Understanding of the puzzling phenomenon of high temperature superconductivity requires reliable spectroscopic information about temperature dependence of the bulk electronic density of states. Here I present a comprehensive analysis of $T-$evolution of bulk electronic spectra in Bi-2212 obtained by Intrinsic Tunneling Spectroscopy on small mesa structures. Unambiguous spectroscopic information is obtained by obviation of self-heating problem and by improving the spectroscopic resolution. The obtained data indicate that the superconducting transition maintains the mean-field character down to moderate underdoping, and is associated with an abrupt opening of the superconducting gap, which is well described by the conventional BCS $T-$dependence. The mean-field critical temperature reaches maximum at the optimal doping and decreases with underdoping. Such behavior is inconsistent with theories assuming intimate connection between superconducting and antiferromagnetic spin gaps, and support proposals associating high temperature superconductivity with the presence of competing ground states and a quantum critical point near optimal doping.
The nodal $d_{x^2-y^2}$ superconducting gap is a hallmark of the cuprate high T$_c$ superconductors. Surprisingly recent angle-resolved photoemission spectroscopy of deeply underdoped cuprates revealed a nodeless energy gap which is adhered to the Fermi surface. Importantly this phenomenon is observed for compounds across several different cuprate families. In this letter we propose an exciting possibility, namely the fully gapped state is a topological superconductor.
In a recent Letter [Phys. Rev. Lett. 97, 207001 (2006)], Doiron-Leyraud et al. reported a study of low-temperature thermal conductivity of underdoped YBa2Cu3Oy across the superconductor-insulator boundary and argued for a novel bosonic mode as well as charge-neutral fermions. In this Comment, we show that both of these claims are dubious.
The letter deals with the spin-freezing process observed by means of NMR-NQR relaxation or by muon spin rotation in underdoped cuprate superconductors. This phenomenon, sometimes referred as coexistence of antiferromagnetic and superconducting order parameters, is generally thought to result from randomly distributed magnetic moments related to charge inhomogeneities (possibly stripes) which exhibit slowing down of their fluctuations on cooling below T$_c$ . Instead, we describe the experimental findings as due to fluctuating, vortex-antivortex, orbital currents state coexisting with d-wave su…
The microscopic theory of superconducting (SC) state in the SU(2) slave-boson model is developed. We show how the pseudogap and Fermi surface (FS) segments in the normal state develop into a d-wave gap in the superconducting state. Even though the superfluid density is of order x (the doping concentration), the physical properties of the low lying quasiparticles are found to resemble those in BCS theory. Thus the microscopic theory lay the foundation for our earlier phenomenological discussion of the unusual SC properties in the underdoped cuprates.
Raman and ARPES experiments have demonstrated that in superconducting underdoped cuprates nodal and antinodal regions are characterized by two energy scales instead of the one expected in BCS. The nodal scale decreases with underdoping while the antinodal one increases. Contrary to the behavior expected for an increasing energy scale, the antinodal Raman intensity decreases with decreasing doping. Using the Yang, Rice and Zhang (YRZ) model, we show that these features are a consequence of the non-conventional nature of the superconducting state in which superconductivity and pseudogap correlat…
By measuring the superconducting diamagnetic moments for an underdoped and an overdoped La_{2-x}Sr_xCuO_4 single crystal with equal qualities and roughly equal transition temperatures, it is found that the underdoped sample has only one transition which corresponds to H_{c2}, but the overdoped sample has two transitions with the higher one at H_{c2}. Further investigation reveals the same upper-critical field H_{c2} for both samples although the overall charge densities are very different, indicating the possibility of a very direct and detailed equivalence of the superconducting condensation …
The superconducting state of underdoped cuprates is often described in terms of a single energy-scale, associated with the maximum of the (d-wave) gap. Here, we report on electronic Raman scattering results, which show that the gap function in the underdoped regime is characterized by two energy scales, depending on doping in opposite manners. Their ratios to the maximum critical temperature are found to be universal in cuprates. Our experimental results also reveal two different quasiparticle dynamics in the underdoped superconducting state, associated with two regions of momentum space: noda…
We present angle-resolved photoemission spectroscopy (ARPES) data on moderately underdoped La$_{1.855}$Sr$_{0.145}$CuO$_4$ at temperatures below and above the superconducting transition temperature. Unlike previous studies of this material, we observe sharp spectral peaks along the entire underlying Fermi surface in the superconducting state. These peaks trace out an energy gap that follows a simple {\it d}-wave form, with a maximum superconducting gap of 14 meV. Our results are consistent with a single gap picture for the cuprates. Furthermore our data on the even more underdoped sample La$_{…
There is increasing experimental evidence that the superconducting energy gap $Δ_0$ in the underdoped cuprates is independent of doping concentration $x$ while the superfluid density is linear in $x$. We show that under these conditions, thermal excitation of the quasiparticles is very effective in destroying the superconducting state, so that $T_c$ is proportional to $xΔ_0$ and part of the gap structure remains in the normal state. We then estimate $H_{c2}$ and predict it to be proportional to $x^2$. We also discuss to what extent the assumptions that go into the quasiparticle description can…
We present fermi liquid expressions for the low temperature behavior of the superfluid stiffness, explain why they differ from those suggested recently by Lee and Wen, and discuss their applicability to data on high-$T_c$ superconductors. We find that a consistent description requires a strong, doping dependent anisotropy, which affects states near the zone corners much more strongly than those near the zone diagonals.
Phenomenological models for the antiferromagnetic (AF) vs. d-wave superconductivity competition in cuprates are studied using conventional Monte Carlo techniques. The analysis suggests that cuprates may show a variety of different behaviors in the very underdoped regime: local coexistence or first-order transitions among the competing orders, stripes, or glassy states with nanoscale superconducting (SC) puddles. The transition from AF to SC does not seem universal. In particular, the glassy state leads to the possibility of "colossal'' effects in some cuprates, analog of those in manganites. U…
I review some of the experimental evidence and theoretical arguments that suggest that pseudogap matter is a new form of matter that coexists with coherent electron matter in the normal state and with superconducting matter below the superconducting transition temperature. I describe work in progress on a phenomenological two-fluid description of the evolution of pseudogap behavior that offers an explanation for the unexpectedly simple scaling behavior for the uniform magnetic susceptibility found in the underdoped cuprates and use this to propose a physical picture of the underdoped cuprates …
The clearly resolved bilayer splitting in ARPES spectra of the underdoped Pb-Bi2212 compound rises the question of how the bonding and antibonding sheets of the Fermi surface are gapped in the superconducting state. Here we compare the superconducting gaps for both split components and show that within the experimental uncertainties they are identical. By tuning the relative intensity of the bonding and antibonding bands using different excitation conditions we determine the precise {\bf k}-dependence of the leading edge gap. Significant deviations from the simple cos($k_{x}$)-cos($k_{y}$) gap…
The recent discovery of superconductivity in infinite-layer nickelates generates tremendous research endeavors, but the ground state of their parent compounds is still under debate. Here, we report experimental evidences for the dominant role of Kondo scattering in the underdoped Nd1-xSrxNiO2 thin films. A resistivity minimum associated with logarithmic temperature dependence in both longitudinal and Hall resistivities are observed in the underdoped Nd1-xSrxNiO2 samples before the superconducting transition. A linear scaling behavior $σ_{xy}^{AHE}\simσ_{xx}$ between anomalous Hall conductivity…
The one-particle spectral function of a state formed by superconducting (SC) clusters is studied via Monte Carlo techniques. The clusters have similar SC amplitudes but randomly distributed phases. This state is stabilized by the competition with anti-ferromagnetism, after quenched disorder is introduced. Fermi arcs between the critical temperature Tc and the cluster formation temperature scale T* are observed, similarly as in the pseudo-gap state of the cuprates. The arcs originate at metallic regions in between the neighboring clusters that present large SC phase differences.
High-temperature superconductivity in iron-arsenic materials (pnictides) near an antiferromagnetic phase raises the possibility of spin-fluctuation-mediated pairing. However, the interplay between antiferromagnetic fluctuations and superconductivity remains unclear in the underdoped regime, which is closer to the antiferromagnetic phase. Here we report that the superconducting gap of the underdoped pnictides scales linearly with the transition temperature, and that a distinct pseudogap coexisting with the SC gap develops on underdoping. This pseudogap occurs on Fermi surface sheets connected b…
Inelastic neutron scattering has been used to determine the dynamic spin fluctuations in an underdoped high temperature superconductor YBCO_{6.8} single crystal. The magnetic resonance, that occurs around 40 meV in overdoped samples, is shifted to a lower energy, E_r= 34 meV. A constant ratio, $E_r/ k_B T_C= 4.9 \pm 0.2$, almost independent of the doping level, is found. According to numerous theoretical approaches, this finding supports the idea that the resonance energy is proportional (approximately twice) to the superconducting gap.
Measurements of thermal conductivity versus temperature over a broad range of doping in YBa$_2$Cu$_3$O$_{6+x}$ and HgBa$_2$Ca$_{n-1}$Cu$_n$O$_{2n+2+δ}$ ($n$=1,2,3) suggest that small domains of localized holes develop for hole concentrations near $p$=1/8. The data imply a mechanism for localization that is intrinsic to the CuO$_2$-planes and is enhanced via pinning associated with oxygen-vacancy clusters.
We study the effect of thermal phase fluctuation on the electron spectral function $A(k,ω)$ in a d-wave superconductor with Monte Carlo simulation. The phase degree of freedom is modeled by a XY-type model with build-in d-wave character. We find a ridge-like structure emerges abruptly on the underlying Fermi surface in $A(k,ω=0)$ above the KT-transition temperature of the XY model. Such a ridge-like structure, which shares the same characters with the Fermi arc observed in the pseudogap phase of the underdoped cuprates, is found to be caused by the vortex-like phase fluctuation of the XY model…
The superconducting gap - an energy scale tied to the superconducting phenomena-opens on the Fermi surface at the superconducting transition temperature (TC) in conventional BCS superconductors. Quite differently, in underdoped high-TC superconducting cuprates, a pseudogap, whose relation to the superconducting gap remains a mystery, develops well above TC. Whether the pseudogap is a distinct phenomenon or the incoherent continuation of the superconducting gap above TC is one of the central questions in high-TC research. While some experimental evidence suggests they are distinct, this issue i…
Magnetization and 63Cu NMR-NQR relaxation measurements are used to study the superconducting fluctuations in YBa2Cu3O6+x (YBCO) oriented powders. In optimally doped YBCO the fluctuating negative magnetization M_{fl}(H,T) is rather well described by an anisotropic Ginzburg-Landau (GL) functional and the curves M_{fl}/sqrt{H} cross at Tc. In underdoped YBCO, instead, over a wide temperature range an anomalous diamagnetism is observed, stronger than in the optimally doped compound by about an order of magnitude. The field and temperature dependences of M_{fl} cannot be described either by an anis…
Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions through which they communicate by Josephson tunneling to establish the macroscopic superconducting state [1]. Although crystals of the cuprate high-Tc superconductors are not granular in a structural sense, theory indicates that at low hole densities the holes can become concentrated at some locations resulting in hole-rich superconducting domains [2-5]. Granular superconductivity due to Josephson tunneling through 'undoped' regions between such domains would represent a new p…
Inelastic neutron scattering measurements have been performed on underdoped Ba(Fe1-xCox)2As2 (x = 4.7%) where superconductivity and long-range antiferromagnetic (AFM) order coexist. The broad magnetic spectrum found in the normal state develops into a magnetic resonance feature below TC that has appreciable dispersion along c-axis with a bandwidth of 3-4 meV. This is in contrast to the optimally doped x = 8.0% composition, with no long-range AFM order, where the resonance exhibits a much weaker dispersion [see Lumsden et al. Phys. Rev. Lett. 102, 107005 (2009)]. The results suggest that the re…
Following a recent study by our group in which a large $T_c$ enhancement was reported in bilayers of the non-superconducting $La_{1.65}Sr_{0.35}CuO_4$ and superconducting $La_{1.88}Sr_{0.12}CuO_4$ films [Phys. Rev. Lett. \textbf{101}, 057005 (2008)], we checked if a similar effect occurs when superconducting $La_{1.88}Sr_{0.12}CuO_4$ islands are coated with a continuous layer of the non superconducting $La_{1.65}Sr_{0.35}CuO_4$. We found that no such phenomenon is observed. The bare superconducting islands film behaves as an insulator where transport occurs via hopping or tunneling between isl…
In a recent Comment [arXiv:0711.4654], Y. Ando raises two valid issues in relation to our low-temperature heat transport study of YBa$_2$Cu$_3$O$_y$ across the insulator-to-superconductor boundary: 1) the possible role of twin boundaries in scattering phonons; 2) the best fitting procedure for extracting a fermionic (linear) term from the data. In this Reply, we show that both concerns can be laid to rest by 1) using new data from a tetragonal (twin-free) sample, and 2) using an analysis that does not involve any fitting.
The extended $t-J$ model is theoretically studied, in the context of hole underdoped cuprates. Based on results obtained by recent numerical studies, we identify the mean field state having both the antiferromagnetic and staggered flux resonating valence bond orders. The random-phase approximation is employed to analyze all the possible collective modes in this mean field state. In the static (Bardeen Cooper Schrieffer) limit justified in the weak coupling regime, we obtain the effective superconducting interaction between the doped holes at the small pockets located around $\bm{k}= (\pm π/2, …
We report an anomalous local structural response in the CuO2 planes associated with the appearance of charge inhomogeneities at low temperature in underdoped but superconducting La2-x(Sr,Ba)xCuO4. We used pair distribution function analysis of neutron powder diffraction data. The increase in the Cu-O bond length distribution at low temperature has an onset temperature which correlates with observations of charge and spin freezing seen by other probes.
Metals interacting via short-range antiferromagnetic fluctuations are unstable to sign-changing superconductivity at low temperatures. For the cuprates, this leading instability leads to the well known $d-$wave superconducting state. However, there is also a secondary instability to an incommensurate charge density wave, with a predominantly $d-$wave form factor, arising from the same antiferromagnetic fluctuations. Recent experiments in the pseudogap regime of the hole-doped cuprates have found strong evidence for such a charge density wave order and, in particular, the predicted $d-$wave for…
The Gaussian fluctuations in slave-boson mean-field theory of $t-J$ model is analyzed in this paper in the low-doping regime where the superconducting to normal (pseudo-gap phase) transition is driven by vanishing of bose-condensation amplitude. By eliminating the boson and constraint fields exactly in the linear response regime we show that the Gaussian theory describes a Fermi liquid superconductor where the superconducting to normal transition is actually a spin-charge separation transition characterized by a change of Landau parameter from $F_1>-1$ in the superconducting phase to $F_1=-1$ …
General theory of d-wave quasiparticles coupled to phase fluctuations of superconducting order parameter is discussed. In the charge sector the superfluid density is found to conform to Uemura scaling, and the charge renormalization factor to decrease with underdoping. The spin susceptibilty exhibits four distinct regimes with increasing frequency and scales with the superconducting Tc, as observed.
A detailed inelastic neutron scattering study of the in-plane anisotropy of magnetic excitations in twin-free YBa$_2$Cu$_3$O$_{6.6}$ ($T_c =$ 61 K) reveals that the spin excitation spectra in the superconducting and normal states are qualitatively different. Below $T_c$, the spectrum consists of upward- and downward-dispersing branches with modest in-plane anisotropy merging at an energy $E_{res} =$ 37.5 meV. In the normal state, the singularity at $E_{res}$ disappears, and the spectrum exhibits a steep dispersion with a strongly anisotropic in-plane geometry. These data have important implica…
Evidence of nematic effects in the mixed superconducting phase of slightly underdoped $\text{Ba}(\text{Fe}_{1-x}\text{Co}_x)_2\text{As}_2$ is reported. We have found strong in-plane resistivity anisotropy for crystals in different strain conditions. For these compositions, there is no magnetic long range order, so the description may be ascribed to the interplay between the superconducting and nematic order parameters. A piezoelectric-based apparatus is used to apply tensile or compressive strain to tune nematic domain orientation in order to examine intrinsic nematicity. Measurements are done…
New tunneling data are reported in underdoped Bi2Sr2CaCu2O8-d using superconductor-insulator-superconductor break junctions. Energy gaps, Delta, of 51+2, 54+2 and 57+3 meV are observed for three crystals with Tc=77, 74, and 70 K respectively. These energy gaps are nearly three times larger than for overdoped crystals with similar Tc. Detailed examination of tunneling spectra over a wide doping range from underdoped to overdoped, including the Josephson IcRn product, indicate that these energy gaps are predominantly of superconducting origin.
Through the measurements of magnetic field dependence of specific heat in $La_{2-x}Sr_xCuO_4$ in zero temperature limit, we find that the nodal slope $v_Δ$ of the superconducting gap has a very similar doping dependence of the pseudogap temperature $T^*$ or value $Δ_p$. Meanwhile the maximum quasiparticle gap derived from $v_Δ$ is quite close to $T^*$. Both indicate a close relationship between the pseudogap and superconductivity. It is also found that $T_c \approx βv_Δγ_n(0)$, where $γ_n(0)$ is the extracted zero temperature value of the normal state specific heat coefficient which is proport…
There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodal-antinodal dichotomy in the structure of the single-particle spectral functions. In this context, we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting "nodal points" and the nematic "cold-spots" on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angle-resolved photoemi…
Single crystals of ${\rm Bi}_{2+x}{\rm Sr}_{2-x}{\rm Ca}_{2}{\rm Cu}_{3}{\rm O}_{10+δ}$(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 tran…
We propose a theoretical description of the superconducting state of under- to overdoped cuprates, based on the short coherence length of these materials and the associated strong pairing fluctuations. The calculated $T_c$ and the zero temperature excitation gap $Δ(0)$, as a function of hole concentration $x$, are in semi-quantitative agreement with experiment. Although the ratio $T_c/Δ(0)$ has a strong $x$ dependence, different from the universal BCS value, and $Δ(T)$ deviates significantly from the BCS prediction, we obtain, quite remarkably, quasi-universal behavior, for the normalized supe…
Measurements of the angular dependence of conductance spectra in the a-b plane of underdoped YBCO junctions are reported. At zero magnetic field the superconducting gap shows a |d+is|-like symmetry. Application of a magnetic field strongly suppresses this gap leaving only the pseudogap feature which also shows a |d+is|-like angular dependence. We thus observe the same symmetry for the superconducting gap and the pseudogap characterizing the YBCO electrodes near the interface with the barrier. An H_{c2} value of about 5T of the secondary (is) order parameter can also be deduced from our results…
For orthorhombic superconductors we define thermodynamic anisotropy $N \equiv d T_c/d ε_{22} - dT_c/d ε_{11}$ as the difference in how superconducting $T_c$ varies with strains $ε_{ii}$, $i=(1, 2)$, along the in-plane directions. We study the hole doping ($p$) dependence of $N$ on detwinned single crystals of underdoped YBa$_2$Cu$_3$O$_y$ (YBCO) using ultrasound technique. While the structural orthorhombicity of YBCO reduces monotonically with decreasing doping over $0.065 <p<0.16$, we find that the thermodynamic anisotropy shows an intriguing enhancement at intermediate doping level, which is…
A generic theory of the quasi-particle superconducting gap in underdoped cuprates is derived in the strong coupling limit, and found to describe extremely well the experimental "second gap" in \textit{absolute scale}. In drastic contrast to the standard theories of Bogoliubov quasi-particle excitations, the quasi-particle gap is shown to originate from anomalous kinetic process, completely unrelated to the pairing strength. Furthermore, the $k$-dependence of the gap deviates significantly from the pure $d_{x^2-y^2}$-wave of the order parameter. Our study reveals a new paradigm for the nature o…
We use inelastic neutron scattering to show that superconductivity in electron-underdoped NaFe0.985Co0.015As induces a dispersive sharp resonance near Er1 = 3:25 meV and a broad dis- persionless mode at Er2 = 6 meV. However, similar measurements on overdoped superconducting NaFe0:955Co0:045As find only a single sharp resonance at Er = 7 meV. We connect these results with the observations of angle-resolved photoemission spectroscopy that the superconducting gaps in the electron Fermi pockets are anisotropic in the underdoped material but become isotropic in the overdoped case. Our analysis indi…
Polarized and unpolarized triple-axis spectrometry has been used to study an underdoped YBa_2Cu3O6.6. Our results indicate that spin excitations in the superconducting state are essentially the same as those in the fully doped material except that the unusual 41 meV resonance is observed at 34.8 meV. The normal state spin excitations are characterized by a weakly energy-dependent continuum whose temperature dependence shows the clear signature of a superconducting gap at Tc. The enhancement at the resonance is accompanied by a suppression of magnetic fluctuations at both higher and lower energ…
Using angle-resolved photoemission (ARPES), it is revealed that the low-energy electronic excitation spectra of highly underdoped superconducting and non-superconducting La(2-x)SrxCuO4 cuprates are gapped along the entire underlying Fermi surface at low temperatures. We show how the gap function evolves to a d(x2-y2) form as increasing temperature or doping, consistent with the vast majority of ARPES studies of cuprates. Our results provide essential information for uncovering the symmetry of the order parameter(s) in strongly underdoped cuprates, which is a prerequisite for understanding the …
The superconducting transition temperature, Tc, of bilayers comprising underdoped La2-xSrxCuO4 films capped by a thin heavily overdoped metallic La1.65Sr0.35CuO4 layer, is found to increase with respect to Tc of the bare underdoped films. The highest Tc is achieved for x = 0.12, close to the 'anomalous' 1/8 doping level, and exceeds that of the optimally-doped bare film. Our data suggest that the enhanced superconductivity is confined to the interface between the layers. We attribute the effect to a combination of the high pairing scale in the underdoped layer with an enhanced phase stiffness …
We study the reconfiguration of the angular resolved photoemission spectrum near $M$ point which occurs in Bi$_2$Sr$_2$CaCu$_2$O$_8$ upon cooling below the superconducting transition temperature. Restricting our attention to the case of underdoped samples we offer a phenomenological mechanism-independent argument which explains the emergence of a peak in the spectrum in terms of the normal state pseudogap. All of the basic experimental observations, including the peak dispersion, `dip-and-hump' shape of the superconducting state spectrum and appearance of the peak at the temperatures somewhat …
We report on results of our analysis of published experimental data of the in-plane infrared response of two representative underdoped high-$T_{\mathrm{c}}$ cuprate superconductors, focusing on a characteristic gap feature in the spectra of the real part of the conductivity and the corresponding structures of the memory function, that develop below a temperature $T^{\mathrm{ons}}$ considerably higher than $T_{\mathrm{c}}$. Several arguments based on comparisons of the data with results of our calculations are provided indicating that the features are due to superconductivity and that $T^{\math…
The temperature dependence of the anisotropy of the superconducting state parameters, γ, was studied by torque magnetometry for the high temperature superconductor SmBa2Cu3Ox in magnetic fields of up to 9 T. The measurements were performed on four underdoped single crystals with oxygen contents corresponding to Tc's varying from 42.8 to 63.6 K. The anisotropy was found to be strongly temperature dependent, while only a weak dependence on the magnetic field was observed. No evidence for a field dependent superfluid density was found. Possible origins of the temperature dependence of the anisotr…
We have measured the superconducting critical temperature (Tc) and the diamagnetic susceptibility of La2-xSrxCuO4 single crystals in various magnetic fields. We observed a field-induced evolution from an apparent Tc phase to an intrinsic Tc1 = 15 K or Tc2 = 30 K phase characterized by "magic" hole concentration which is commensurate with that of a two dimensional electronic lattice. The onset Tc of the intrinsic superconducting phases remains robust up to H = 5 Tesla. We suggest that the intrinsic superconducting phases at "magic" doping concentrations are the pristine electronic phases of hig…
The underdoped cuprates have a number of interesting and unusual properties that often seem hard to reconcile with one another. In this paper we show how many of these diverse phenomena can be synthesized into a single coherent theoretical picture. Specifically we present a description where a pseudogap and gapless Fermi arcs exist in the normal state above the superconducting transition temperature ($T_c$), but give way to the observed quantum oscillations and other phenomena at low temperature when the superconductivity is suppressed by a magnetic field. We show the consistency between these…
We report angle-resolved photoemission spectroscopy measurements of the excitation gap in underdoped superconducting thin films of Bi_2Sr_2Ca_{1-x}Dy_xCu_2O_{8+d}. As Tc is reduced by a factor of 2 by underdoping, the superconducting state gap Δdoes not fall proportionally, but instead stays constant or increases slightly, in violation of the BCS mean-field theory result. The different doping dependences of Δand kT_c indicate that they represent different energy scales. The measurements also show that Δis highly anisotropic and consistent with a d_{x^2-y^2} order parameter, as in previous stud…
The Josephson Plasma Resonance is used to study the c-axis supercurrent in the superconducting state of underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ with varying degrees of controlled point-like disorder, introduced by high-energy electron irradiation. As disorder is increased, the Josephson Plasma frequency decreases proportionally to the critical temperature. The temperature dependence of the plasma frequency does not depend on the irradiation dose, and is in quantitative agreement with a model for quantum fluctuations of the superconducting phase in the CuO$_{2}$ layers.
The thermal conductivity kappa of the iron-arsenide superconductor Ba1-xKxFe2As2 was measured for heat currents parallel and perpendicular to the tetragonal c axis at temperatures down to 50 mK and in magnetic fields up to 15 T. Measurements were performed on samples with compositions ranging from optimal doping (x = 0.34; Tc = 39 K) down to dopings deep into the region where antiferromagnetic order coexists with superconductivity (x = 0.16; Tc = 7 K). In zero field, there is no residual linear term in kappa(T) as T goes to 0 at any doping, whether for in-plane or inter-plane transport. This s…
The in-plane London penetration depth, $Δλ(T)$, was measured using a tunnel diode resonator in single crystals of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ for five doping levels $x$ ranging from underdoped, $T_c$=11 K ($x$=0.17), to optimally doped, $T_c=$38 K ($x_\textmd{\scriptsize opt}$= 0.35). In the optimally doped samples, $Δλ(T)$ shows exponential saturation in $T \to 0$ limit suggesting a fully gapped superconductivity. The lowest-$T_c$ samples show much stronger non-exponential variation of $Δλ(T)$. Fitting the data to a power-law, $Δλ(T)= AT^n$, reveals a monotonic decrease of the exponent $n$ wi…
We have investigated the doping dependence of the penetration depth vs. temperature in electron doped Pr$_{2-x}$Ce$_x$CuO$_{4-δ}$ using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a $d_{x^2-y^2}$ pairing gap in the underlying spectrum, we find nodeless behavior of the low-$T$ penetration depth in underdoped case, in accord with experimental results. As doping increases, a linear-in-$T$ behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level…
The magnetic susceptibility measured in neutron scattering experiments in underdoped YBa$_2$Cu$_3$O$_{7-y}$ is interpreted based on the self-consistent solution of the t-J model of a Cu-O plane. The calculations reproduce correctly the frequency and momentum dependencies of the susceptibility and its variation with doping and temperature in the normal and superconducting states. This allows us to interpret the maximum in the frequency dependence -- the resonance peak -- as a manifestation of the excitation branch of localized Cu spins and to relate the frequency of the maximum to the size of t…
The momentum dependence of the superconducting gap in the cuprates has been debated, with most experiments reporting a deviation from a simple $d_{x^2-y^2}$ form in the underdoped regime and a few experiments claiming that a simple $d_{x^2-y^2}$ form persists down to the lowest dopings. We affirm that the superconducting gap function in sufficiently underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) deviates from a simple \textit{d}-wave form near the antinode. This is observed in samples where doping is controlled only by oxygen annealing, in contrast to claims that this effect is only seen i…
The thermal conductivity $κ$ of underdoped \Y was measured in the $T \to 0$ limit as a function of hole concentration $p$ across the superconducting critical point at $p_{SC}$ = 5.0%. ``Time doping'' was used to resolve the evolution of bosonic and fermionic contributions with high accuracy. For $p \leqslant p_{SC}$, we observe an additional $T^3$ contribution to $κ$ which we attribute to the boson excitations of a phase with long-range spin or charge order. Fermionic transport, manifest as a linear term in $κ$, is seen to persist unaltered through $p_{SC}$, showing that the state just below $…
In underdoped cuprates fluctuations of the phase of the superconducting order parameter play a role due to the small superfluid density. We consider the effects of phase fluctuations assuming the exchange of spin fluctuations to be the predominant pairing interaction. Spin fluctuations are treated in the fluctuation-exchange approximation, while phase fluctuations are included by Berezinskii-Kosterlitz-Thouless theory. We calculate the stiffness against phase fluctuations, ns(omega)/m*, as a function of doping, temperature, and frequency, taking its renormalization by phase fluctuations into a…
The role of antiferromagnetic spin correlations in high-temperature superconductors remains a matter of debate. We present inelastic neutron scattering evidence that gapless spin fluctuations coexist with superconductivity in La$_{1.905}$Ba$_{0.095}$CuO$_4$. Furthermore, we observe that both the low-energy magnetic spectral weight and the spin incommensurability are enhanced by the onset of superconducting correlations. We propose that the coexistence occurs through intertwining of spatial modulations of the pair wave function and the antiferromagnetic correlations. This proposal is also direc…
We present a theoretical model to show that the transition from an antiferromagnetic (AFM) phase to the $d_{x^2-y^2}$-wave superconductivity occurs through a robust companion of a finite momentum pairing between $({\bf k},\uparrow)$ and $(-{\bf k}-{\bf Q},\downarrow)$ electrons, namely pair-density wave (PDW) state, where ${\bf Q}=(π,π)$ is the AFM wavevector. Interestingly, the spatial structure of the PDW is constrained to be a $p+ip$-wave symmetry, which follows $p_{\bf k}=p_{-{\bf k}-{\bf Q}}$ under fermions exchange in cuprates, dictating a spin-singlet pairing. Furthermore, the PDW state…
