Quasi-2D Fermi surface in the anomalous superconductor UTe2.

The heavy fermion paramagnet UTe2 exhibits numerous characteristics of spin-triplet superconductivity. Efforts to understand the microscopic details of this exotic superconductivity have been impeded by uncertainty regarding the underlying electronic structure. Here we directly probe the Fermi surface of UTe2 by measuring magnetic quantum oscillations in pristine quality crystals. We find an angular profile of quantum oscillatory frequency and amplitude that is characteristic of a quasi-2D Fermi surface, which we find is well described by two cylindrical Fermi sheets of electron- and hole-type respectively. Additionally, we find that both cylindrical Fermi sheets possess considerable undulation but negligible small-scale corrugation, which may allow for their near-nesting and therefore promote magnetic fluctuations that enhance the triplet pairing mechanism. Importantly, we find no evidence for the presence of any 3D Fermi surface sections. Our results place strong constraints on the possible symmetry of the superconducting order parameter in UTe2.

Author Correction: Superconductivity mediated by polar modes in ferroelectric metals.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Superconductivity mediated by polar modes in ferroelectric metals.

The occurrence of superconductivity in doped SrTiO3 at low carrier densities points to the presence of an unusually strong pairing interaction that has eluded understanding for several decades. We report experimental results showing the pressure dependence of the superconducting transition temperature, Tc, near to optimal doping that sheds light on the nature of this interaction. We find that Tc increases dramatically when the energy gap of the ferroelectric critical modes is suppressed, i.e., as the ferroelectric quantum critical point is approached in a way reminiscent to behaviour observed in magnetic counterparts. However, in contrast to the latter, the coupling of the carriers to the critical modes in ferroelectrics is predicted to be small. We present a quantitative model involving the dynamical screening of the Coulomb interaction and show that an enhancement of Tc near to a ferroelectric quantum critical point can arise due to the virtual exchange of longitudinal hybrid-polar-modes, even in the absence of a strong coupling to the transverse critical modes.

Prospects and applications near ferroelectric quantum phase transitions: a key issues review.

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T c's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.

Heavy fermions. Unconventional Fermi surface in an insulating state.

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 insulating 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 behavior.

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 YBa2Cu3(6+δ). Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveals similar Fermi surface properties to YBa2Cu3(6+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 YBa2Cu3(6+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.

Normal-state nodal electronic structure in underdoped high-Tc copper oxides.

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 thermal fluctuations can be studied using applied magnetic fields that are sufficiently strong to suppress long-range superconductivity at low temperatures. Proposals in which the normal ground state is characterized 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 as 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 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.

Quantum oscillations from nodal bilayer magnetic breakdown in the underdoped high temperature superconductor YBa2Cu3O(6+x).

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±10, 532±2, and 620±10 T to be clearly resolved. We show that a small nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0-ΔF, F0, and F0+ΔF 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.

Chemical potential oscillations from nodal Fermi surface pocket in the underdoped high-temperature superconductor YBa2Cu3O(6+x).

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 YBa2Cu3O(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.

Metal-insulator quantum critical point beneath the high Tc superconducting dome.

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 T(c) 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 YBa(2)Cu(3)O(6+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 T(c) 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.

Spin-order driven Fermi surface reconstruction revealed by quantum oscillations in an underdoped high Tc superconductor.

We use quantum oscillation measurements to distinguish between spin and orbital components of the lowest energy quasiparticle excitations in YBa(2)Cu(3)O(6.54), each of which couple differently to a magnetic field. Our measurements reveal the phase of the observed quantum oscillations to remain uninverted over a wide angular range, indicating that the twofold spin degeneracy of the Landau levels is virtually unaltered by the magnetic field. The inferred suppression of the spin degrees of freedom indicates a spin-density wave is responsible for creation of the small Fermi surface pockets in underdoped YBa(2)Cu(3)O(6+x)--further suggesting that excitations of this phase are important contributors to the unconventional superconducting pairing mechanism.

A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor.

To understand the origin of superconductivity, it is crucial to ascertain the nature and origin of the primary carriers available to participate in pairing. Recent quantum oscillation experiments on high-transition-temperature (high-T(c)) copper oxide superconductors have revealed the existence of a Fermi surface akin to that in normal metals, comprising fermionic carriers that undergo orbital quantization. The unexpectedly small size of the observed carrier pocket, however, leaves open a variety of possibilities for the existence or form of any underlying magnetic order, and its relation to d-wave superconductivity. Here we report experiments on quantum oscillations in the magnetization (the de Haas-van Alphen effect) in superconducting YBa(2)Cu(3)O(6.51) that reveal more than one carrier pocket. In particular, we find evidence for the existence of a much larger pocket of heavier mass carriers playing a thermodynamically dominant role in this hole-doped superconductor. Importantly, characteristics of the multiple pockets within this more complete Fermi surface impose constraints on the wavevector of any underlying order and the location of the carriers in momentum space. These constraints enable us to construct a possible density-wave model with spiral or related modulated magnetic order, consistent with experimental observations.

Superconductivity without phonons.

The idea of superconductivity without the mediating role of lattice vibrations (phonons) has a long history. It was realized soon after the publication of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity 50 years ago that a full treatment of both the charge and spin degrees of freedom of the electron predicts the existence of attractive components of the effective interaction between electrons even in the absence of lattice vibrations--a particular example is the effective interaction that depends on the relative spins of the electrons. Such attraction without phonons can lead to electronic pairing and to unconventional forms of superconductivity that can be much more sensitive than traditional (BCS) superconductivity to the precise details of the crystal structure and to the electronic and magnetic properties of a material.

de Haas-van Alphen effect in ZrZn2 under pressure: crossover between two magnetic states.

We report measurements of the de Haas-van Alphen effect in ZrZn2 under hydrostatic pressures up to 21 kbar where the Curie temperature vanishes. The exchange splitting of a Fermi surface changes in behavior with increasing magnetic field, which is qualitatively consistent with the behavior of the high-field magnetization, suggesting the existence of a crossover between two distinct magnetic states. These and previously unexplained findings may be understood in terms of a p-T-B phase diagram qualitatively similar to that of the ferromagnetic superconductor UGe2.

Fermi-liquid breakdown in the paramagnetic phase of a pure metal.

Fermi-liquid theory (the standard model of metals) has been challenged by the discovery of anomalous properties in an increasingly large number of metals. The anomalies often occur near a quantum critical point--a continuous phase transition in the limit of absolute zero, typically between magnetically ordered and paramagnetic phases. Although not understood in detail, unusual behaviour in the vicinity of such quantum critical points was anticipated nearly three decades ago by theories going beyond the standard model. Here we report electrical resistivity measurements of the 3d metal MnSi, indicating an unexpected breakdown of the Fermi-liquid model--not in a narrow crossover region close to a quantum critical point where it is normally expected to fail, but over a wide region of the phase diagram near a first-order magnetic transition. In this regime, corrections to the Fermi-liquid model are expected to be small. The range in pressure, temperature and applied magnetic field over which we observe an anomalous temperature dependence of the electrical resistivity in MnSi is not consistent with the crossover behaviour widely seen in quantum critical systems. This may suggest the emergence of a well defined but enigmatic quantum phase of matter.

Ferromagnetic superconductivity driven by changing Fermi surface topology.

We introduce a simple but powerful zero temperature Stoner model to explain the unusual phase dia-gram of the ferromagnetic superconductor, UGe2. Triplet superconductivity is driven in the ferromagnetic phase by tuning the majority spin Fermi level through one of two peaks in the paramagnetic density of states (DOS). Each peak is associated with a metamagnetic jump in magnetization. The twin-peak DOS may be derived from a tight-binding, quasi-one-dimensional band structure, inspired by previous band-structure calculations.

Evolution of Fermi-liquid interactions in Sr2RuO4 under pressure.

We have measured the temperature and field dependence of the resistivity of the unconventional superconductor Sr2RuO4 at pressures up to 3.3 GPa. Using the Shubnikov-de Haas effect, we find that the Fermi surface sheet believed to be primarily responsible for superconductivity becomes more two-dimensional with increasing pressure, a surprising result that is, however, consistent with a recent model of orbital-dependent superconductivity in this system. Many-body enhancements and the superconducting transition temperature all fall gradually with increasing pressure, contrary to previous suggestions of a ferromagnetic quantum critical point at approximately 3 GPa.

Metamagnetic quantum criticality in metals.

We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent z = 3) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on Sr3Ru2O7 except very near to the critical point itself.

Non-Fermi-liquid nature of the normal state of itinerant-electron ferromagnets.

A century of research on magnetic phenomena had led to the view that the normal state of itinerant-electron ferromagnets such as Fe, Ni and Co could be described in terms of the standard model of the metallic state or its extension known as the nearly ferromagnetic Fermi liquid theory. In recent years, however, a large body of observations has accumulated from various complex intermetallic systems that raises the possibility that this assumption might be wrong. Here we examine this issue by means of high-precision measurements of the electrical transport and magnetic properties of pure ferromagnets-in particular, MnSi-in which the Curie temperature is tuned towards absolute zero by the application of hydrostatic pressure. With this method, it is possible for us to study the normal state over an extraordinarily large range of temperature of up to five orders of magnitude above the Curie temperature. Our results using MnSi reveal a particularly striking combination of properties-most notably a T3/2 power law for the resistivity-showing clearly that the normal state of this itinerant-electron ferromagnet cannot be described in terms of the standard model of metals.