Antiferromagnetism and hole pair checkerboard in the vortex state of high T(c) superconductors

Hall effect in quantum critical charge-cluster glass

Upon doping, cuprates undergo a quantum phase transition from an insulator to a d-wave superconductor. The nature of this transition and of the insulating state is vividly debated. Here, we study the Hall effect in La2-xSrxCuO4(LSCO) samples doped near the quantum critical point atx∼ 0.06. Dramatic fluctuations in the Hall resistance appear belowTCG∼ 1.5 K and increase as the sample is cooled down further, signaling quantum critical behavior. We explore the doping dependence of this effect in detail, by studying a combinatorial LSCO library in which the Sr content is varied in extremely fine steps,Δx∼ 0.00008. We observe that quantum charge fluctuations wash out when superconductivity emerges but can be restored when the latter is suppressed by applying a magnetic field, showing that the two instabilities compete for the ground state.

Experimental observation of the crystallization of a paired holon state

An excitation at 201 meV is observed in the doped-hole ladder cuprate Sr14Cu24O41, using ultraviolet resonance Raman scattering with incident light at 3.7 eV polarized along the rungs. The excitation is of charge nature, with a temperature independent excitation energy, and can be understood via an intraladder pair-breaking process. The intensity tracks closely the order parameter of the charge density wave in the ladder CDW(L), but persists above its transition temperature T(CDW(L)), indicating a strong local pairing above the T(CDW(L)). The 201 meV excitation vanishes in La6Ca8Cu24O(41+δ), and La5Ca9Cu24O41 which are samples with no holes in the ladders. Our results suggest that the doped holes in the ladder are composite bosons consisting of paired holons that order below T(CDW).

Imaging the impact on cuprate superconductivity of varying the interatomic distances within individual crystal unit cells

Many theoretical models of high-temperature superconductivity focus only on the doping dependence of the CuO(2)-plane electronic structure. However, such models are manifestly insufficient to explain the strong variations in superconducting critical temperature, T(c), among cuprates that have identical hole density but are crystallographically different outside of the CuO(2) plane. A key challenge, therefore, has been to identify a predominant out-of-plane influence controlling the superconductivity, with much attention focusing on the distance d(A) between the apical oxygen and the planar copper atom. Here we report direct determination of how variations in interatomic distances within individual crystalline unit cells affect the superconducting energy-gap maximum Delta of Bi(2)Sr(2)CaCu(2)O(8+delta). In this material, quasiperiodic variations of unit cell geometry occur in the form of a bulk crystalline "supermodulation." Within each supermodulation period, we find approximately 9 +/- 1% cosinusoidal variation in local Delta that is anticorrelated with the associated d(A) variations. Furthermore, we show that phenomenological consistency would exist between these effects and the random Delta variations found near dopant atoms if the primary effect of the interstitial dopant atom is to displace the apical oxygen so as to diminish d(A) or tilt the CuO(5) pyramid. Thus, we reveal a strong, nonrandom out-of-plane effect on cuprate superconductivity at atomic scale.

Fourfold structure of vortex-core states in Bi2Sr2CaCu2O8+delta

We present a detailed study of vortex-core spectroscopy in slightly overdoped Bi2Sr2CaCu2O8+delta using a low-temperature scanning tunneling microscope. Inside the vortex core, we observe a fourfold symmetric modulation of the local density of states with an energy-independent period of (4.3 +/- 0.3)a0. Furthermore, we demonstrate that this square modulation is related to the vortex-core states which are located at +/-6 meV. Since the core-state energy is proportional to the superconducting gap magnitude , our results strongly suggest the existence of a direct relation between the superconducting state and the local electronic modulations in the vortex core.

Magic doping fractions for high-temperature superconductors

We report hole-doping dependence of the in-plane resistivity rho(ab) in a cuprate superconductor La(2-x)Sr(x)CuO4, carefully examined using a series of high-quality single crystals. Our detailed measurements find a tendency towards charge ordering at particular rational hole-doping fractions of 1/16, 3/32, 1/8, and 3/16. This observation appears to suggest a specific form of charge order and is most consistent with the recent theoretical prediction of the checkerboard-type ordering of the Cooper pairs at rational doping fractions x = (2m+1)/2n, with integers m and n.

Large magnetic field-induced spectral weight enhancement of high-energy spin excitations in La1.88Sr0.12CuO4

We report electronic Raman scattering experiments on a superconducting La(1.88)Sr(0.12)CuO(4) single crystal in a magnetic field. At low temperatures, the spectral weight of the high-energy two-magnon peak increases linearly with field and is amplified by a factor of more than two at 14 T. The effect disappears at elevated temperatures and is not present in undoped La(2)CuO(4). This observation is discussed in terms of an electronically inhomogeneous state in which the field enhances the volume fraction of a phase with local antiferromagnetic order at the expense of the superconducting phase.

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.

A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2

The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the 'pseudogap' regime. This regime is rich in peculiar electronic phenomena, prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca2-xNaxCuO2Cl2. Tunnelling spectroscopy (at energies |E| > 100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E| < 100 meV, the spectrum exhibits a V-shaped energy gap centred on E = 0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO2-unit-cell square 'checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca2-xNaxCuO2Cl2.

Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O(8+delta)

We report atomic-scale characterization of the pseudogap state in a high-Tc superconductor, Bi2Sr2CaCu2O(8+delta). The electronic states at low energies within the pseudogap exhibit spatial modulations having an energy-independent incommensurate periodicity. These patterns, which are oriented along the copper-oxygen bond directions, appear to be a consequence of an electronic ordering phenomenon, the observation of which correlates with the pseudogap in the density of electronic states. Our results provide a stringent test for various ordering scenarios in the cuprates, which have been central in the debate on the nature of the pseudogap and the complex electronic phase diagram of these compounds.

Field-induced thermal metal-to-insulator transition in underdoped La(2-x)Sr(x)CuO(4+delta)

The transport of heat and charge in cuprates was measured in single crystals of La(2-x)Sr(x)CuO(4+delta) (LSCO) across the doping phase diagram at low temperatures. In underdoped LSCO, the thermal conductivity is found to decrease with increasing magnetic field in the T-->0 limit, in striking contrast to the increase observed in all superconductors, including cuprates at higher doping. In heavily underdoped LSCO, where superconductivity can be entirely suppressed with an applied magnetic field, we show that a novel thermal metal-to-insulator transition takes place upon going from the superconducting state to the field-induced normal state.

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.