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The pseudogap phenomenon in cuprates is the most mysterious puzzle in theresearch of high-temperature superconductivity. In particular, whether thepseudogap is associated with a crossover or phase transition has been along-standing controversial issue. The tetragonal cuprateHgBa$_2$CuO$_{4+\delta}$, with only one CuO$_2$ layer per primitive cell, is anideal system to tackle this puzzle. Here, we measure the anisotropy of magneticsusceptibility within the CuO$_2$ plane with exceptionally high-precisionmagnetic torque experiments. Our key finding is that a distinct two-foldin-plane anisotropy sets in below the pseudogap temperature $T^*$, whichprovides thermodynamic evidence for a nematic phase transition with brokenfour-fold symmetry. Most surprisingly, the nematic director orients along thediagonal direction of the CuO$_2$ square lattice, in sharp contrast to the bondnematicity reported in various iron-based superconductors and double-layerYBa$_2$Cu$_3$O$_{6+\delta}$, where the anisotropy axis is along the Fe-Fe andCu-O-Cu directions, respectively. Another remarkable feature is that theenhancement of the diagonal nematicity with decreasing temperature issuppressed around the temperature at which short-range charge-density-wave(CDW) formation occurs. This is in stark contrast toYBa$_2$Cu$_3$O$_{6+\delta}$, where the bond nematicity is not influenced by theCDW. Our result suggests a competing relationship between diagonal nematic andCDW order in HgBa$_2$CuO$_{4+\delta}$.

Diagonal Nematicity in the Pseudogap Phase of HgBa$_2$CuO$_{4+\delta}$