Session L33: Superconductivity: Electronic Structure I

IR Hall measurements in overdoped $Pr_{2-x}Ce_{x}CuO_{4}$: evidence for magnon induced current-vertex corrections

In overdoped $Pr_{2-x}Ce_{x}CuO_{4}$, the dc Hall coefficient achieves its expected value $R_{H} \propto 1+x$ consistent with the large hole-like Fermi surface observed in ARPES, but only at low temperatures. As temperature is raised, the dc Hall coefficient falls off and becomes negative at a temperature that increases with $x$. We have measured the IR Hall angle of two overdoped $Pr_{2-x}Ce_{x}CuO_{4}$ samples at sufficiently low optical excitation energies (below 10meV) to directly probe the Fermi-surface properties. The observed large deviations from the classical result correspond to the addition of electron-like contributions to $\sigma_{xy}$, even at T=0, due to the finite frequency. Results of a model developed by H. Kontani of the low frequency IR Hall response which incorporates current-vertex corrections induced by magnon scattering are directly compared to the data. The model fully captures the salient features of the measured Hall response as a function of doping, temperature, and frequency. These results demonstrate that the anomalous Hall effect in the cuprates is a consequence of current vertex corrections to $\sigma_{xy}$.   

Fermi surface reconstruction in e-doped cuprates: IR Hall measurements in underdoped $Pr_{2-x}Ce_{x}CuO_{4}$

The complex IR Hall angle is measured in PCCO at doping levels ranging from 10\% to 15\% at low optical excitation energy (10 meV). A precipitous decrease in Hall mass with a decrease in doping level in the underdoped regime is strong evidence of Fermi surface reconstruction and pocket formation, an observation consistent with ARPES and optical spectroscopy measurements. The data over the entire underdoped region is consistent with the predicted IR Hall response based upon ARPES data and Boltzmann theory. The temperature dependence of the Hall mass indicate a gradual roll-over from small pockets to the large unreconstructed Fermi surface expected in overdoped PCCO.   

Evidence for Fermi surface reconstruction in h-doped cuprates: IR Hall measurements in underdoped $La_{2-x}Sr_{x}CuO_{4}$

We measure the IR Hall angle in $La_{2-x}Sr_{x}CuO_{4}$ as a function of doping ranging from 7\% to 16.5\%. The optimally doped sample is shown to be consistent with ARPES measurements. However, large deviations at low doping between the Hall mass and the IR Hall response predicted by the measured Fermi arcs in ARPES experiments is observed. The rapid decrease in Hall mass with underdoping is a hallmark signature of Fermi surface reconstruction exhibited in systems which are well known to fractionalize into Fermi pockets (underdoped PCCO). Comparisons with Fermi surface models will be discussed.   

Quantum Oscillations in the Specific Heat of Ultraclean YBCO in 45T magnetic fields

We report specific heat measurements of Ortho-II YBCO in a magnetic field as large as 45T to directly compare the superconducting state with the normal state at low temperatures. This thermodynamic measurement of the electronic density of states determines the total number of carrier pockets in the two-dimensional Fermi surface of Ortho-II YBCO. These measurements also reveal quantum oscillations in the specific heat that provide a bulk measurement of the quasiparticle density of states in the d-wave mixed state.   

De Haas-Van Alphen Experiments on BaNi$_2$P$_2$

We have observed de Haas-van Alphen (dHvA) oscillations in BaNi$_2$P$_2$, which is isostructural with BaFe$_2$As$_2$ and becomes superconducting below $T_c$ ~ 3 K without doping [T. Mine et al., Solid State Commun. 147, 111 (2008)]. It is a suitable compound to study how differnet electronic structures are between iron and nickel-based superconductors. The single crystals used in the study were obtained by high- pressure synthesis. dHvA frequencies up to 8 kT were observed, and their sizes and angular dependences can be explained very well by a band-structure calculation. Effective masses are two to three times largere than the corresponding band masses, suggesting moderate mass enhancement due to electron-phonon and electron-electron interactions.   

de Haas van Alphen Effect in Strongly Interacting Systems

We present calculations of de Haas van Alphen (dHvA) oscillations for strongly interacting systems, for (1) systems near a quantum phase transition (QPT); and/or (2) 2D and quasi-2D systems. The standard Lifshitz-Kosevich (LK) results are then inapplicable. Near a QPT, the electronic interaction scale goes to zero, giving strong corrections to LK. In 2D, LK breaks down entirely in the presence of interactions. Recently, dHvA oscillations in high Tc systems have been measured, but their form does not yet rule out non-Fermi liquid behaviour. We calculate the expected magnetization response assuming various Fermi reconstruction scenarios. The response depends crucially on the inter-plane couplings, and we find deviations from LK if the reconstruction is interaction-driven.   

Interpreting the Gap Signatures in the Raman Spectra of Hg-1201.

Recently, peaks in the B1g and B2g Raman spectra of the Hg-1201 high-Tc cuprate superconductor have been interpreted in terms of two gaps. These are i) a gap near the Brillouin zone boundary that decreases monotonically with doping, and ii) a gap near the zone-diagonals that follows the dome-shaped doping dependence of the superconducting transition temperature. The former has come to be interpreted as the pseudogap and the latter the superconducting gap. However, this dome shaped superconducting gap contradicts other measurements (specific heat and infra-red spectroscopy) which suggest a simple monotonic decrease with doping. By performing calculations in which the doping dependence of the Fermi arcs is taken into account, we show that the apparent Raman B2g gap is modified by the pseudogap and that the actual superconducting gap deduced from Raman data is in fact consistent with the monotonic decrease seen in these other spectroscopies.   

Gap structure and mean-field $T_c$ in HTS cuprates

We show that phase and amplitude fluctuations set in simultaneously in high-Tc cuprates and determine the mean-field transition temperature $T_c^{mf}$ which is found to increase substantially above $T_c$ in optimal and underdoped cuprates (by up to 60 or 70K). We find $\Delta/k_BT_c^{mf}$=2.5, little more than the weak-coupling BCS $d$-wave value. On the other hand the pseudogap $T^*$ has a distinct doping dependence from $T_c^{mf}$ and correlates with the pseudogap energy $E_g$. The gap structure for $\Delta$ and $E_g$ are characterised and shown to be distinct.   

The existence of substantial Ca 3\textit{d} derived states at \textit{E}$_{F}$ in Ca-intercalated graphite superconductor CaC$_{6}$

We have performed soft x-ray photoemission studies of Ca-intercalated graphite superconductor CaC$_{6 }(T_{c}$ = 11.2 K). The valence band spectrum shows six main structures that correspond to those of calculated DOS that predicts large Ca 3$d$ contribution at the Fermi level ($E_{F})$. The Ca 2$p$ core level spectrum has a very large asymmetric line shape, suggesting the existence of Ca 3$d$ derived conduction electrons at Ca sites. These results provide spectroscopic evidence for the existence of Ca 3$d$ electrons at $E_{F}$, which probably play a crucial role for the unusually superconductivity. The electronic structure of CaC$_{6}$ is compared with the electronic structures of other graphite intercalation compounds, providing deeper understanding of the superconductivity of CaC$_{6}$.   

Orbital excitation in Sr$_{2}$CuO$_{2}$Cl$_{2}$ resonant inelastic x-ray scattering at the Cu K pre-edge

$d-d$ excitations has attracted much attention due to its fundamental importance in elucidating electronic structure. However, experimental study of these excitations is difficult, since direct optical transition is dipole forbidden. We show that the Cu \underline {1}\underline {\textit{s}}-3$d$ intermediate state, which can be reached via electric quadrupole operator, provides an excellent high-resolution means for studying $d-d$ excitations in cuprates, and complements other well established techniques. Since quadrupole operator is sensitive to the symmetry of the intermediate state, considerable information on the symmetry of $d-d$ excitation can be gained by exploiting this resonance. We have carried out comprehensive angle resolved x-ray absorption spectroscopy experiment, which clearly demonstrates the quadrupole nature of the absorption. We find that our RIXS spectra at this quadrupole resonance exhibit a broad excitation centered at 2 eV. We suggest that the scattering angle dependence of the quadrupole resonance agrees well with the calculated polarization dependence of quadrupole matrix element and information on the symmetry of $d-d$ excitation can be obtained. Our analysis show that the quadrupole resonance at 2eV is consistent with the excitation involving 3$d_{yz, zx}$ symmetry.   

Quantum oscillation experiments on YBa$_2$Cu$_3$O$_{6.60}$

Pulsed magnetic fields of up to 75~T and temperatures down to 0.40~K have been used to study single crystals of YBa$_2$Cu$_3$O$_{6.60}$. The samples are measured using a MHz technique that is sensitive to small changes in penetration depth in the superconducting state, and to changes in the skin depth in the normal state. Two series of magnetic quantum oscillations are observed, periodic in inverse field; the frequencies are $590\pm 20$~T and $1990\pm 40$~T. This suggests that the predicted large Fermi surface is broken into smaller pockets due to nesting. These findings are discussed in the context of other recent observations of quantum oscillations in the cuprates, and a magnetically-mediated mechanism for superconductivity, driven by the topological mapping of the d-wave Cooper-pair wavefunction onto the antiferromagnetic fluctuations (due to Fermi-surface nesting) that are observed across the whole cuprate phase diagram [R.D. McDonald et al., J. Phys.: Condens. Matter, in press (2008)].   

Five Principles of Photoemission of High Temperature Superconducting Cuperates Deduced from the Dipolon Theory

In the process of the theoritical explanation of the observed photoemission result of high temperature superconducting cuprates we have been able to derive by means of the dipolon theory [1,2] five principles of photoemission in various situations of doping, temperature and Fermi level crossing.These five principles interrelate the peak-dip-hump phenomenon,the kink structure (including the predicted high energy kinks [3]) in the quasiparticale energy dispersion and electron velocities at different energies with respect to the charactristic dipolon excitations in the system.Details of the five principles will be presented. The theory contains Mott renormalization and all important and necessary electron-electron correlations. \\[3pt] [1] R.R. Sharma, phys. rev.{\bf63}, 054506 (2001)\\[0pt] [2] R.R. Sharma, Physica {\bf C439},47 (2006).\\[0pt] [3] R.R. Sharma,Physica C{\bf468}190 (2008).   

Circular dichroism in angle-resolved photoemission spectrum as a technique to probe symmetry breaking in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$

We report first-principles computations of the ARPES response with circularly polarized light in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Comparison with available experimental results shows that the measured circular dichroism is reproduced within one-step computations, which include the effects of the ARPES matrix element. Employing the average orthorhombic crystal structure our study clearly establishes the sensitivity of the dichroism to experimental and structural details, and indicates that the detection of time-reversal symmetry breaking via ARPES using circularly polarized light will be complicated by the masking effects of the lattice distortions. Due to the surface sensitivity of ARPES dichroic measurements can be used to study the symmetry and quality of single crystal surfaces. \\[4pt] [1] V. Arpiainen, V. Zalobotnyy, A. A. Kordyuk, S. V. Borisenko, and M. Lindroos, Phys. Rev. B {\bf 77}, 024520 (2008) \\[0pt] [2] V. Arpiainen, A. Bansil, and M. Lindroos, Submitted to Phys. Rev. Lett. (2008)   

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

We use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion of a strongly interacting Fermi gas of atoms. In these photoemission experiments, an rf photon ejects an atom from our strongly interacting system via a spin-flip transition to a weakly interacting state. This new measurement technique for ultracold atom gases, like photoemission spectroscopy for electronic materials, directly probes low energy excitations and thus can reveal excitation gaps and/or pseudogaps. We observe a back-bending of the excitation spectrum consistent with a BCS-like dispersion curve.   

Ab initio calculation of core-valence-valence Auger spectra in closed shell systems.

We propose an ab initio method to evaluate the core-valence-valence Auger spectrum of systems with filled valence bands. The method is based on the Cini-Sawatzky theory, and aims at estimating the parameters by first-principles calculations in the framework of DFT. Photoemission energies and the interaction energy for the two holes in the final state are evaluated by performing DFT simulations for the system with varied population of electronic levels. Transition matrix elements are taken from atomic results. The approach takes into account the non spherical density of states of the emitting atom, spin-orbit interaction in core and valence, and non quadratic terms in the total energy expansion with respect to fractional occupation numbers. It is tested on two benchmark systems, Zn and Cu metals, leading in both cases to $L$23$M$45$M$45 Auger peaks within 2 eV from the experimental ones. Especially problematic is the evaluation of the hole-hole interaction for systems with broad valence bands: our method underestimates its value in Cu, while we obtain excellent results for this quantity in Zn.