Underdoped Bi Research Articles

Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in underdoped Bi2Sr2CaCu2O8+δ.

Superconducting phase transitions in two dimensions lie beyond the description of the Ginzburg-Landau symmetry-breaking paradigm for three-dimensional superconductors. They are Berezinskii-Kosterlitz-Thouless (BKT) transitions of paired-electron condensate driven by the unbinding of topological excitations, i.e. vortices. The recently discovered monolayers of layered high-transition-temperature ([Formula: see text]) cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212) meant that this 2D superconductor promised to be ideal for the study of unconventional superconductivity. But inhomogeneity posed challenges for distinguishing BKT physics from charge correlations in this material. Here, we utilize the phase sensitivity of scanning superconducting quantum interference device microscopy susceptometry to image the local magnetic response of underdoped Bi2212 from the monolayer to the bulk throughout its phase transition. The monolayer segregates into domains with independent phases at elevated temperatures below [Formula: see text]. Within a single domain, we find that the susceptibility oscillates with flux between diamagnetism and paramagnetism in a Fraunhofer-like pattern up to [Formula: see text]. The finite modulation period, as well as the broadening of the peaks when approaching [Formula: see text] from below, suggests well-defined vortices that are increasingly screened by the dissociation of vortex-antivortex plasma through a BKT transition. In the multilayers, the susceptibility oscillation differs in a small temperature regime below [Formula: see text], consistent with a dimensional crossover led by interlayer coupling. Serving as strong evidence for BKT transition in the bulk, we observe a sharp jump in phase stiffness and paramagnetism at small fields just below [Formula: see text]. These results unify the superconducting phase transitions from the monolayer to the bulk underdoped Bi2212, and can be collectively referred to as the BKT transition with interlayer coupling.

Restoring the surface layer of Bi2Sr2CaCu2O8+δ single crystals by current injection

In 2010, we reported a new method to electronically tailor the hole concentration of the high-Tc superconductor Bi2Sr2CaCu2O8+δ (Bi-2212). We discovered that current injection along the c-axis of Bi-2212 provides a convenient tool to reversibly increase the carrier concentration. In this study, we have investigated the current injection effect on the surface junction of Bi-2212 by a series of current injection experiments carried out in samples of slightly overdoped and of extremely underdoped Bi-2212 crystals. The c-axis transport characteristics of bulk and surface intrinsic Josephson junctions are examined in a wide range of doping by current injection. Before injection treatment, typically, our samples demonstrate non-superconducting characteristics across their surface junctions, because standard preparation procedures cause the topmost CuO2 layers to be heavily degraded by oxygen loss. The electronic doping enables to substantially restore the hole concentration of the topmost CuO2 layers. The contact resistance is significantly reduced, and the intrinsic junction at the surface gets back its superconducting tunneling characteristic. We examine systematically the doping results of surface and bulk junction stacks and discuss the enhancement of their superconducting properties.

Anisotropic evolution of energy gap in Bi2212 superconductor

We present a systematic analysis of the energy gap in underdoped Bi2212 superconductor as a function of temperature and hole doping level. Within the framework of the theoretical model containing the electron-phonon and electron-electron-phonon pairing mechanism, we reproduced the measurement results of modern ARPES experiments with very high accuracy. We showed that the energy-gap amplitude is very weakly dependent on the temperature but clearly dependent on the level of doping. The evidence for a non-zero energy gap above the critical temperature, referred to as a pseudogap, was also obtained.

Variable-range hopping theory for the gap observed in strongly underdoped cuprateBi2Sr2−xLaxCuO6+δ

Recent angle resolved photoemission spectrascope (ARPES) experiments on strongly underdoped Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ cuprates have reported an unusual gap in the nodal direction. Transport experiments on these cuprates found variable range hopping behavior observed. These cuprates have both electron and hole doping which has led to proposals that this cuprate is analogous to a partially compensated semiconductors. The nodal gap then corresponds to the Efros-Schklovskii(ES) gap in such semiconductors. We calculate the doping dependence and temperature dependence of a ES gap model and find support for an Efros-Schklovskii model.

Charge-screening role ofc-axis atomic displacements inYBa2Cu3O6+xand related superconductors

The importance of charge reservoir layers for supplying holes to the CuO$_2$ planes of cuprate superconductors has long been recognized. Less attention has been paid to the screening of the charge transfer by the intervening ionic layers. We address this issue in the case of YBa$_2$Cu$_3$O$_{6+x}$, where CuO chains supply the holes for the planes. We present a simple dielectric-screening model that gives a linear correlation between the relative displacements of ions along the $c$ axis, determined by neutron powder diffraction, and the hole density of the planes. Applying this model to the temperature dependent shifts of ions along the $c$ axis, we infer a charge transfer of 5-10% of the hole density from the planes to the chains on warming from the superconducting transition to room temperature. Given the significant coupling of $c$-axis displacements to the average charge density, we point out the relevance of local displacements for screening charge modulations and note recent evidence for dynamic screening of in-plane quasiparticles. This line of argument leads us to a simple model for atomic displacements and charge modulation that is consistent with images from scanning-tunneling microscopy for underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$.

Nanoscale phase separation in deeply underdopedBi2Sr2CuO6+δandCa2CuO2Cl2

We demonstrate that tunneling spectra in deeply underdoped Bi$_{2}$Sr$_{2}$CuO$_{6+\delta}$ (Bi2201) and Ca$_2$CuO$_2$Cl$_2$ (CCOC) provide clear evidence for nanoscale phase separation (NPS), causing the gap to fill with doping rather than close. The phase separation extends over a doping range from half filling to approximately $x\sim 0.09$. Assuming the NPS is in the form of stripes, then the nodal gap -- which we model as a Coulomb gap -- arises from impurity pinning of the charged stripes, ultimately driving a metal-insulator transition.

Localization of charge carriers in the normal state of underdoped Bi2+xSr2−xCuO6+δ

We report the transport results of underdoped Bi${}_{2+x}$Sr${}_{2\ensuremath{-}x}$CuO${}_{6+\ensuremath{\delta}}$ ($0.05\ensuremath{\le}x\ensuremath{\le}0.40$) single crystals. A close relationship between the upturn of in-plane resistivity [${\ensuremath{\rho}}_{ab}(T)$] and the sign of magnetoresistance in the normal state upon Bi substitutions is found. Combining the results of the field and angular dependence of magnetoresistance, the model fitting of ${\ensuremath{\rho}}_{ab}(T)$, as well as the Hall coefficient results, we suggest a crossover from weak to strong localization of charge carriers in the underdoped Bi${}_{2+x}$Sr${}_{2\ensuremath{-}x}$CuO${}_{6+\ensuremath{\delta}}$, which may be responsible for the rather narrow superconducting dome in this system.

Impact of pseudogap on photoinduced superconducting phase transition in underdoped Bi2212

We report nonequilibrium quasiparticle (QP) dynamics in underdoped Bi2212 crystals using ultrafast optical spectroscopy, which allows to analyze the dynamics associated with the superconducting (SC) and psuedogap (PG) QPs independently. In the saturation condition of the SC component, where the SC condensate is fully destroyed within the photoexcited volume, we found a delay of the SC state recovery associated with a transient normal state. The delay increases linearly with increasing the pump fluence. The QP dynamics also shows a contribution of the PG component, whose magnitude at the start of the SC state recovery was almost constant at various pump fluences, suggesting a critical level of PG order before the SC condensate can recover.

Comparison of 2-D Quantum and Thermal Critical Fluctuations of Underdoped Bi2Sr2CaCu2O8+δ with Ultrathin YBa2Cu3O7−δ

This paper addresses two issues. Underdoped Bi-2212 has been shown to exhibit two-dimensional quantum fluctuations, with Tc vs. Ns(0) scaling qualitatively similar to ultrathin YBCO films that are 2-D by construction. The present paper shows that the quantitative difference in scaling is resolved by growing Bi-2212 films that are much smoother than previously used. Also, the absence of 2-D thermal critical behavior from the superfluid density of Bi-2212 films that exhibit 2-D quantum scaling is not likely due to an inhomogeneous Tc smearing out the 2-D thermal transition. Finally, we emphasize that there is as yet no consensus on the physics that drives the T-dependence of Ns at low to intermediate temperatures.

Prepairing and the “filling” gap in the cuprates from the tomographic density of states

We use the tomographic density of states (TDoS), which is a measure of the density of states for a single slice through the band structure of a solid, to study the temperature evolution of the superconducting gap in the cuprates. The TDoS provides unprecedented accuracy in determining both the superconducting pair-forming strength, $\Delta$, and the pair-breaking rate, $\Gamma$. In both optimally- and under-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we find the near-nodal $\Delta$ smoothly evolves through the superconducting transition temperature - clear evidence for the existence of pre-formed pairs. Additionally, we find the long observed `filling' of the superconducting gap in the cuprates is due to the strongly temperature dependent $\Gamma$.

Intrinsic Tunneling Spectroscopy for Pb-Substituted Bi2212 in the Underdoped Region

We measured intrinsic tunneling spectroscopy in mesa structures (S = 1 × 1μm2) of Bi1.9Pb0.1Sr2CaCu2O8+δ (PbBi2212) and Hall effect in PbBi2212 cleaved thin crystals. The doping level p of the PbBi2212 is estimated quantitatively through the comparison with LSCO, which is in the underdoped region. It is found that the Josephson critical current density Jc of PbBi2212 is less deviated from Ambegaokar Baratoff critical current density JcAB ≍ π Δ/2eRNS than the case of underdoped Bi2212. It is interpreted that the Pb substitution makes the tunnel barrier lower, resulting in a high superconducting pair density even with a lower doping.

Evidence of two-dimensional quantum critical behavior in the superfluid density of extremely underdoped Bi2Sr2CaCu2O8+x

Evidence of two-dimensional (2D) quantum critical fluctuations is observed in the superfluid density ns(T) \propto $\lambda$ -2(T) of deeply underdoped Bi2Sr2CaCu2O8+x (Bi-2212) films, indicating that quantum fluctuations play a dominant role in underdoped cuprates in general. 2D fluctuations are expressed by the linear scaling, Tc \propto ns(0). 2D scaling in Bi-2212 contrasts with 3D scaling seen in the much less anisotropic YBa2Cu3O7-x. Quantum critical fluctuations could also account for the absence of thermal critical behavior in \lambda^{-2}(T) of strongly underdoped Bi-2212 samples, Tc < 48 K.

Electronic liquid crystal physics of underdoped cuprates

Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra–unit-cell (IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi2Sr2CaCu2O8+δ. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting fluctuating stripes. We also present a microscopic mechanism of IUC nematic order driven by on-site and near-neighbor repulsions. Finally we discuss open questions in the context of these results.

Superconductivity in the pseudogap region of Bi2Sr1.4La0.6CuO6+δfrom angular-dependent torque measurements

We show in-plane and out-of-plane angular dependent torque data on underdoped Bi${}_{2}$Sr${}_{1.4}$La${}_{0.6}$CuO${}_{6+\ensuremath{\delta}}$ single crystals. We find that the superconducting signal persists well into the normal state, at least up to twice the zero-field superconducting transition temperature ${T}_{c0}$. The superconductivity is highly anisotropic below ${T}_{c0}$, while its anisotropy decreases significantly just above ${T}_{c0}$. In this latter $T$ regime the Cooper pairs lose their long-range phase coherence.

Quasiparticle relaxation dynamics in underdoped Bi2Sr2CaCu2O8+δby two-color pump-probe spectroscopy

We investigate the relaxation dynamics of photoexcited quasiparticles (QPs) in underdoped Bi${}_{2}$Sr${}_{2}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$ (${T}_{\mathrm{c}}=78$ K). By changing the excitation energy and polarization of the probe beam, two different types of relaxation dynamics, associated with superconducting (SC) and pseudogap (PG) QPs, are quantitatively analyzed independently. From the temperature dependencies, we obtained the SC gap, ${\ensuremath{\Delta}}_{\text{SC}}(0)=24$ meV, using BCS-type temperature-dependent gap and the pseudogap, ${\ensuremath{\Delta}}_{\text{PG}}=41$ meV. The pump fluence ($\mathcal{F}$) dependence of the SC-dominated transients shows a contribution of the PG component above the saturation condition of the SC component (${\mathcal{F}}_{\text{th}}=16\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}{\mathrm{J}/\mathrm{cm}}^{2}$), where Cooper pairs with long-range order are fully destroyed within the photoexcited volume. Assuming a temperature-independent PG decay time, we successfully isolate the native SC transient even above ${\mathcal{F}}_{\text{th}}$ by subtracting the PG response from the original data. In the saturation regime, the exponential decay (recovery of SC) is fast (${\ensuremath{\tau}}_{\text{SC}}\ensuremath{\sim}2--3$ ps), suggesting an efficient nonequilibrium phonon relaxation in this compound. We also find a flat-top response preceding the exponential decay at $\mathcal{F}g{\mathcal{F}}_{\text{th}}$, which appears as a delay of SC recovery in the original data. This response is visible over the whole temperature range below ${T}_{\mathrm{c}}$ and its duration increases with increasing $\mathcal{F}$. The response is attributable to a photoinduced SC to non-SC phase transition arising from excitation by the nonthermal QPs and/or high-frequency phonons. The consistently near-constant magnitude of the PG response at the start of the SC state recovery from the non-SC phase suggests a correlation between the SC and PG QPs.

Analysis of laser angle-resolved photoemission spectra of Ba2Sr2CaCu2O8+δin the superconducting state: Angle-resolved self-energy and the fluctuation spectrum

We analyze the ultra high resolution laser angle resolved photo-emission spectroscopy (ARPES) intensity from the slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ in the superconductive (SC) state. The momentum distribution curves (MDC) were fitted at each energy $\w$ employing the SC Green's function along several cuts perpendicular to the Fermi surface with the tilt angle $\theta$ with respect to the nodal cut. The clear observation of particle-hole mixing was utilized such that the complex self-energy as a function of $\omega$ is directly obtained from the fitting. The obtained angle resolved self-energy is then used to deduce the Eliashberg function $\alpha^2 F^{(+)}(\th,\w)$ in the diagonal channel by inverting the d-wave Eliashberg equation using the maximum entropy method. Besides a broad featureless spectrum up to the cutoff energy $\omega_c$, the deduced $\alpha^2 F$ exhibits two peaks around 0.05 eV and 0.015 eV. The former and the broad feature are already present in the normal state, while the latter emerges only below $T_c$. Both peaks become enhanced as $T$ is lowered or the angle $\th$ moves away from the nodal direction. The implication of these findings are discussed.

Intrinsic tunneling spectroscopy for Bi2−xPbxSr2CaCu2O8+δ of nm-thickness mesa structure

We have investigated intrinsic tunneling spectroscopy (ITS) with short-pulse bias to mesa structures consisting of several layers of intrinsic Josephson junction superlattices of Bi1.8Pb0.2Sr2CaCu2O8+δ(PbBi2212). Through ITS, the superconducting gap 2Δ=75meV (at 10K) is obtained for a PbBi2212 crystal. The large 2Δ value corresponds to the underdoped property of Pb-free Bi2212, which is consistent with the ab-plane transport measurement results performed simultaneously. The normal tunneling resistance RN derived from the high bias region of the I–V characteristics is significantly small in comparison with underdoped Bi2212. Moreover, Jc of PbBi2212 is less deviated from the Ambegaokar–Baratoff value than the case of underdoped Bi2212. It is interpreted that the Pb substitution makes the tunnel barrier lower, resulting in a reduced anisotropy and a high Jc even with a lower doping.

Electron-boson spectral density function of underdopedBi2Sr2CaCu2O8+δandYBa2Cu3O6.50

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature dependence; it is higher than the actual $T_c$ at all measured temperatures and decreases with temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.

Diamagnetism above Tc in Underdoped Bi2.2Sr1.8Ca2Cu3O10+δ

Single crystals of ${\rm Bi}_{2+x}{\rm Sr}_{2-x}{\rm Ca}_{2}{\rm Cu}_{3}{\rm O}_{10+\delta}$(Bi2223) with $x=0.2$ were grown by a traveling solvent floating zone method in order to investigate the superconducting properties of highly underdoped Bi2223.Grown crystals were characterized by X-ray diffraction, DC susceptibility and resistivity measurements, confirming Bi2223 to be the main phase.The crystals were annealed under various oxygen partial pressures to adjust their carrier densities from optimally doped to highly underdoped.The fluctuation diamagnetic component above the superconducting transition temperature $T_{\rm c}$ extracted from the anisotropic normal state susceptibilities $\chi_{ab}(T)$ ($H\perp c$) and $\chi_{c}(T)$ ($H\parallel c$) was found to increase with underdoping, suggesting a decrease in the superconducting dimensionality and/or increase in the fluctuating vortex liquid region.

Doping-Dependent Nodal Fermi Velocity of the High-Temperature SuperconductorBi2Sr2CaCu2O8+δRevealed Using High-Resolution Angle-Resolved Photoemission Spectroscopy

The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O(8+δ) (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is nonuniversal, in contrast with assumed phenomenology. This is used together with laser ARPES measurements of the gap velocity (v2) to resolve discrepancies with thermal conductivity measurements.