In-plane magnetoresistance obeys Kohler's rule in the pseudogap phase of cuprate superconductors

Transport properties and doping evolution of the Fermi surface in cuprates

Measured transport properties of three representative cuprates are reproduced within the paradigm of two electron subsystems, itinerant and localized. The localized subsystem evolves continuously from the Cu 3d[Formula: see text] hole at half-filling and corresponds to the (pseudo)gapped parts of the Fermi surface. The itinerant subsystem is observed as a pure Fermi liquid (FL) with material-independent universal mobility across the doping/temperature phase diagram. The localized subsystem affects the itinerant one in our transport calculations solely by truncating the textbook FL integrals to the observed (doping- and temperature-dependent) Fermi arcs. With this extremely simple picture, we obtain the measured evolution of the resistivity and Hall coefficients in all three cases considered, including LSCO which undergoes a Lifshitz transition in the relevant doping range, a complication which turns out to be superficial. Our results imply that prior to evoking polaronic, quantum critical point, quantum dissipation, or even more exotic scenarios for the evolution of transport properties in cuprates, Fermi-surface properties must be addressed in realistic detail.

Negative Magnetoresistance in Hopping Regime of Lightly Doped Thermoelectric SnSe

Semiconducting SnSe, an analog of black phosphorus, recently attracted great scientific interest due to a disputed report of a large thermoelectric figure of merit, which has not been reproduced subsequently. Here we concentrate on the low-temperature ground state. To gain a better understanding of the system, we present magneto-transport properties in high-quality single crystals of as-grown, lightly doped SnSe down to liquid helium temperatures. We show that SnSe behaves as a p-type doped semiconductor in the vicinity of a metal-insulator transition. Electronic transport at the lowest temperatures is dominated by the hopping mechanism. Negative magnetoresistance at low fields is well described by antilocalization, while positive magnetoresistance at higher fields is consistent with the shrinkage of localized impurity wavefunctions. At higher temperatures, a dilute metallic regime is realized where elusive T² and B² resistivity dependence is observed, posing a challenge to theoretical comprehension of the underlying physical mechanism.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

High-T c Cuprates: a Story of Two Electronic Subsystems

A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of 1 + p charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper-oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.

Incoherent transport across the strange-metal regime of overdoped cuprates

Strange metals possess highly unconventional electrical properties, such as a linear-in-temperature resistivity^1-6, an inverse Hall angle that varies as temperature squared^7-9 and a linear-in-field magnetoresistance^10-13. Identifying the origin of these collective anomalies has proved fundamentally challenging, even in materials such as the hole-doped cuprates that possess a simple bandstructure. The prevailing consensus is that strange metallicity in the cuprates is tied to a quantum critical point at a doping p* inside the superconducting dome^14,15. Here we study the high-field in-plane magnetoresistance of two superconducting cuprate families at doping levels beyond p*. At all dopings, the magnetoresistance exhibits quadrature scaling and becomes linear at high values of the ratio of the field and the temperature, indicating that the strange-metal regime extends well beyond p*. Moreover, the magnitude of the magnetoresistance is found to be much larger than predicted by conventional theory and is insensitive to both impurity scattering and magnetic field orientation. These observations, coupled with analysis of the zero-field and Hall resistivities, suggest that despite having a single band, the cuprate strange-metal region hosts two charge sectors, one containing coherent quasiparticles, the other scale-invariant 'Planckian' dissipators.

Fermi Surface Reconstruction and Electron Dynamics at the Charge-Density-Wave Transition in TiSe_{2}

The evolution of the charge carrier concentrations and mobilities are examined across the charge-density-wave (CDW) transition in TiSe_{2}. Combined quantum oscillation and magnetotransport measurements show that a small electron pocket dominates the electronic properties at low temperatures while an electron and hole pocket contribute at room temperature. At the CDW transition, an abrupt Fermi surface reconstruction and a minimum in the electron and hole mobilities are extracted from two-band and Kohler analysis of magnetotransport measurements. The minimum in the mobilities is associated with the overseen role of scattering from the softening CDW mode. With the carrier concentrations and dynamics dominated by the CDW and the associated bosonic mode, our results highlight TiSe_{2} as a prototypical system to study the Fermi surface reconstruction at a density-wave transition.

Anisotropic Raman spectrum and transport properties of AuTe2Br flakes

Topological semimetal (TSM) AuTe₂Br thin flakes have been studied by Raman spectroscopy and magneto-transport measurement. The angle-resolved polarized Raman spectrum of AuTe₂Br (bulk and thin flake) shows strong anisotropy. Together with high resolution transmission electron microscopy (TEM), we establish a non-destructive method to determine the crystallographic orientation of AuTe₂Br flakes. At high temperature (T  >  50 K), the magneto-resistance (MR) of AuTe₂Br thin flakes shows typical parabolic-like behavior, which can be well fitted by the two-fluid model. However, at low temperature (T  ⩽  30 K), the MR of thin flakes (<17 nm) clearly deviates from the two-fluid model as well as from the Kohler's rule, suggesting a new type of scattering emerging below 30 K. Several possible scattering mechanisms are discussed and the respective corrections to MR are compared with our experimental data. In addition, the conductivity of these metallic crystals is also found to be highly anisotropic, with the hole mobility along the a axis about five times higher than that along the c axis.

Low temperature hidden Fermi-liquid charge transport in under doped La x Sr1-x CuO2 infinite layer electron-doped thin films

We have studied the low temperature electrical transport properties of La _x Sr_1-x CuO₂ thin films grown by oxide molecular beam epitaxy on (1 1 0) GdScO₃ and TbScO₃ substrates. The transmission electron microscopy measurements and the x-ray diffraction analysis confirmed the epitaxy of the obtained films and the study of their normal state transport properties, removing the ambiguity regarding the truly conducting layer, allowed to highlight the presence of a robust hidden Fermi liquid charge transport in the low temperature properties of infinite layer electron doped cuprate superconductors. These results are in agreement with recent observations performed in other p  and n doped cuprate materials and point toward a general description of the superconducting and normal state properties in these compounds.

Tuning the magnetotransport behavior of topological insulator with a transition-metal oxide layer

The interaction between topological insulator (TI) and its adjacent magnetic layer serves as a basis for exploring the device application of TI. Here we investigate the modulation of the magnetotransport behavior of Bi₂Te₃ TI with a transition-metal oxide layer NiO. It is found that the weak-antilocalization effect is absent at low magnetic fields and the magnetoresistance ratio decreases monotonically with increasing the NiO growth temperature from 300 to 473 K, indicating the suppression of the topological surface states of Bi₂Te₃. Such behaviors are attributed to the decomposition of NiO and the concomitant formation of magnetic impurities at the Bi₂Te₃/NiO interface. Differently, the weak-antilocalization shows no significant weakening with the growth of Cr₂O₃ top layer, due to its better chemical stability. Our observation would be significant for the material selection for the device integration of TI.

Diagonal nematicity in the pseudogap phase of HgBa2CuO4+δ

The pseudogap phenomenon in the cuprates is arguably the most mysterious puzzle in the field of high-temperature superconductivity. The tetragonal cuprate HgBa₂CuO_4+δ, with only one CuO₂ layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the magnetic susceptibility anisotropy within the CuO₂ plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy sets in below the pseudogap temperature T^*, which provides thermodynamic evidence for a nematic phase transition with broken four-fold symmetry. Surprisingly, the nematic director orients along the diagonal direction of the CuO₂ square lattice, in sharp contrast to the bond nematicity along the Cu-O-Cu direction. Another remarkable feature is that the enhancement of the diagonal nematicity with decreasing temperature is suppressed around the temperature at which short-range charge-density-wave formation occurs. Our result suggests a competing relationship between diagonal nematic and charge-density-wave order in HgBa₂CuO_4+δ.

Hole pocket-driven superconductivity and its universal features in the electron-doped cuprates

After three decades of intensive research attention, the emergence of superconductivity in cuprates remains an unsolved puzzle. One major challenge has been to arrive at a satisfactory understanding of the unusual metallic "normal state" from which the superconducting state emerges upon cooling. A second challenge has been to achieve a unified understanding of hole- and electron-doped compounds. Here, we report detailed magnetoresistance measurements for the archetypal electron-doped cuprate Nd_2-x Ce _x CuO_4+δ that, in combination with previous data, provide crucial links between the normal and superconducting states and between the electron- and hole-doped parts of the phase diagram. The characteristics of the normal state (magnetoresistance, quantum oscillations, and Hall coefficient) and those of the superconducting state (superfluid density and upper critical field) consistently indicate two-band (electron and hole) features and point to hole pocket-driven superconductivity in these nominally electron-doped materials. We show that the approximate Uemura scaling between the superconducting transition temperature and the superfluid density found for hole-doped cuprates also holds for the small hole component of the superfluid density in electron-doped cuprates.

Unusual behavior of cuprates explained by heterogeneous charge localization

The discovery of high-temperature superconductivity in cuprates ranks among the major scientific milestones of the past half century, yet pivotal questions regarding the complex phase diagram of these materials remain unanswered. Generally thought of as doped charge-transfer insulators, these complex oxides exhibit pseudogap, strange-metal, superconducting, and Fermi liquid behavior with increasing hole-dopant concentration. Motivated by recent experimental observations, here we introduce a phenomenological model wherein exactly one hole per planar copper-oxygen unit is delocalized with increasing doping and temperature. The model is percolative in nature, with parameters that are highly consistent with experiments. It comprehensively captures key unconventional experimental results, including the temperature and the doping dependence of the pseudogap phenomenon, the strange-metal linear temperature dependence of the planar resistivity, and the doping dependence of the superfluid density. The success and simplicity of the model greatly demystify the cuprate phase diagram and point to a local superconducting pairing mechanism.

Emergence of superconductivity in the cuprates via a universal percolation process

A pivotal step toward understanding unconventional superconductors would be to decipher how superconductivity emerges from the unusual normal state. In the cuprates, traces of superconducting pairing appear above the macroscopic transition temperature Tc, yet extensive investigation has led to disparate conclusions. The main difficulty has been to separate superconducting contributions from complex normal-state behaviour. Here we avoid this problem by measuring nonlinear conductivity, an observable that is zero in the normal state. We uncover for several representative cuprates that the nonlinear conductivity vanishes exponentially above Tc, both with temperature and magnetic field, and exhibits temperature-scaling characterized by a universal scale Ξ0. Attempts to model the response with standard Ginzburg-Landau theory are systematically unsuccessful. Instead, our findings are captured by a simple percolation model that also explains other properties of the cuprates. We thus resolve a long-standing conundrum by showing that the superconducting precursor in the cuprates is strongly affected by intrinsic inhomogeneity.

Topological order in the pseudogap metal

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

Hourglass Dispersion and Resonance of Magnetic Excitations in the Superconducting State of the Single-Layer Cuprate HgBa_{2}CuO_{4+δ} Near Optimal Doping

We use neutron scattering to study magnetic excitations near the antiferromagnetic wave vector in the underdoped single-layer cuprate HgBa_{2}CuO_{4+δ} (superconducting transition temperature T_{c}≈88  K, pseudogap temperature T^{*}≈220  K). The response is distinctly enhanced below T^{*} and exhibits a Y-shaped dispersion in the pseudogap state, whereas the superconducting state features an X-shaped (hourglass) dispersion and a further resonancelike enhancement. A large spin gap of about 40 meV is observed in both states. This phenomenology is reminiscent of that exhibited by bilayer cuprates. The resonance spectral weight, irrespective of doping and compound, scales linearly with the putative binding energy of a spin exciton described by an itinerant-spin formalism.

Hidden Fermi-liquid Charge Transport in the Antiferromagnetic Phase of the Electron-Doped Cuprate Superconductors

Systematic analysis of the planar resistivity, Hall effect, and cotangent of the Hall angle for the electron-doped cuprates reveals underlying Fermi-liquid behavior even deep in the antiferromagnetic part of the phase diagram. The transport scattering rate exhibits a quadratic temperature dependence, and is nearly independent of doping and compound and carrier type (electrons versus holes), and hence is universal. Our analysis moreover indicates that the material-specific resistivity upturn at low temperatures and low doping has the same origin in both electron- and hole-doped cuprates.

Emergent gauge fields and the high-temperature superconductors

The quantum entanglement of many states of matter can be represented by electric and magnetic fields, much like those found in Maxwell's theory. These fields 'emerge' from the quantum structure of the many-electron state, rather than being fundamental degrees of freedom of the vacuum. I review basic aspects of the theory of emergent gauge fields in insulators in an intuitive manner. In metals, Fermi liquid (FL) theory relies on adiabatic continuity from the free electron state, and its central consequence is the existence of long-lived electron-like quasi-particles around a Fermi surface enclosing a volume determined by the total density of electrons, via the Luttinger theorem. However, long-range entanglement and emergent gauge fields can also be present in metals. I focus on the 'fractionalized Fermi liquid' (FL*) state, which also has long-lived electron-like quasi-particles around a Fermi surface; however, the Luttinger theorem on the Fermi volume is violated, and this requires the presence of emergent gauge fields, and the associated loss of adiabatic continuity with the free electron state. Finally, I present a brief survey of some recent experiments in the hole-doped cuprate superconductors, and interpret the properties of the pseudogap regime in the framework of the FL* theory.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic quantum critical point in two dimensions, in which preemptive orders in both charge and superconducting (SC) sectors emerge, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SC fluctuations are dominant and argue that they are unstable towards the formation of a resonant excitonic state at the pseudogap temperature T (*). We discuss the implications of this scenario for a few key experiments.

Single reconstructed Fermi surface pocket in an underdoped single-layer cuprate superconductor

The observation of a reconstructed Fermi surface via quantum oscillations in hole-doped cuprates opened a path towards identifying broken symmetry states in the pseudogap regime. However, such an identification has remained inconclusive due to the multi-frequency quantum oscillation spectra and complications accounting for bilayer effects in most studies. We overcome these impediments with high-resolution measurements on the structurally simpler cuprate HgBa₂CuO_4+δ (Hg1201), which features one CuO₂ plane per primitive unit cell. We find only a single oscillatory component with no signatures of magnetic breakdown tunnelling to additional orbits. Therefore, the Fermi surface comprises a single quasi-two-dimensional pocket. Quantitative modelling of these results indicates that a biaxial charge density wave within each CuO₂ plane is responsible for the reconstruction and rules out criss-crossed charge stripes between layers as a viable alternative in Hg1201. Lastly, we determine that the characteristic gap between reconstructed pockets is a significant fraction of the pseudogap energy.

The identification of broken symmetry states in underdoped cuprate superconductors via quantum oscillation measurements remains inconclusive. Here, Chan et al. report the reconstructed Fermi surface of HgBa₂CuO_4+δ comprises only a single pocket indicating a biaxial charge-density-wave order within each CuO₂ plane.

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO(4+δ)

Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa₂CuO_4+δ. Here we report neutron-scattering results for HgBa₂CuO_4+δ (superconducting transition temperature T_c≈71 K, pseudogap temperature T*≈305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of the cuprates: the X-shaped ‘hourglass' response and the resonance mode in the superconducting state. Instead, the response is Y-shaped, gapped and significantly enhanced below T*, and hence a prominent signature of the pseudogap state.

In the cuprates, antiferromagnetic correlations might be the cause of the pseudogap phenomenon. Here the authors use neutron scattering on the tetragonal cuprate HgBa₂CuO_4+δ revealing commensurate antiferromagnetic excitations as a signature of the pseudogap state.

Quantum dimer model for the pseudogap metal

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S = 1/2, charge +e fermionic dimers. The model realizes a "fractionalized Fermi liquid" with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8 × 8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

Two-component energy spectrum of cuprates in the pseudogap phase and its evolution with temperature and at charge ordering

In the search for mechanisms of high-temperature superconductivity it is critical to know the electronic spectrum in the pseudogap phase from which superconductivity evolves. The lack of angle-resolved photoemission data for every cuprate family precludes an agreement as to its structure, doping and temperature dependence and the role of charge ordering. Here we show that, in the entire Fermi-liquid-like regime that is ubiquitous in underdoped cuprates, the spectrum consists of holes on the Fermi arcs and an electronic pocket. We argue that experiments on the Hall coefficient identify the latter as a permanent feature at doped hole concentration x > 0.08-0.10, in contrast to the idea of the Fermi surface reconstruction via charge ordering. The longstanding issue of the origin of the negative Hall coefficient in YBCO and Hg1201 at low temperature is resolved: the electronic contribution prevails as mobility of the latter (evaluated by the Dingle temperature) becomes temperature independent, while the mobility of holes scattered by the short-wavelength charge density waves decreases.

Charge order and its connection with Fermi-liquid charge transport in a pristine high-T(c) cuprate

Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge-density-wave correlations in the model cuprate superconductor HgBa2CuO(4+δ) (T(c)=72 K) via bulk Cu L3-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa2CuO(4+δ) and with corresponding results for YBa2Cu3O(6+δ), which indicates that charge-density-wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.