducting transition is typically broad and/or multisteplike [black filled circles and green (dark gray) open circles], indicating that the sample should be further annealed in order to change the overall oxygen concentration and/or to obtain better homogeneity. For a sufficiently long annealed sample [red (light gray) filled circles], the transition is sharp, which implies a macroscopically homogeneous oxygen distribution. As shown in the inset, typical ZFC and FC (measured/cooled in 5 Oe, $B\perp ab$) data for an insufficiently long annealed sample are not sensitive enough to a possibly broad distribution of transition temperatures. Those curves, although quite sharp, may suggest an incorrect value of $T_c$. We note that the FC/ZFC ratio is rather low because the measurement was performed on a larger crystal $\left(\approx 100\text{mg}\right)$, subsequently used for an inelastic-neutron-scattering study. Large crystals tend to have more pinning centers. The key observation is that the REM measurement allows us to determine whether our crystals are thoroughly annealed. (b) Temperature dependences of the ZFC, FC, and REM magnetic susceptibilities (measured moment divided by the applied magnetic field) for a homogeneous sample measured/cooled in high (40 Oe, $B\perp ab$; black points) and low fields [6 Oe, $B\perp ab$; red (light gray) points]. Inset: schematic temperature dependence of the upper $\left(H_{c2}\right)$ and lower critical fields $\left(H_{c1}\right)$ of the HTSC (not to scale) (Ref. 30).

Figure 3

(Color online) (a) Resistivity for three underdoped crystals that were annealed at $520°\text{C}$ in air (and subsequently quenched by placing them onto a room-temperature metal plate) to yield $T_c=81\text{K}$. The approximate crystal dimensions were $0.5\times 0.5\times 0.75{\text{mm}}^3$ and the absolute value of the resistivity was determined to within $\approx 20\%$. (b) The remarkable agreement of the three resistivity curves when normalized at 400 K reveals the high sample quality. Resistivity is a bulk probe that is very sensitive to disorder and the presence of secondary phases. The excellent agreement among the three curves suggests that the samples are electronically identical. The low-temperature deviation from linearity suggests that for underdoped Hg1201 with $T_c=81\text{K}$, the pseudogap temperature is $T^{\ast }=250\left(20\right)\text{K}$. The resistivity was measured using electrical leads placed as shown in the inset.

Figure 4

(Color online) Surfaces of two cleaved Hg1201 crystals photographed by use of an optical microscope. One of the surfaces is enlarged to demonstrate its high quality.

Figure 5

(Color online) X-ray photoemission wide-energy survey scan (energy resolution: 1eV) reveals elemental composition of the surface. Within the resolution of the measurement, no trace of unwanted elements is found. All peaks are observed at the expected energy, as listed in the Table .

Figure 6

(Color online) (a) Based on the empirical equation for the dependence of $T_c$ on hole concentration, $T_c=T_{c,\text{max}}\left[1-82.6{\left(p-0.16\right)}^2\right]$ (Ref. 39), the estimated doping range is $0.08<p<0.22$, which covers a large region of the phase diagram. We note that $T_c$ is defined as the transition midpoint. The highest onset transition temperature observed in our crystals was 97 K. (b) ZFC temperature dependences of the magnetic susceptibility and corresponding annealing conditions (Table ) for eight different dopings.