Fragile charge order in the nonsuperconducting ground state of the underdoped high-temperature superconductors

The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa₂Cu₃O6+δ. Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa₂Cu₄O₈, which reveals similar Fermi surface properties to YBa₂Cu₃O6+δ, despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa₂Cu₃O6+δ. Fermi surface reconstruction in YBa₂Cu₄O₈ is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations.The normal state of the underdoped copper oxide superconductors has proven to be even more perplexing than the d-wave superconducting state in these materials. At high temperatures in zero magnetic fields, the normal state of the underdoped cuprates comprises an unconventional Fermi surface of truncated “Fermi arcs” in momentum space, which is referred to as the pseudogap state (1). At low temperatures in high magnetic fields, quantum oscillations reveal the nonsuperconducting ground state in various families of underdoped hole-doped copper oxide superconductors to comprise small Fermi surface pockets (2–15). These small Fermi pockets in YBa₂Cu₃O6+δ have been identified as nodal electron pockets (2, 3, 11, 16, 17) originating from Fermi surface reconstruction associated with charge order measured by X-ray diffraction (18–20), ultrasound (21), nuclear magnetic resonance (22), and optical reflectometry (23). However, various aspects of the underlying charge order and the associated Fermi surface reconstruction remain obscure. A central question pertains to the origin of this charge order, curious features of which include a short correlation length in zero magnetic field that grows with increasing magnetic field and decreasing temperature (20). It is crucial to understand the nature of this ground-state order that is related to the high-temperature pseudogap state and delicately balanced with the superconducting ground state. Here, we shed light on the nature of this state by performing extended magnetic field, temperature, and tilt angle-resolved quantum oscillation experiments in the stoichiometric copper oxide superconductor YBa₂Cu₄O₈ (24). This material with double CuO chains has fixed oxygen stoichiometry, making it a model system to study. YBa₂Cu₄O₈ avoids disorder associated with the fractional oxygen stoichiometry in the YBa₂Cu₃O6+δ chains, which has been shown by microwave conductivity to be the dominant source of weak-limit (Born) scattering (25).Intriguingly, we find magnetic field- and angle-dependent signatures of quantum oscillations in YBa₂Cu₄O₈ (13, 14) that are very similar to those in YBa₂Cu₃O6+δ, indicating a similar nodal Fermi surface that arises from Fermi surface reconstruction by charge order with orthogonal wave vectors (16). However, the same X-ray diffraction measurements that show a Bragg peak characteristic of charge order in YBa₂Cu₃O6+δ for a range of hole dopings from 0.084≤p≤0.164 (19, 20, 26) have, thus far, not revealed a Bragg peak in the case of YBa₂Cu₄O₈ (19). We suggest that charge order enhanced by applied magnetic fields reconstructs the Fermi surface in YBa₂Cu₄O₈, whereas charge order is revealed even in zero magnetic fields in YBa₂Cu₃O6+δ because of pinning by increased disorder from oxygen vacancies.