Single reconstructed Fermi surface pocket in an underdoped single layer cuprate superconductor

The observation of a small reconstructed Fermi surface with quantum oscillations in bilayer YBa$_{\mathrm{2}}$Cu$_{\mathrm{3}}$O$_{\mathrm{6+x}}$ opened a path towards identifying broken symmetry states in underdoped cuprates. However, the multi-frequency spectrum of quantum oscillations and complications from bilayer coupling has rendered such an identification inconclusive. Our high resolution quantum oscillation study of the structurally simpler single layer cuprate HgBa$_{\mathrm{2}}$CuO$_{\mathrm{4+\delta }}$ (Hg1201) reveal a single oscillatory component with no signatures of magnetic breakdown tunneling. From this, we conclude that the reconstructed Fermi surface of Hg1201 is comprised of only a single pocket with negligible c-axis warping. Quantitative modeling of these results allow us to determine that biaxial charge-density-wave order is responsible for Fermi surface reconstruction. We find that the characteristic reconstruction gap is a significant fraction of the pseudogap energy. `Criss-crossed' uniaxial charge stripes is ruled out as a viable alternative to biaxial order within a CuO$_{\mathrm{2}}$ plane for Hg1201.