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 field
s, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3O6+x. Here we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveal similar Fermi surface properties to YBa2Cu3O6+x, despite an absence of charge order signatures in the same spectroscopic techniques such as x-ray diffraction that revealed signatures of charge order in YBa2Cu3O6+x. 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 symmetry, and/or its occurrence as a subsidiary to more robust underlying electronic correlations.
One of the leading challenges of condensed matter physics in the past few decades in an understanding of the high-temperature copper-oxide superconductors. While the d-wave character of the superconducting state is well understood, the normal state i
n the underdoped regime has eluded understanding. Here we review the past few years of quantum oscillation measurements performed in the underdoped cuprates that have culminated in an understanding of the normal ground state of these materials. A nodal electron pocket created by charge order is found to characterise the normal ground state in YBa2Cu3O6+x and is likely universal to a majority of the cuprate superconductors. An open question remains regarding the origin of the suppression of the antinodal density of states at the Fermi energy in the underdoped normal state, either from mainly charge correlations, or more likely, from mainly pairing and / or magnetic correlations that precede charge order.
An outstanding problem in the field of high-transition-temperature (high Tc) superconductivity is the identification of the normal state out of which superconductivity emerges in the mysterious underdoped regime. The normal state uncomplicated by the
rmal fluctuations is effectively accessed by the use of applied magnetic fields sufficiently strong to suppress long-range superconductivity at low temperatures. Proposals in which the normal ground state is characterised by small Fermi surface pockets that exist in the absence of symmetry breaking have been superseded by models based on the existence of a superlattice that breaks the translational symmetry of the underlying lattice. 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) has been proposed a replacement for the prevalent superlattice models that position the Fermi pocket in the vicinity of the pseudogap at the antinodes (where the superconducting gap is maximum). Although some ingredients of symmetry breaking have been recently revealed by crystallographic studies, their relevance to the electronic structure remains unresolved. Here we report angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa2Cu3O6+x. These measurements reveal a normal ground state comprising electron-like Fermi surface pockets located in the vicinity of the superconducting gap minima (or nodes), and further 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.
Insulators occur in more than one guise, a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here we report the observation of an unusual insulating state with an electrically in
sulating bulk that simultaneously yields bulk quantum oscillations with characteristics of an unconventional Fermi liquid. We present quantum oscillation measurements of magnetic torque in high purity single crystals of the Kondo insulator SmB6, which reveal quantum oscillation frequencies characteristic of a large three-dimensional conduction electron Fermi surface similar to the metallic rare earth hexaborides such as PrB6 and LaB6. The quantum oscillation amplitude strongly increases at low temperatures, appearing strikingly at variance with conventional metallic behaviour.
Insight into the electronic structure of the pnictide family of superconductors is obtained from quantum oscillation measurements. Here we review experimental quantum oscillation data that reveal a transformation from large quasi-two dimensional elec
tron and hole cylinders in the paramagnetic overdoped members of the pnictide family to significantly smaller three-dimensional Fermi surface sections in the antiferromagnetic parent members, via a potential quantum critical point at which an effective mass enhancement is observed. Similarities with the Fermi surface evolution from the overdoped to the underdoped normal state of the cuprate superconducting family are discussed, along with the enhancement in antiferromagnetic correlations in both these classes of materials, and the potential implications for superconductivity.
We report quantum oscillations in underdoped YBa2Cu3O6.56 over a significantly large range in magnetic field extending from 24 to 101 T, enabling three well-spaced low frequencies at 440 T, 532 T, and 620 T to be clearly resolved. We show that a smal
l nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0 - {Delta}F, F0, and F0 + {Delta}F and accompanying beat pattern similar to that observed experimentally, on invoking magnetic breakdown tunneling at the nodes. The relative amplitudes of the multiple frequencies observed experimentally in quantum oscillation measurements are shown to be reproduced using a value of nodal bilayer gap quantitatively consistent with that measured in photoemission experiments in the underdoped regime.
We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high m
agnetic fields in the underdoped cuprates that reveal a small Fermi surface section comprising quasiparticles that obey Fermi-Dirac statistics, unaccompanied by other states of comparable thermodynamic mass at the Fermi level. The location of the observed Fermi surface section at the nodes is indicated by a body of evidence including the collapse in Fermi velocity measured by quantum oscillations, which is found to be associated with the nodal density of states observed in angular resolved photoemission, the persistence of quantum oscillations down to low fields in the vortex state, the small value of density of states from heat capacity and the multiple frequency quantum oscillation pattern consistent with nodal magnetic breakdown of bilayer-split pockets. A nodal Fermi surface pocket is further consistent with the observation of a density of states at the Fermi level concentrated at the nodes in photoemission experiments, and the antinodal pseudogap observed by photoemission, optical conductivity, nuclear magnetic resonance Knight shift, as well as other complementary diffraction, transport and thermodynamic measurements. One of the possibilities considered is that the small Fermi surface pockets observed at high magnetic fields can be understood in terms of Fermi surface reconstruction by a form of small wavevector charge order, observed over long lengthscales in experiments such as nuclear magnetic resonance and x-ray scattering, potentially accompanied by an additional mechanism to gap the antinodal density of states.
The mystery of the normal state in the underdoped cuprates has deepened with the use of newer and complementary experimental probes. While photoemission studies have revealed solely `Fermi arcs centered on nodal points in the Brillouin zone at which
holes aggregate upon doping, more recent quantum oscillation experiments have been interpreted in terms of an ambipolar Fermi surface, that includes sections containing electron carriers located at the antinodal region. To address the question of whether an ambipolar Fermi surface truly exists, here we utilize measurements of the second harmonic quantum oscillations, which reveal that the amplitude of these oscillations arises mainly from oscillations in the chemical potential, providing crucial information on the nature of the Fermi surface in underdoped YBa2Cu3O6+x. In particular, the detailed relationship between the second harmonic amplitude and the fundamental amplitude of the quantum oscillations leads us to the conclusion that there exists only a single underlying quasi-two dimensional Fermi surface pocket giving rise to the multiple frequency components observed via the effects of warping, bilayer splitting and magnetic breakdown. A range of studies suggest that the pocket is most likely associated with states near the nodal region of the Brillouin zone of underdoped YBa2Cu3O6+x at high magnetic fields.
We report the direct observation of multiple `spin zeroes in angle-dependent magnetic quantum oscillations measured up to 85T in YBa2Cu3O6+x, at which the amplitude falls to a deep minimum accompanied by a phase inversion of the measured quantum osci
llations, enabling the product of the effective mass and effective g-factor m*g* to be tightly constrained. We find an evolution of the location of the spin zeros with applied magnetic field, and suggest that this effect and the absence of a spin zero at low angles can be produced by more than one Fermi surface component, and an effective g-factor with a subtle anisotropy between in-plane and out-of-plane crystalline directions.
An enduring question in correlated systems concerns whether superconductivity is favoured at a quantum critical point (QCP) characterised 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 ultra-strong 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 centred at a critical Fermi surface instability.
