High field phase diagram of cuprates derived from the Nernst effect

Broadened quantum critical ground state in a disordered superconducting thin film

A superconductor-insulator transition (SIT) in two dimensions is a prototypical quantum phase transition (QPT) with a clear quantum critical point (QCP) at zero temperature (T = 0). The SIT is induced by a field B and observed in disordered thin films. In some of weakly disordered or crystalline thin films, however, an anomalous metallic (AM) ground state emerges over a wide B range between the superconducting and insulating phases. It remains a fundamental open question how the QPT picture of the SIT is modified when the AM state appears. Here we present measurements of the Nernst effect N, which has great sensitivity to the fluctuations of the superconducting order parameter. From a thorough contour map of N in the B-T plane, we found a thermal-to-quantum crossover line of the superconducting fluctuations, a so-called ghost-temperature line associated with the QPT, as well as a ghost-field line associated with a thermal transition. The QCP is identified as a T = 0 intercept of the ghost-temperature line inside the AM state, which verifies that the AM state is a broadened critical state of the SIT.

Nernst response, viscosity and mobile entropy in vortex liquids

In a liquid of superconducting vortices, a longitudinal thermal gradient generates a transverse electric field. This Nernst signal peaks at an intermediate temperature and magnetic field, presumably where the entropy difference between the vortex core and the superfluid environment is largest. There is a puzzling similarity of the amplitude of this peak across many different superconductors. This peak can be assimilated to a minimum in the viscosity to entropy density ratio of the vortex liquid. Expressed in units ofℏkB, this minimum is one order of magnitude larger than what is seen in common liquids. Moreover, the entropy stocked in the vortex core isnotidentical to the entropy bound to a moving magnetic flux line. Due to a steady exchange of normal quasi-particles, entropy can leak from the vortex core. A slowly moving vortex will be peeled off its entropy within a distance of the order of a superconducting coherence length, provided that theΔEFratio is sufficiently large.

Quantum Criticality inside the Anomalous Metallic State of a Disordered Superconducting Thin Film

The field-induced superconductor-insulator transition (SIT) in two-dimensional (2D) systems is a famous example of a quantum phase transition. However, an emergence of an anomalous metallic state induced by field has been a long-standing problem in 2D superconductors. While theories predicted that the emergence is attributed to strong phase fluctuations of the superconducting order parameter due to quantum fluctuations, usual resistance measurements have not probed them directly. Here, using Nernst effect measurements, we uncover superconducting fluctuations in the vicinity of the field-induced metallic state in an amorphous Mo_{x}Ge_{1-x} thin film. The field range where the vortex Nernst signals are detectable remains nonzero toward zero temperature, and it locates inside the metallic state defined by the magnetoresistance, indicating that the metallic state results from quantum vortex liquid (QVL) with phase fluctuations due to quantum fluctuations. Slow decay of transport entropy of vortices in the QVL with decreasing temperature suggests that the metallic state originates from broadening of a quantum critical point in SIT.

AC measurement of the Nernst effect of thin films at low temperatures

We describe an alternating current method to measure the Nernst effect in superconducting thin films at low temperatures. The Nernst effect is an important tool in the understanding of superconducting fluctuations and, in particular, vortex motion near critical points. However, in most materials, the Nernst signal in a typical experimental setup rarely exceeds a few μV, in some cases being as low as a few nV. DC measurements of such small signals require extensive signal processing and protection against stray pickups and offsets, limiting the sensitivity of such measurements to >1 nV. Here, we describe a method utilizing a one-heater-two-thermometer setup with the heating element and thermometers fabricated on-chip with the sample, which helped to reduce the thermal load and temperature lag between the substrate and the thermometer. Using AC heating power and 2ω measurement, we are able to achieve sub-nanovolt sensitivity in 20 nm-30 nm thin superconducting films on a glass substrate, compared to a sensitivity of ∼10 nV using DC techniques on the same setup.

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.

Pseudo-spin skyrmions in the phase diagram of cuprate superconductors

Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vortex core below T _c, as well as in a wide temperature region above T _c, which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale T ^*. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with q  =  0 phase transitions, of both nematic and loop currents characters.

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.

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.

Observation of orbital resonance Hall effect in (TMTSF)2ClO4

We report the observation of a Hall effect driven by orbital resonance in the quasi-1-dimensional (q1D) organic conductor (TMTSF)2ClO4. Although a conventional Hall effect is not expected in this class of materials due to their reduced dimensionality, we observed a prominent Hall response at certain orientations of the magnetic field B corresponding to lattice vectors of the constituent molecular chains, known as the magic angles (MAs). We show that this Hall effect can be understood as the response of conducting planes generated by an effective locking of the orbital motion of the charge carriers to the MA driven by an electron-trajectory resonance. This phenomenon supports a class of theories describing the rich behavior of MA phenomena in q1D materials based on altered dimensionality. Furthermore, we observed that the effective carrier density of the conducting planes is exponentially suppressed in large B, which indicates possible density wave formation.

Superconductivity and the pseudogap in the two-dimensional Hubbard model

Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.

Origin of the magnetic field induced changes of the transverse plasma mode in the c-axis infrared response of underdoped YBa2Cu3O(7-δ)

We report on results of our theoretical study of magnetic field induced changes of the c-axis infrared response of bilayer cuprate superconductors using the phenomenological multilayer model involving the conductivity of the spacing layers and that of the bilayer units. For H perpendicular to the planes, the local conductivities have been expressed in terms of a two-fluid approximation--as weighted averages of the superconducting state ones and the normal state ones representing contributions of the vortex cores, the weight of the latter increasing linearly with the field. This allows us to reproduce and interpret the fast decrease with increasing H of the well known 400 cm(-1) peak (transverse plasma mode) in the c-axis conductivity, observed by LaForge and co-workers. For the local conductivities of underdoped YBa(2)Cu(3)O(7-δ) with T(c)=58 K reported by Dubroka and co-workers and the fraction of the normal state (T ≈ T(c)) component given by (μ(0)H/25 T), the computed field induced changes of the reflectivity are in quantitative agreement with the data. This suggests that the response at H=0 and T ≈ T(c) is close to that at H=25 T < H(c2) and T ≪ T(c), in accord with theories attributing the above T(c) state to that of a superconductor lacking long-range phase coherence. Also discussed are changes of the response induced by H parallel to the CuO(2) planes.

The Nernst effect and the boundaries of the Fermi liquid picture

Following the observation of an anomalous Nernst signal in cuprates, the Nernst effect has been explored in a variety of metals and superconductors during the past few years. This paper reviews the results obtained during this exploration, focusing on the Nernst response of normal quasi-particles as opposed to the one generated by superconducting vortices or by short-lived Cooper pairs. Contrary to what has been often assumed, the so-called Sondheimer cancelation does not imply a negligible Nernst response in a Fermi liquid. In fact, the amplitude of the Nernst response measured in various metals in the low-temperature limit is scattered over six orders of magnitude. According to the data, this amplitude is roughly set by the ratio of electron mobility to Fermi energy, in agreement with the implications of semi-classical transport theory.

Giant Nernst effect due to fluctuating cooper pairs in superconductors

A theory of the fluctuation-induced Nernst effect is developed for a two-dimensional superconductor in a perpendicular magnetic field. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter signal is shown to be large even far from the transition and may exceed by orders of magnitude the Fermi liquid terms. We also present a complete microscopic calculation of the Nernst coefficient for arbitrary magnetic fields and temperatures, which is based on the Matsubara-Kubo formalism. It is shown that the magnitude and the behavior of the Nernst signal observed experimentally in disordered superconducting films can be well understood on the basis of superconducting fluctuation theory.

Fluctuating superconductivity in organic molecular metals close to the Mott transition

On cooling through the transition temperature T(c) of a conventional superconductor, an energy gap develops as the normal-state charge carriers form Cooper pairs; these pairs form a phase-coherent condensate that exhibits the well-known signatures of superconductivity: zero resistivity and the expulsion of magnetic flux (the Meissner effect). However, in many unconventional superconductors, the formation of the energy gap is not coincident with the formation of the phase-coherent superfluid. Instead, at temperatures above the critical temperature a range of unusual properties, collectively known as 'pseudogap phenomena', are observed. Here we argue that a key pseudogap phenomenon-fluctuating superconductivity occurring substantially above the transition temperature-could be induced by the proximity of a Mott-insulating state. The Mott-insulating state in the kappa-(BEDT-TTF)2X organic molecular metals can be tuned, without doping, through superconductivity into a normal metallic state as a function of the parameter t/U, where t is the tight-binding transfer integral characterizing the metallic bandwidth and U is the on-site Coulomb repulsion. By exploiting a particularly sensitive probe of superconducting fluctuations, the vortex-Nernst effect, we find that a fluctuating regime develops as t/U decreases and the role of Coulomb correlations increases.

Nernst effect and disorder in the normal state of high-T(c) cuprates

We have studied the influence of disorder induced by electron irradiation on the Nernst effect in optimally and underdoped YBa2Cu3O(7-delta) single crystals. The fluctuation regime above T(c) expands significantly with disorder, indicating that the T(c) decrease is partly due to the induced loss of phase coherence. In pure crystals the temperature extension of the Nernst signal is found to be narrow whatever the hole doping, contrary to data reported in the low-T(c) cuprate families. Our results show that the presence of intrinsic disorder can explain the enhanced range of the Nernst signal found in the pseudogap phase of the latter compounds.

Field-enhanced diamagnetism in the pseudogap state of the cuprate Bi2Sr2CaCu2O(8+delta) superconductor in an intense magnetic field

In hole-doped cuprates, Nernst experiments imply that the superconducting state is destroyed by spontaneous creation of vortices which destroy phase coherence. Using torque magnetometry on Bi2Sr2CaCu2O(8+delta), we uncover a field-enhanced diamagnetic signal M above the transition temperature Tc that increases with applied field to 32 Tesla and scales just like the Nernst signal. The magnetization results above Tc distinguish M from conventional amplitude fluctuations and strongly support the vortex scenario for the loss of phase coherence at Tc.

Possible field-tuned superconductor-insulator transition in high-Tc superconductors: implications for pairing at high magnetic fields

The behavior of some high temperature superconductors (HTSC), such as La(2-x)Sr(x)CuO(4) and Bi(2)Sr(2-x)La(x)CuO(6 + delta), at very high magnetic fields, is similar to that of thin films of amorphous InOx near the magnetic-field-tuned superconductor-insulator transition. Analyzing the InOx data at high fields in terms of persisting local pairing amplitude, we argue by analogy that the local pairing amplitude also persists well into the dissipative state of the HTSCs, the regime commonly denoted as the "normal state" in very high magnetic field experiments.

77Se NMR probe of magnetic excitations of the magic angle effect in (TMTSF)2PF6

We report 77Se spin-lattice relaxation rates for (TMTSF)2PF6, carried out in the regime where a set of spectacular transport anomalies known as the "magic angle effects" are observed. In situ resistance measurements (R(zz)) were used to verify the experimental conditions and give precise sample alignment information. We found that the 77Se T-11 exhibits no significant changes as the magnetic-field orientation is rotated through the magic angles, and conclude that there is no evidence for either a single-particle gap or a spin gap. The clearly observed field-induced spin-density wave transition temperature is also, unexpectedly, not enhanced at the magic angles.

Nernst effect in poor conductors and in the cuprate superconductors

We calculate the Nernst signal in disordered conductors with the chemical potential near the mobility edge. The Nernst effect originates from the interference of itinerant and localized-carrier contributions to the thermomagnetic transport. It reveals a strong temperature and magnetic field dependence, which describes quantitatively the anomalous Nernst signal in high-Tc cuprates.

Pair density wave in the pseudogap state of high temperature superconductors

Recent scanning tunneling microscopy experiments of Bi(2)Sr(2)CaCu(2)O(8+delta) have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [Science 303, 1995 (2004)]]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.

Staggered flux vortices and the superconducting transition in the layered cuprates

We propose an effective model for the superconducting transition in the high-T(c) cuprates motivated by the SU(2) gauge theory approach. In addition to variations of the superconducting phase we allow for local admixture of staggered flux order. This leads to an unbinding transition of vortices with a staggered flux core that are energetically preferable to conventional vortices. Based on parameter estimates for the two-dimensional t-J model we argue that the staggered flux vortices provide a way to understand a phase with a moderate density of mobile vortices over a large temperature range above T(c) that yet exhibits otherwise normal transport properties. This picture is consistent with the large Nernst signal observed in this region.

Magnetic-field-induced finite-size effect in the nigh-temperature superconductor YBa2Cu3O(7-delta): a comparison with rotating superfluid 4He

The effect of strong magnetic fields (11 T) on superconductivity in YBa2Cu3O(7-delta) is investigated using high-resolution thermal expansion. We show that the field-induced broadening of the superconducting transition is due to a finite-size effect resulting from the field-induced vortex-vortex length scale. The physics of this broadening has recently been elucidated for the closely related case of rotating superfluid 4He [Phys. Rev. B 60, 12 373 (1999)]]. Our results imply that the primary effect of magnetic fields of the order of 10 T is to destroy the phase coherence; the pairing, on the other hand, appears to be quite insensitive to these fields.

Ambipolar Nernst effect in NbSe2

The first study of the Nernst effect in NbSe2 reveals a large quasiparticle contribution with a magnitude comparable and a sign opposite to the vortex signal. Comparing the effect of the charge density wave (CDW) transition on Hall and Nernst coefficients, we argue that this large Nernst signal originates from the thermally induced counterflow of electrons and holes and indicates a drastic change in the electron scattering rate in the CDW state. The results provide new input for the debate on the origin of the anomalous Nernst signal in high-T(c) cuprates.

Dependence of upper critical field and pairing strength on doping in cuprates

We have determined the upper critical field Hc2 as a function of hole concentration in bismuth-based cuprates by measuring the voltage induced by vortex flow in a driving temperature gradient (the Nernst effect), in magnetic fields up to 45 tesla. We found that Hc2 decreased steeply as doping increased, in both single and bilayer cuprates. This relationship implies that the Cooper pairing potential displays a trend opposite to that of the superfluid density versus doping. The coherence length of the pairs xi(0) closely tracks the gap measured by photoemission. We discuss implications for understanding the doping dependence of the critical temperature Tc0.