Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ

Close to optimal doping, the copper oxide superconductors show 'strange metal' behaviour, suggestive of strong fluctuations associated with a quantum critical point. Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting 'dome'. The underdoped region of the temperature-doping phase diagram from which superconductivity emerges is referred to as the 'pseudogap' because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa2Cu3O6+δ is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behaviour and therefore superconductivity in the copper oxide superconductors.

Scale-invariant magnetoresistance in a cuprate superconductor

The anomalous metallic state in the high-temperature superconducting cuprates is masked by superconductivity near a quantum critical point. Applying high magnetic fields to suppress superconductivity has enabled detailed studies of the normal state, yet the direct effect of strong magnetic fields on the metallic state is poorly understood. We report the high-field magnetoresistance of thin-film La_2-x Sr _x CuO₄ cuprate in the vicinity of the critical doping, 0.161 ≤ p ≤ 0.190. We find that the metallic state exposed by suppressing superconductivity is characterized by magnetoresistance that is linear in magnetic fields up to 80 tesla. The magnitude of the linear-in-field resistivity mirrors the magnitude and doping evolution of the well-known linear-in-temperature resistivity that has been associated with quantum criticality in high-temperature superconductors.

Resonant torsion magnetometry in anisotropic quantum materials

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

Unfolding the physics of URu2Si2 through silicon to phosphorus substitution

The heavy fermion intermetallic compound URu₂Si₂ exhibits a hidden-order phase below the temperature of 17.5 K, which supports both anomalous metallic behavior and unconventional superconductivity. While these individual phenomena have been investigated in detail, it remains unclear how they are related to each other and to what extent uranium f-electron valence fluctuations influence each one. Here we use ligand site substituted URu₂Si_2-xP_x to establish their evolution under electronic tuning. We find that while hidden order is monotonically suppressed and destroyed for x≤0.035, the superconducting strength evolves non-monotonically with a maximum near x≈0.01 and that superconductivity is destroyed near x≈0.028. This behavior reveals that hidden order depends strongly on tuning outside of the U f-electron shells. It also suggests that while hidden order provides an environment for superconductivity and anomalous metallic behavior, it's fluctuations may not be solely responsible for their progression.

The heavy fermion compound URu₂Si₂ displays a hidden order phase and superconductivity at low temperatures. Here, the authors perform substitution studies—partially replacing silicon with phosphorus—and study the effects on hidden order and superconductivity.

Nodal bilayer-splitting controlled by spin-orbit interactions in underdoped high-Tc cuprates

The highest superconducting transition temperatures in the cuprates are achieved in bilayer and trilayer systems, highlighting the importance of interlayer interactions for high Tc. It has been argued that interlayer hybridization vanishes along the nodal directions by way of a specific pattern of orbital overlap. Recent quantum oscillation measurements in bilayer cuprates have provided evidence for a residual bilayer-splitting at the nodes that is sufficiently small to enable magnetic breakdown tunneling at the nodes. Here we show that several key features of the experimental data can be understood in terms of weak spin-orbit interactions naturally present in bilayer systems, whose primary effect is to cause the magnetic breakdown to be accompanied by a spin flip. These features can now be understood to include the equidistant set of three quantum oscillation frequencies, the asymmetry of the quantum oscillation amplitudes in c-axis transport compared to ab-plane transport, and the anomalous magnetic field angle dependence of the amplitude of the side frequencies suggestive of small effective g-factors. We suggest that spin-orbit interactions in bilayer systems can further affect the structure of the nodal quasiparticle spectrum in the superconducting phase. PACS numbers: 71.45.Lr, 71.20.Ps, 71.18.+y.

Magnetic field tuning of an excitonic insulator between the weak and strong coupling regimes in quantum limit graphite

The excitonic insulator phase has long been predicted to form in proximity to a band gap opening in the underlying band structure. The character of the pairing is conjectured to crossover from weak (BCS-like) to strong coupling (BEC-like) as the underlying band structure is tuned from the metallic to the insulating side of the gap opening. Here we report the high-magnetic field phase diagram of graphite to exhibit just such a crossover. By way of comprehensive angle-resolved magnetoresistance measurements, we demonstrate that the underlying band gap opening occurs inside the magnetic field-induced phase, paving the way for a systematic study of the BCS-BEC-like crossover by means of conventional condensed matter probes.

Branch-cut singularities in thermodynamics of Fermi liquid systems

The recently measured spin susceptibility of the two-dimensional electron gas exhibits a strong dependence on temperature, which is incompatible with the standard Fermi liquid phenomenology. In this article, we show that the observed temperature behavior is inherent to ballistic two-dimensional electrons. Besides the single-particle and collective excitations, the thermodynamics of Fermi liquid systems includes effects of the branch-cut singularities originating from the edges of the continuum of pairs of quasiparticles. As a result of the rescattering induced by interactions, the branch-cut singularities generate nonanalyticities in the thermodynamic potential that reveal themselves in anomalous temperature dependences. Calculation of the spin susceptibility in such a situation requires a nonperturbative treatment of the interactions. As in high-energy physics, a mixture of the collective excitations and pairs of quasiparticles can effectively be described by a pole in the complex momentum plane. This analysis provides a natural explanation for the observed temperature dependence of the spin susceptibility, both in sign and in magnitude.

Robust spin correlations at high magnetic fields in the harmonic honeycomb iridates

The complex antiferromagnetic orders observed in the honeycomb iridates are a double-edged sword in the search for a quantum spin-liquid: both attesting that the magnetic interactions provide many of the necessary ingredients, while simultaneously impeding access. Focus has naturally been drawn to the unusual magnetic orders that hint at the underlying spin correlations. However, the study of any particular broken symmetry state generally provides little clue about the possibility of other nearby ground states. Here we use magnetic fields approaching 100 Tesla to reveal the extent of the spin correlations in γ-lithium iridate. We find that a small component of field along the magnetic easy-axis melts long-range order, revealing a bistable, strongly correlated spin state. Far from the usual destruction of antiferromagnetism via spin polarization, the high-field state possesses only a small fraction of the total iridium moment, without evidence for long-range order up to the highest attainable magnetic fields.The complex antiferromagnetic orders observed in the honeycomb iridates prevent access to a spin-liquid ground state. Here the authors apply extremely high magnetic fields to destroy the antiferromagnetic order in γ-lithium iridate and reveal a bistable, strongly correlated spin state.

Spin polarization of electrons by nonmagnetic heterostructures: the basics of spin optics

We propose to use the lateral interface between two regions with different strengths of the spin-orbit interaction(s) to spin polarize the electrons in gated two-dimensional semiconductor heterostructures. For a beam with a nonzero angle of incidence, the transmitted electrons will split into two spin polarization components propagating at different angles. We analyze the refraction at such an interface and outline the basic schemes for filtration and control of the electron spin.

Vortex viscosity in magnetic superconductors due to radiation of spin waves

In type-II superconductors that contain a lattice of magnetic moments, vortices polarize the magnetic system inducing additional contributions to the vortex mass, vortex viscosity, and vortex-vortex interaction. Extra magnetic viscosity is caused by radiation of spin waves by a moving vortex. Like in the case of Cherenkov radiation, this effect has a characteristic threshold behavior and the resulting vortex viscosity may be comparable to the well-known Bardeen-Stephen contribution. The threshold behavior leads to an anomaly in the current-voltage characteristics, and a drop in dissipation for a current interval that is determined by the magnetic excitation spectrum.

Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa2CuO4+δ

High magnetic fields have revealed a surprisingly small Fermi surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue concerns the doping extent of such a state and its relationship to the principal pseudogap and superconducting phases. We employ pulsed magnetic-field measurements on the cuprate [Formula: see text]Cu[Formula: see text] to identify signatures of Fermi-surface reconstruction from a sign change of the Hall effect and a peak in the temperature-dependent planar resistivity. We trace the termination of Fermi-surface reconstruction to two hole concentrations where the superconducting upper critical fields are found to be enhanced. One of these points is associated with the pseudogap endpoint near optimal doping. These results connect the Fermi-surface reconstruction to both superconductivity and the pseudogap phenomena.

One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning

The unusual correlated state that emerges in URu2Si2 below T HO = 17.5 K is known as "hidden order" because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are "hidden." We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across T HO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

Universality of single-particle spectra of cuprate superconductors

All the available data for the dispersion and linewidth of the single-particle spectra above the superconducting gap and the pseudogap in metallic cuprates for any doping have universal features. The linewidth is linear in energy below a scale omega(c) and constant above. The cusp in the linewidth at omega(c) mandates, due to causality, a waterfall, i.e., a vertical feature in the dispersion. These features are predicted by a recent microscopic theory. We find that all data can be quantitatively fitted by the theory with a coupling constant lambda(0) and an upper cutoff at omega(c), which vary by less than 50% among the different cuprates and for varying dopings. The microscopic theory also gives these values to within factors of O(2).

Screening of point charge impurities in highly anisotropic metals: application to mu+-spin relaxation in underdoped cuprate superconductors

We calculate the screening charge density distribution due to a point charge, such as that of a positive muon (mu+), placed between the planes of a highly anisotropic layered metal. In underdoped hole cuprates the screening charge converts the charge density in the metallic-plane unit cells in the vicinity of the mu+ to nearly its value in the insulating state. The current-loop-ordered state observed by polarized neutron diffraction then vanishes in such cells, and also in nearby cells over a distance of order the intrinsic correlation length of the loop-ordered state. This strongly suppresses the magnetic field at the mu+ site. We estimate this suppressed field in underdoped YBa2Cu3O6+x and La2-xSrxCuO4, and find consistency with the observed approximately 0.2 G field in the former case and the observed upper bound of approximately 0.2 G in the latter case. This resolves the controversy between the neutron diffraction and mu-spin relaxation experiments.

Thermodynamic and electrical transport investigation of URu2Si2-x P x

Magnetic susceptibility, electrical resistivity, and heat capacity results are reported for the chemical substitution series URu₂Si_2-x P _x for [Formula: see text]. This study expands in detail on work recently reported in Gallagher et al (2016 Nat. Commun. 10712), which focused on the small x region of this substitution series. Measurements presented here reveal persistent hybridization between the f- and conduction electrons and strong variation of the low temperature behavior with increasing x. Hidden order and superconductivity are rapidly destroyed for [Formula: see text] and are replaced for [Formula: see text] by a region with Kondo coherence but no ordered state. Antiferromagnetism abruptly appears for [Formula: see text]. This phase diagram differs significantly from those produced by most other tuning strategies in URu₂Si₂, including applied pressure, high magnetic fields, and isoelectronic chemical substitution (i.e. Ru  →  Fe and Os), where hidden order and magnetism share a common phase boundary. Besides revealing an intriguing evolution of the low temperature states, this series provides a setting in which to investigate the influence of electronic tuning, where probes that are sensitive to the Fermi surface and the symmetry of the ordered states will be useful to unravel the anomalous behavior of URu₂Si₂.