Normal-state magnetotransport in superconducting Tl2Ba2CuO6+ delta to millikelvin temperatures

Observation of quantum oscillations near the Mott-Ioffe-Regel limit in CaAs3

The Mott-Ioffe-Regel limit sets the lower bound of the carrier mean free path for coherent quasiparticle transport. Metallicity beyond this limit is of great interest because it is often closely related to quantum criticality and unconventional superconductivity. Progress along this direction mainly focuses on the strange-metal behaviors originating from the evolution of the quasiparticle scattering rate, such as linear-in-temperature resistivity, while the quasiparticle coherence phenomena in this regime are much less explored due to the short mean free path at the diffusive bound. Here we report the observation of quantum oscillations from Landau quantization near the Mott-Ioffe-Regel limit in CaAs3. Despite the insulator-like temperature dependence of resistivity, CaAs3 presents giant magnetoresistance and prominent Shubnikov-de Haas oscillations from Fermi surfaces, indicating highly coherent band transport. In contrast, quantum oscillation is absent in the magnetic torque. The quasiparticle effective mass increases systematically with magnetic fields, manifesting a much larger value than what is expected based on magneto-infrared spectroscopy. This suggests a strong many-body renormalization effect near the Fermi surface. We find that these unconventional behaviors may be explained by the interplay between the mobility edge and the van Hove singularity, which results in the formation of coherent cyclotron orbits emerging at the diffusive bound. Our results call for further study on the electron correlation effect of the van Hove singularity.

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.

Charge density waves and Fermi surface reconstruction in the clean overdoped cuprate superconductor Tl2Ba2CuO6+δ

Hall effect and quantum oscillation measurements on high temperature cuprate superconductors show that underdoped compositions have small Fermi surface pockets whereas when heavily overdoped, a single much larger pocket is found. The origin of this change in electronic structure has been unclear, but may be related to the high temperature superconductivity. Here we show that the clean overdoped single-layer cuprate Tl₂Ba₂CuO_6+δ (Tl2201) displays CDW order with a remarkably long correlation length ξ ≈ 200 Å which disappears above a hole doping of p_CDW ≈ 0.265. We show that the evolution of the electronic properties of Tl2201 as the doping is lowered may be explained by a Fermi surface reconstruction which accompanies the emergence of the CDW below p_CDW. Our results demonstrate importance of CDW correlations in understanding the electronic properties of overdoped cuprates.

The origin of the Fermi surface reconstruction that occurs in cuprate superconductors as hole doping increases remains unclear. Here, the authors observe long range charge density wave (CDW) order in the overdoped single-layer cuprate Tl₂Ba₂CuO_6+δ, which then disappears above a hole concentration 0.265, suggesting a correlation between Fermi surface reconstruction and the emergence of the CDW.

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.

Crossover to strange metal phase: quantum criticality in one unit cell Bi2Sr2CaCu2O[Formula: see text]

Transport measurements can be used to determine the phase diagram of high temperature superconductors by detecting variations in temperature dependence of resistance in different regions of the phase diagram. While for bulk measurements several samples with varying chemical doping are used, we continuously vary carrier density in our ultra-thin two-dimensional Bi₂Sr₂CaCu₂O[Formula: see text] device by electrostatic means and the space charge doping method. Here we concentrate on a low-disorder, high quality single unit cell thick sample. We establish the crossover to strange metal from the pseudogap and Fermi liquid phases in the normal state, close to the superconducting dome. By extrapolation we demarcate a critical doping region which is thought to correspond to a quantum phase transition at very low temperature.

Logarithmic Upturn in Low-Temperature Electronic Transport as a Signature of d-Wave Order in Cuprate Superconductors

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulatinglike behavior in underdoped material versus temperature T, in which resistivity increases on cooling with a puzzling log(1/T) form. We instead use microwave measurements of flux-flow resistivity in YBa_{2}Cu_{3}O_{6+y} and Tl_{2}Ba_{2}CuO_{6+δ} to study charge transport deep inside the superconducting phase, in the low-temperature and low-field regime. Here, the transition from metallic low-temperature resistivity (dρ/dT>0) to a log(1/T) upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The log(1/T) form is thus likely a signature of d-wave superconducting order, and the field-revealed normal state's log(1/T) resistivity may indicate the free-flux-flow regime of a phase-disordered d-wave superconductor.

A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates

The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.

Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa2Cu4O8

Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that, inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations [Doiron-Leyraud N, et al. (2007) Nature 447(7144):565-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110(15):5774-5778], and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys Rev B 93:064513] point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa₂Cu₄O₈ that are consistent with a T² resistivity extending down to 1.5 K. The magnitude of the T² coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket.

Anisotropic breakdown of Fermi liquid quasiparticle excitations in overdoped La₂-xSrxCuO₄

High-temperature superconductivity emerges from an un-conventional metallic state. This has stimulated strong efforts to understand exactly how Fermi liquids breakdown and evolve into an un-conventional metal. A fundamental question is how Fermi liquid quasiparticle excitations break down in momentum space. Here we show, using angle-resolved photoemission spectroscopy, that the Fermi liquid quasiparticle excitations of the overdoped superconducting cuprate La1.77Sr0.23CuO4 is highly anisotropic in momentum space. The quasiparticle scattering and residue behave differently along the Fermi surface and hence the Kadowaki-Wood's relation is not obeyed. This kind of Fermi liquid breakdown may apply to a wide range of strongly correlated metal systems where spin fluctuations are present.

The metallic transport of (TMTSF)2X organic conductors close to the superconducting phase

Comparing resistivity data of the quasi-one-dimensional superconductors (TMTSF)2PF6 and (TMTSF)2ClO4 along the least conducting c(⋆)-axis and along the high conductivity a-axis as a function of temperature and pressure, a low temperature regime is observed in which a unique scattering time governs the transport along both directions of these anisotropic conductors. However, the pressure dependence of the anisotropy implies a large pressure dependence of the interlayer coupling. This is in agreement with the results of first-principles density functional theory calculations implying methyl group hyperconjugation in the TMTSF molecule. In this low temperature regime, both materials exhibit for ρ(c) a temperature dependence aT + bT(2). Taking into account the strong pressure dependence of the anisotropy, the T-linear ρ(c) is found to correlate with the suppression of the superconducting Tc, in close analogy with ρ(a) data. This work reveals the domain of existence of the three-dimensional coherent regime in the generic (TMTSF)2X phase diagram and provides further support for the correlation between T-linear resistivity and superconductivity in non-conventional superconductors.

Dichotomy in the T-linear resistivity in hole-doped cuprates

From analysis of the in-plane resistivity ρ(ab)(T) of La(2-x)Sr(x)CuO(4), we show that normal state transport in overdoped cuprates can be delineated into two regimes in which the electrical resistivity varies approximately linearly with temperature. In the low-temperature limit, the T-linear resistivity extends over a very wide doping range, in marked contrast to expectations from conventional quantum critical scenarios. The coefficient of this T-linear resistivity scales with the superconducting transition temperature T(c), implying that the interaction causing this anomalous scattering is also associated with the superconducting pairing mechanism. At high temperatures, the coefficient of the T-linear resistivity is essentially doping independent beyond a critical doping p(crit)=0.19 at which the ratio of the two coefficients is maximal. Taking our cue from earlier thermodynamic and photoemission measurements, we conclude that the opening of the normal-state pseudogap at p(crit) is driven by the loss of coherence of anti-nodal quasi-particles at low temperatures.

Hidden Fermi liquid: self-consistent theory for the normal state of high-Tc superconductors

Hidden Fermi liquid theory explicitly accounts for the effects of Gutzwiller projection in the t-J Hamiltonian, widely believed to contain the essential physics of the high-T(c) superconductors. We derive expressions for the entire "strange metal," normal state relating angle-resolved photoemission, resistivity, Hall angle, and by generalizing the formalism to include the Fermi surface topology-angle-dependent magnetoresistance. We show this theory to be the first self-consistent description for the normal state of the cuprates based on transparent, fundamental assumptions. Our well-defined formalism also serves as a guide for further experimental confirmation.

Multiple quantum oscillations in the de Haas-van Alphen spectra of the underdoped high-temperature superconductor YBa2Cu3O6.5

By improving the experimental conditions and extensive data accumulation, we have achieved very high precision in the measurements of the de Haas-van Alphen effect in the underdoped high-temperature superconductor YBa2Cu3O6.5. We find that the main oscillation, so far believed to be single frequency, is composed of three closely spaced frequencies. We attribute this to bilayer splitting and warping of a single quasi-2D Fermi surface, indicating that c axis coherence is restored at low temperature in underdoped cuprates. Our results do not support the existence of a larger frequency of the order of 1650 T reported recently in the same compound [S. E. Sebastian, Nature (London) 454, 200 (2008)].

X-ray absorption spectra reveal the inapplicability of the single-band Hubbard model to overdoped cuprate superconductors

X-ray absorption spectra on the overdoped high-temperature superconductors Tl2Ba2CuO(6+delta) and La(2-x)SrxCuO(4+/-delta) reveal a striking departure in the electronic structure from that of the underdoped regime. The upper Hubbard band, identified with strong correlation effects, is not observed on the oxygen K edge, while the lowest-energy prepeak gains less intensity than expected above p approximately 0.21. This suggests a breakdown of the Zhang-Rice singlet approximation and a loss of correlation effects or a significant shift in the most fundamental parameters of the system, rendering single-band Hubbard models inapplicable. Such fundamental changes suggest that the overdoped regime may offer a distinct route to understanding in the cuprates.

Fermi surface reconstruction in high-T(c) superconductors

The recent observation of quantum oscillations in underdoped high-T(c) superconductors, combined with their negative Hall coefficient at low temperature, reveals that the Fermi surface of hole-doped cuprates includes a small electron pocket. This strongly suggests that the large hole Fermi surface characteristic of the overdoped regime undergoes a reconstruction caused by the onset of some order which breaks translational symmetry. Here we consider the possibility that this order is 'stripe' order, a form of combined charge/spin modulation observed most clearly in materials like Eu-doped and Nd-doped LSCO (La(2-x)Sr(x)CuO(4)). In these materials, the onset of stripe order coincides with major changes in transport properties, providing strong evidence that stripe order is indeed the cause of Fermi surface reconstruction. We identify the critical doping where this reconstruction occurs and show that the temperature dependence of transport coefficients at that doping is typical of metals at a quantum critical point. We discuss how the pseudogap phase may be a fluctuating precursor of the stripe-ordered phase.

Anomalous criticality in the electrical resistivity of La2-xSrxCuO4

The presence or absence of a quantum critical point and its location in the phase diagram of high-temperature superconductors have been subjects of intense scrutiny. Clear evidence for quantum criticality, particularly in the transport properties, has proved elusive because the important low-temperature region is masked by the onset of superconductivity. We present measurements of the low-temperature in-plane resistivity of several highly doped La2-xSrxCuO4 single crystals in which the superconductivity had been stripped away by using high magnetic fields. In contrast to other quantum critical systems, the resistivity varies linearly with temperature over a wide doping range with a gradient that scales monotonically with the superconducting transition temperature. It is maximal at a critical doping level (pc) approximately 0.19 at which superconductivity is most robust. Moreover, its value at pc corresponds to the onset of quasi-particle incoherence along specific momentum directions, implying that the interaction that first promotes high-temperature superconductivity may ultimately destroy the very quasi-particle states involved in the superconducting pairing.

Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor

Despite twenty years of research, the phase diagram of high-transition-temperature superconductors remains enigmatic. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected 'Fermi arcs'. The fundamental question, then, is whether underdoped copper oxides have a Fermi surface, and if so, whether it is topologically different from that seen in the overdoped regime. Here we report the observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxide YBa2Cu3O6.5, establishing the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides, once superconductivity is suppressed by a magnetic field. The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Two possible interpretations are discussed: either a small pocket is part of the band structure specific to YBa2Cu3O6.5 or small pockets arise from a topological change at a critical point in the phase diagram. Our understanding of high-transition-temperature (high-T(c)) superconductors will depend critically on which of these two interpretations proves to be correct.

Fermi surface and quasiparticle excitations of overdoped Tl2Ba2CuO6 + delta

The high-T(c) superconductor Tl(2)Ba(2)CuO(6 + delta) is studied by angle-resolved photoemission spectroscopy. For a very overdoped T(c) = 30 K sample, the Fermi surface consists of a single large hole pocket centered at (pi, pi) and is approaching a topological transition. Although a superconducting gap with d(x(2)-y(2)) symmetry is tentatively identified, the quasiparticle evolution with momentum and binding energy exhibits a marked departure from the behavior observed in under and optimally doped cuprates. The relevance of these findings to scattering, many-body, and quantum-critical phenomena is discussed.

A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor

All conventional metals are known to possess a three-dimensional Fermi surface, which is the locus in reciprocal space of the long-lived electronic excitations that govern their electronic properties at low temperatures. These excitations should have well-defined momenta with components in all three dimensions. The high-transition-temperature (high-T(c)) copper oxide superconductors have unusual, highly two-dimensional properties above the superconducting transition. This, coupled with a lack of unambiguous evidence for a three-dimensional Fermi surface, has led to many new and exotic models for the underlying electronic ground state. Here we report the observation of polar angular magnetoresistance oscillations in the overdoped superconductor Tl2Ba2CuO6+delta in high magnetic fields, which firmly establishes the existence of a coherent three-dimensional Fermi surface. Analysis of the oscillations reveals that at certain symmetry points, however, this surface is strictly two-dimensional. This striking form of the Fermi surface topography, long-predicted by electronic band structure calculations, provides a natural explanation for a wide range of anisotropic properties both in the normal and superconducting states. Our data reveal that, despite their extreme electrical anisotropy, the high-T(c) materials at high doping levels can be understood within a framework of conventional three-dimensional metal physics.

Magnetic-field-induced localization of quasiparticles in underdoped La(2-x)SrxCuO4 single crystals

Magnetic-field-induced ordering of electrons around vortices is a striking phenomenon recently found in high-T(c) cuprates. To identify its consequence in the quasiparticle dynamics, the magnetic-field (H) dependence of the low-temperature thermal conductivity kappa of La(2-x)SrxCuO4 crystals is studied for a wide doping range. It is found that the behavior of kappa(H) in the subkelvin region changes drastically across optimum doping, and the data for underdoped samples are indicative of unusual magnetic-field-induced localization of quasiparticles; this localization phenomenon is probably responsible for the unusual "insulating normal state" under high magnetic fields.

Heat transport in a strongly overdoped cuprate: Fermi liquid and a pure d-wave BCS superconductor

The transport of heat and charge in the overdoped cuprate superconductor Tl(2)Ba2CuO(6+delta) was measured down to low temperature. In the normal state, obtained by applying a magnetic field greater than the upper critical field, the Wiedemann-Franz law is verified to hold perfectly. In the superconducting state, a large residual linear term is observed in the thermal conductivity, in quantitative agreement with BCS theory for a d-wave superconductor. This is compelling evidence that the electrons in overdoped cuprates form a Fermi liquid, with no indication of spin-charge separation.

Far-infrared resonance in Sr(2)RuO(4)

The far-infrared c-axis reflectance of Sr(2)RuO(4) has been measured above and below the 2.5 K superconducting transition temperature of the sample. A plasma edge develops near 70 cm(-1) as the temperature is lowered, which corresponds to a Drude peak in the real optical conductivity associated with the onset of the coherent motion of the carriers. A gaplike suppression of the frequency-dependent scattering rate at low temperatures indicates that the coherent transport is related to a loss of scattering below 60 cm(-1). A strong resonance near 9 meV is responsible for the scattering that destroys coherence.

Doping and magnetic field dependence of in-plane tunneling into YBa(2)Cu(3)O(7-x): possible evidence for the existence of a quantum critical point

We present tunneling measurements into (1,1,0) YBa(2)Cu(3)O(7-x) films at various doping levels around the optimum. We find that, above a certain doping level near optimum doping, a spontaneous zero bias conductance peak splitting, delta, appears. It increases with doping. It also increases with magnetic field applied along the c axis, for both underdoped and overdoped films. The low field susceptibility chi = d delta /dH/(H-->0) is maximum, possibly diverging when the spontaneous value of delta goes to zero. These results suggest a transition from a pure d(x(2)-y(2)) to a d+id(xy) or d+is order parameter.