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The compound HgBa$_2$CuO$_{4+\Delta}$ (Hg1201) exhibits a simple tetragonalcrystal structure and the highest superconducting transition temperature(T$_c$) among all single Cu-O layer cuprates, with T$_c$ = 97 K (onset) atoptimal doping. Due to a lack of sizable single crystals, experimental work onthis very attractive system has been significantly limited. Thanks to a recentbreakthrough in crystal growth, such crystals have now become available. Here,we demonstrate that it is possible to identify suitable heat treatmentconditions to systematically and uniformly tune the hole concentration ofHg1201 crystals over a wide range, from very underdoped (T$_c$ = 47 K, holeconcentration p ~ 0.08) to overdoped (T$_c$ = 64 K, p ~ 0.22). We then presentquantitative magnetic susceptibility and DC charge transport results thatreveal the very high-quality nature of the studied crystals. Using XPS oncleaved samples, we furthermore demonstrate that it is possible to obtain largesurfaces of good quality. These characterization measurements demonstrate thatHg1201 should be viewed as a model high-temperature superconductor, and theyprovide the foundation for extensive future experimental work.

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