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The electronic structure of the normal state of the underdoped cuprates has thus far remained mysterious, with neither the momentum space location nor the charge carrier type of constituent small Fermi surface pockets being resolved. Whereas quantum oscillations have been interpreted in terms of a nodal-antinodal Fermi surface including electrons at the antinodes, photoemission indicates a solely nodal density-of-states at the Fermi level. Here we examine both these possibilities using extended quantum oscillation measurements. Second harmonic quantum oscillations in underdoped YBa 2 Cu 3 O 6+ x are shown to arise chiefly from oscillations in the chemical potential. We show from the relationship between the phase and amplitude of the second harmonic with that of the fundamental quantum oscillations that there exists a single carrier Fermi surface pocket, likely located at the nodal region of the Brillouin zone, with the observed multiple frequencies arising from warping, bilayer splitting and magnetic breakdown. It is unclear whether the Fermi surface in the normal state of underdoped cuprates is ambipolar or solely nodal. Here, measuring the second harmonic oscillations in underdoped YBa 2 Cu 3 O 6+x reveals the origin as an oscillatory chemical potential, based on which a Fermi surface consisting of a nodal pocket is identified.

Quantum oscillation measurements in the underdoped copper oxide YBa 2 Cu 3 O 6 +  x reveal a nodal electronic structure from charge order, which helps to characterize the normal state out of which superconductivity emerges in the underdoped regime. In search of a ground state For decades, the identity of the normal state from which high-temperature superconductivity originates in copper-oxide materials has remained a mystery. Now Suchitra Sebastian et al . have taken a step towards solving the mystery by obtaining angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa 2 Cu 3 O 6 + x . These measurements reveal a normal ground state comprising Fermi surface pockets in the vicinity of the superconducting gap minima (or nodes). The authors identify a biaxial superlattice structure responsible for the creation of electron-like pockets in this region. An outstanding problem in the field of high-transition-temperature (high- T c ) superconductivity is the identification of the normal state out of which superconductivity emerges in the mysterious underdoped regime 1 . The normal state uncomplicated by thermal fluctuations can be studied using applied magnetic fields that are sufficiently strong to suppress long-range superconductivity at low temperatures 2 , 3 . Proposals in which the normal ground state is characterized by small Fermi surface pockets that exist in the absence of symmetry breaking 1 , 4 , 5 , 6 , 7 , 8 have been superseded by models based on the existence of a superlattice that breaks the translational symmetry of the underlying lattice 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 . Recently, a charge superlattice model that positions a small electron-like Fermi pocket in the vicinity of the nodes (where the superconducting gap is minimum) 8 , 9 , 16 , 17 has been proposed as a replacement for the prevalent superlattice models 10 , 11 , 12 , 13 , 14 that position the Fermi pocket in the vicinity of the pseudogap at the antinodes (where the superconducting gap is maximum) 18 . Although some ingredients of symmetry breaking have been recently revealed by crystallographic studies, their relevance to the electronic structure remains unresolved 19 , 20 , 21 . Here we report angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa 2 Cu 3 O 6 +  x . These measurements reveal a normal ground state comprising electron-like Fermi surface pockets located in the vicinity of the nodes, and also point to an underlying superlattice structure of low frequency and long wavelength with features in common with the charge order identified recently by complementary spectroscopic techniques 14 , 19 , 20 , 21 , 22 .

An enduring question in correlated systems concerns whether superconductivity is favored at a quantum critical point (QCP) characterized by a divergent quasiparticle effective mass. Despite such a scenario being widely postulated in high Tc cuprates and invoked to explain non-Fermi liquid transport signatures, experimental evidence is lacking for a critical divergence under the superconducting dome. We use ultrastrong magnetic fields to measure quantum oscillations in underdoped YBa₂Cu₃O₆₊x, revealing a dramatic doping-dependent upturn in quasiparticle effective mass at a critical metal-insulator transition beneath the superconducting dome. Given the location of this QCP under a plateau in Tc in addition to a postulated QCP at optimal doping, we discuss the intriguing possibility of two intersecting superconducting subdomes, each centered at a critical Fermi surface instability.