Unusual Normal State Research Articles

Abnormal transport properties of Bi-III superconducting phase in pressurized bismuth single crystal

Resistivity, magnetoresistance, and upper critical field, have been comprehensively studied for the bismuth (Bi)-III superconducting phase in the pressure range of 2.9 GPa ⩽ P⩽ 6.2 GPa. It is discovered that the transition temperature T c of the Bi-III phase is gradually suppressed with increasing pressure. Strikingly, the temperature-dependent resistivity above T c in the Bi-III region reveals notable non-Fermi-liquid behaviors, resembling many unconventional superconducting systems. As the pressure increases, the magnetoresistance effect progressively grows and reaches a maximum value of 212% at pressure ∼6.2 GPa and field of 5 T, indicating a possible contribution to the charge conduction by Dirac electrons. Moreover, the zero-temperature upper critical field for the Bi-III phase displays relatively low values concerning the moderate T c values, and the reduced upper critical field for different pressures deviates from the single-band Werthamer–Helfand–Hohenberg model. These unusual normal state transport properties and unique behavior of the upper critical field point to possible unconventional superconductivity for the Bi-III superconducting phase.

Quantum phase transition inside the superconducting dome of Ba(Fe1−xCox)2As2 from diamond-based optical magnetometry

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature Tc acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe1−xCox)2As2. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe2(As1−xPx)2 compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic–magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ(x) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

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.

The unusual normal state and charge-density-wave order in 2H-NbSe2

Competition between collective states like charge-density-wave and superconductivity, unencumbered by the spin degrees of freedom, is played out in some of the transition metal dichalcogenides. Although 2H-NbSe2 has received much less attention than some of the other members of the family (such as 1T-TiSe2 and 2H-TaSe2) of late, it shows superconductivity at 7.2 K and incommensurate charge ordering at 33 K. Recent experiments, notably angle resolved photoemission spectroscopy, have cast serious doubts on the theories based on Fermi surface nesting and electron–phonon interaction. The normal state has been found to be a poor, incoherent metal and remarkably, the coherence increases in the broken symmetry state. From a preformed excitonic liquid scenario, we show that there exists a natural understanding of the experimental data on 2H-NbSe2, based on electron–electron interaction. The collective instabilities, in this scenario, are viewed as a condensation of an incoherent excitonic liquid already present at high temperature.

Emergence of superconductivity in heavy-electron materials.

Although the pairing glue for the attractive quasiparticle interaction responsible for unconventional superconductivity in heavy-electron materials has been identified as the spin fluctuations that arise from their proximity to a magnetic quantum critical point, there has been no model to describe their superconducting transition at temperature Tc that is comparable to that found by Bardeen, Cooper, and Schrieffer (BCS) for conventional superconductors, where phonons provide the pairing glue. Here we propose such a model: a phenomenological BCS-like expression for Tc in heavy-electron materials that is based on a simple model for the effective range and strength of the spin-fluctuation-induced quasiparticle interaction and reflects the unusual properties of the heavy-electron normal state from which superconductivity emerges. We show that it provides a quantitative understanding of the pressure-induced variation of Tc in the "hydrogen atoms" of unconventional superconductivity, CeCoIn5 and CeRhIn5, predicts scaling behavior and a dome-like structure for Tc in all heavy-electron quantum critical superconductors, provides unexpected connections between members of this family, and quantifies their variations in Tc with a single parameter.

Electronic phase diagram of high-temperature copper oxide superconductors

In order to understand the origin of high-temperature superconductivity in copper oxides, we must understand the normal state from which it emerges. Here, we examine the evolution of the normal state electronic excitations with temperature and carrier concentration in Bi(2)Sr(2)CaCu(2)O(8+δ) using angle-resolved photoemission. In contrast to conventional superconductors, where there is a single temperature scale T(c) separating the normal from the superconducting state, the high-temperature superconductors exhibit two additional temperature scales. One is the pseudogap scale T(∗), below which electronic excitations exhibit an energy gap. The second is the coherence scale T(coh), below which sharp spectral features appear due to increased lifetime of the excitations. We find that T(∗) and T(coh) are strongly doping dependent and cross each other near optimal doping. Thus the highest superconducting T(c) emerges from an unusual normal state that is characterized by coherent excitations with an energy gap.

Unusual Nernst effect and spin density wave precursors in superconducting LaFeAsO1−xFx

The Nernst effect has recently proven as a sensitive probe for detecting unusual normal state properties of unconventional superconductors. Here we present a systematic study of the Nernst effect of the iron pnictide superconductor \laf with a particular focus on its evolution upon doping. For the parent compound we observe a huge negative Nernst coefficient accompanied with a severe violation of the Sondheimer cancellation in the spin density wave (SDW) ordered state. Surprisingly, an unusual and enhanced Nernst signal is also found at underdoping ($x=0.05$) despite the presence of bulk superconductivity and the absence of static magnetic order, strongly suggestive of SDW precursors at $T\lesssim150$ K. A more conventional normal state Nernst response is observed at optimal doping ($x=0.1$) where it is rather featureless with a more complete Sondheimer cancellation.

Microscopic approach to high-temperature superconductors within the t-J model

Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature ${T}_{c}$ is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have $d$-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.

Novel superconducting characteristics and unusual normal-state properties in iron-based pnictide superconductors: 57FeNMR and 75AsNQR/NMR studies in REFeAsO 1− y (RE = La, Pr, Nd) and Ba 0.6K 0.4Fe 2As 2

We discuss the novel superconducting characteristics and unusual normal-state properties of iron (Fe)-based pnictide superconductors REFeAsO 1− y (RE = La, Pr, Nd) and Ba 0.6K 0.4Fe 2As 2 ( T c = 38 K) by means of 57FeNMR and 75AsNQR/NMR. In the superconducting state of LaFeAsO 0.7 ( T c = 28 K), the spin component of the 57Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of the superconducting state formed by spin-singlet Cooper pairing. The nuclear spin–lattice relaxation rates (1/ T 1) in LaFeAsO 0.7 and Ba 0.6K 0.4Fe 2As 2 exhibit a T 3-like dependence without a coherence peak just below T c , indicating that an unconventional superconducting state is commonly realized in these Fe-based pnictide compounds. All these events below T c are consistently argued in terms of an extended s ±-wave pairing with a sign reversal of the order parameter among Fermi surfaces. In the normal state, 1/ T 1 T decreases remarkably upon cooling for both the Fe and As sites of LaFeAsO 0.7. In contrast, it gradually increases upon cooling in Ba 0.6K 0.4Fe 2As 2. Despite the similarity between the superconducting properties of these compounds, a crucial difference was observed in their normal-state properties depending on whether electrons or holes are doped into the FeAs layers. These results may provide some hint to address a possible mechanism of Fe-based pnictide superconductors.

Normal state properties at a field-tuned quantum-critical point in the heavy-fermion superconductor [formula omitted

CeRhIn 5 is a prototypical heavy-fermion antiferromagnet where the localized 4f electron of Ce hybridizes weakly with ligand electrons. Applying pressure suppresses the antiferromagnetism and induces unconventional superconductivity when the same Ce 4f electrons become delocalized and participate in the formation of Cooper pairs. The emergent superconducting phase unavoidably hides the existence of quantum-critical point, preventing direct access to it. Measurements of the heat capacity and electrical resistivity under magnetic field and pressure reveal unusual normal state properties at a projected quantum-critical point ( P 2 ) : divergence in C / T and sublinear temperature dependence in the resistivity.

Unusual Hall effect in quasi two-dimensional strongly correlated metal CeCoIn5

We report on the systematic study of Hall effect in quasi two-dimensional strongly correlated metal CeCoIn5, ranging from non-Fermi liquid to Fermi liquid regime by using pressure as a tuning parameter. We found that unusual normal-state transport properties in CeCoIn5 bear a striking resemblance to that in high-Tc cuprates. We also found that at ambient pressure in the vicinity of quantum critical point (QCP), the magnitude of Hall coefficient RH dramatically increases with decreasing temperature. The enhancement of RH is strongly suppressed by applying pressure and magnetic field. These results indicate that the anomalous transport properties are governed by anisotropic scattering due to strong spin fluctuations in the vicinity of the QCP.

Progress in the understanding of the normal state of the cuprates

Over the last years there has been increasing evidence that the normal state of the cuprates can not be described adequately with individual quasiparticles within Fermi-liquid theory. While the low-lying excitations in the superconducting state are nevertheless possibly of quasiparticle character, this character vanishes with the loss of superconducting phase coherence when going to the normal conducting state. Generally, this normal state is characterized by strong heterogeneity. In real space this manifests in charge and spin ordering, either static or dynamical, the so-called ‘stripes’. The spectral signatures of various models describing this unusual metallic normal state together with less exotic non-Fermi-liquid models, like the marginal Fermi liquid, will be compared to photoemission spectra with high angular and energy resolution and to results obtained by other methods.

Layered tungsten bronzes: Tuning the optical properties by changing the layer thickness

We investigated the optical properties of a series of monophosphate tungsten bronzes (P02)4(W03)2m (m=2,4, 6,7) as a function of layer thickness, with special attention on the m=7 density wave superconductor. These materials have several layers of corner-sharing WO6 octahedra separated by one PO4 layer, leading to a tunable octahedral layer thickness with m. In the optical regime, the spectra of the m=2, 4, 6, and 7 materials display an anisotropic electronic excitation, originating from the W intra t2g d to d transition. The intensities and frequencies of these excitations vary with the octahedral layer thickness, consistent with a softer lattice with increasing m. The low-frequency electrodynamics of the monophosphate tungsten bonzes show a gap or pseudogap feature in the infrared, demonstrating a ubiquitous bound camer response. The m=7 density wave superconductor is especially interesting. The variable temperature ab-plane spectra display a suppression of the optical conductivity along the b-axis below 140 K, giving rise to charge localization and anisotropic charge density wave gap formation near 1400 cm-1. This middle infrared charge localization is directly related to the appearance of both flat and dispersive bands along b. Although oscillator strength is redistributed among the free carrier response, charge density wave gap absorption, and d to d transition in the density wave states, the spectral weight is largely conserved below the plasma frequency. Based upon these observations, P4W 14050 is another example of a superconductor with an unusual normal state.

Anisotropicab-plane optical response of the charge-density-wave superconductorP4W14O50

We report the polarized optical reflectance of ${\mathrm{P}}_{4}{\mathrm{W}}_{14}{\mathrm{O}}_{50},$ the only charge-density-wave (CDW) superconductor in the monophosphate tungsten bronze family, over a wide frequency range. The 300-K infrared spectra are dominated by two-dimensional behavior: high reflectance with weak phonons in the conducting $\mathrm{ab}$ plane and low reflectance with strong vibrational modes along the interlayer direction. An anisotropic intra-${t}_{2g}\stackrel{\ensuremath{\rightarrow}}{d}d$ excitation $(\ensuremath{\sim}10000 {\mathrm{cm}}^{\ensuremath{-}1})$ reveals the ``hidden'' one-dimensional band structures in ${\mathrm{P}}_{4}{\mathrm{W}}_{14}{\mathrm{O}}_{50}.$ The variable temperature $\mathrm{ab}$-plane spectra clearly show a suppression of the optical conductivity along the b axis below 140 K, giving rise to charge localization and anisotropic CDW gap formation at $\ensuremath{\sim}1400 {\mathrm{cm}}^{\ensuremath{-}1}.$ Although the oscillator strength is redistributed among the free-carrier response, the CDW gap absorption, and the $\stackrel{\ensuremath{\rightarrow}}{d}d$ transition in the density wave states, the spectral weight is largely conserved below the plasma frequency. The $\mathrm{ab}$-plane phonons become well resolved in the CDW states due to reduced screening. Based upon these observations, ${\mathrm{P}}_{4}{\mathrm{W}}_{14}{\mathrm{O}}_{50}$ is another example of a superconductor with an unusual normal state.

Unconventional superconductivity in CeCoIn 5—a high pressure study

The hybridization between a periodic lattice of almost localized (core like) electrons (of lanthanides or actinides) and band electrons has challenged researchers for over 30 years to unravel its microscopic origin and the many puzzling physical phenomena related to it. Among such phenomena are very unusual normal state properties, which differ strongly from Landau–Fermi liquid (FL) behavior or exciting unconventional forms of superconductivity. Here, we report on experimental studies of a recently discovered new class of these heavy fermion superconductors: CeTIn 5 (T: transition metal). Our studies point towards the realization of unconventional superconductivity in these compounds. In both CeIrIn 5 and in CeCoIn 5 the specific heat C( T), thermal conductivity κ( T) and nuclear spin-relaxation rate decrease as a power law of temperature instead of exponentially for T< T c. We present results of measurements of the heat capacity of CeCoIn 5 at hydrostatic pressures p⩽1.6 GPa. In CeCoIn 5 (as well as in CeIrIn 5), T c increases with increasing pressure, while the effective mass of the quasiparticles, m eff, decreases as indicated by the ratio C/ T( T⩾ T c). As a working hypothesis based on theories of a nearly antiferromagnetic FL this may be interpreted as the stabilization of the superconducting state by the increase of the characteristic spin-fluctuation temperature T SF( T SF∝ k F 2/ m eff). Interestingly, in CeIrIn 5 the ratio Δ C/ γT c=0.8 is small and almost stays constant with increasing pressure, while in CeCoIn 5 Δ C/ γT c≈5 is extremely large but starts to decrease rapidly at p⩾0.8 GPa where T c( p) approaches a maximum.

Coherent view on fullerenes: phonon-mediated correlated superconductivity and unusual normal state optical conductivity

The wide range of experimental observations on fullerene superconductors can be understood if the Coulomb repulsion is included in addition to the electron–phonon interaction in the pairing kernel. These are characterized by λ≈0.7–0.8 and V C N F≈0.3–0.4, where λ is the dimensionless electron–phonon coupling constant, V C the screened Coulomb repulsion, and N F is the density of states at the Fermi level. This view of phonon-mediated correlated superconductivity is applied to the normal state fullerenes to check if an unusual feature observed in the normal state can also be understood within the view: the suppressed Drude weight and concomitant mid-infrared (MIR) peak in the optical conductivity. The Drude weight in the calculated optical conductivity is strongly suppressed, being ∼0.4 of the total intraband spectral weight, and is transferred to the MIR region around and above 0.06 eV which is somewhat less pronounced and much broader compared with the experimental observation by DeGiorgi et al.

The role of density of states fluctuations in the normal state properties of highTcsuperconductors

During the last decade a lot of efforts have been undertaken to explain the unusual normal state properties of high temperature superconductors (HTS) in the framework of unconventional theories based on strongly interacting electrons, pre-formed Cooper pairs, polaron mechanism of super conductivity etc. A different approach to this problem would be to develop the perturbation theory for interacting electrons in the normal phase of strongly anisotropic superconductors without specifying the origin of this interaction. The Cooper channel of interelectron interaction is equivalent to the superconducting fluctuations which are unusually strong in HTS. We show that the peculiarities of such systems not only lead to the increase of the magnitude but are also frequently responsible for the change of the hierarchy of different fluctuation effects and even of the sign of the total corrections. As a result the fluctuation contributions can manifest themselves in very unusual forms. The first and well known result is that that now one has the 'pre-formed Cooper pairs' automatically, from ab initio calculations: taking into account thermal fluctuations leads to the appearance of a non-zero density of fluctuating Cooper pairs (with finite lifetime) within layers without the establishment of long range order in the system. The fluctuation Cooper pair density decreases with temperature very slowly(∼ln T c/(T - T c) in the 2D case). The formation of these pairs of normal electrons leads to the decrease of the density of one-electron states (DOS renormalization) at the Fermi level, and this turns out to be the key effect in our discussion. The DOS contribution to the most of characteristics is negligible for traditional superconducting materials. However, it becomes dominant when highly anisotropic materials are discussed, and therefore is very important in HTS, especially when transport along the c-axis is considered. We analyse the role of the DOS fluctuations in the properties of HTS and show how, taking into account this effect, many puzzling and long debated properties of HTS materials (such as the steep increase of the electrical resistivity along the c-axis just above T c, the anomalous magnetoresistance, effects of the magnetic field on the resistive transition along the c-axis, the c-axis far infrared absorption spectrum, NMR characteristics around the critical temperature etc.) can be understood leading to a simple, consistent description in terms of the fluctuation theory.

Spin dynamic effects on the resistivity and the magnetoresistance of a La1.85Sr0.15(Cu1−xLix)O4 system with 0.0⩽x⩽0.15

The interplay between hole doping, spin fluctuations, and unusual normal-state properties in layered cuprates is relevant for the physics of high temperature superconductors. For better understanding of the role of magnetic interactions on the conduction mechanism, a systematic study of the normal-state resistivity ρ(x,T) of the La1.85Sr0.15(Cu1−xLix)O4 system with 0.0⩽x⩽0.15 was performed down to 4.2 K. A logarithmic contribution was found to properly describe the ρ(x,T) deviation from linearity as Tc is approached. Scattering of the carriers by spin fluctuations at the Cu–O2 conduction planes is proposed to be the source of the Kondo-like behavior. Negative magnetoresistance measurements up to 8 T, with an increasing intensity with x, confirm the role of spin degrees in the resistivity behavior.

THEORY OF THE UNUSUAL NORMAL AND SUPERCONDUCTING STATES OF UNDERDOPED CUPRATES

We review our SU(2) formulation of the t– J model as a description of the underdoped cuprates. The model incorporates spin–charge separation and successfully explains many unusual normal state properties, including the existence of a spin gap and the appearance of a Fermi surface segment. Very recently, we extended our theory to the superconducting state to show how BCS-like quasi-particles evolve out of the Fermi surface segment.

THE NEW GENERATION HIGH-TEMPERATURE SUPERCONDUCTORS

▪ Abstract The layered perovskite cuprate materials are a unique class of superconductors with unusual normal-state and superconducting properties. The common physics to all these materials is that of the underlying CuO2 planes. This review provides a survey of and guide to their physical properties as it relates to the superconductivity of this interesting group of conducting oxides.