On `maximal' poles of zeta functions, roots of b-functions and monodromy Jordan blocks

The main objects of study in this paper are the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a polynomial or (germ of) holomorphic function in n variables. We are interested in poles of maximal possible order n. In all known cases (curves, non-degenerate polynomials) there is at most one pole of maximal order n which is then given by the log canonical threshold of the function at the corresponding singular point. For an isolated singular point we prove that if the log canonical threshold yields a pole of order n of the corresponding (local) zeta function, then it induces a root of the Bernstein-Sato polynomial of the given function of multiplicity n (proving one of the cases of the strongest form of a conjecture of Igusa-Denef-Loeser). For an arbitrary singular point we show under the same assumption that the monodromy eigenvalue induced by the pole has a Jordan block of size n on the (perverse) complex of nearby cycles.Comment: 8 pages, to be published in Journal of Topolog

Formation of metallic magnetic clusters in a Kondo-lattice metal: Evidence from an optical study

Magnetic materials are usually divided into two classes: those with localised magnetic moments, and those with itinerant charge carriers. We present a comprehensive experimental (spectroscopic ellipsomerty) and theoretical study to demonstrate that these two types of magnetism do not only coexist but complement each other in the Kondo-lattice metal, Tb2PdSi3. In this material the itinerant charge carriers interact with large localised magnetic moments of Tb(4f) states, forming complex magnetic lattices at low temperatures, which we associate with self-organisation of magnetic clusters. The formation of magnetic clusters results in low-energy optical spectral weight shifts, which correspond to opening of the pseudogap in the conduction band of the itinerant charge carriers and development of the low- and high-spin intersite electronic transitions. This phenomenon, driven by self-trapping of electrons by magnetic fluctuations, could be common in correlated metals, including besides Kondo-lattice metals, Fe-based and cuprate superconductors.Comment: 30 pages, 6 Figure

High-Resolution Photoemission Study of MgB2

We have performed high-resolution photoemission spectroscopy on MgB2 and observed opening of a superconducting gap with a narrow coherent peak. We found that the superconducting gap is s-like with the gap value of 4.5 meV at 15 K. The temperature dependence (15 - 40 K) of gap value follows well the BCS form, suggesting that 2Delta/kBTc at T=0 is about 3. No pseudogap behavior is observed in the normal state. The present results strongly suggest that MgB2 is categorized into a phonon-mediated BCS superconductor in the weak-coupling regime.Comment: 3 pages, 3 figures, accepted in Physical Review Letter

Abrupt Onset of Second Energy Gap at Superconducting Transition of Underdoped Bi2212

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 is still under intense debate. A crucial piece of evidence to firmly establish this two-gap picture is still missing: a direct and unambiguous observation of a single-particle gap tied to the superconducting transition as function of temperature. Here we report the discovery of such an energy gap in underdoped Bi2212 in the momentum space region overlooked in previous measurements. Near the diagonal of Cu-O bond direction (nodal direction), we found a gap which opens at TC and exhibits a canonical (BCS-like) temperature dependence accompanied by the appearance of the so-called Bogoliubov quasiparticles, a classical signature of superconductivity. This is in sharp contrast to the pseudogap near the Cu-O bond direction (antinodal region) measured in earlier experiments. The emerging two-gap phenomenon points to a picture of richer quantum configurations in high temperature superconductors.Comment: 16 pages, 4 figures, authors' version Corrected typos in the abstrac

Quasiparticles and Energy Scaling in Bi2_2Sr2_2Can−1_{n-1}Cun_nO2n+4_{2n+4} (n\it{n}=1-3): Angle-Resolved Photoemission Spectroscopy

Angle-resolved photoemission spectroscopy (ARPES) has been performed on the single- to triple-layered Bi-family high-{\it T$_c$} superconductors (Bi$_2$Sr$_2$Ca$_{n-1}$Cu$_n$O$_{2n+4}$, $\it{n}$=1-3). We found a sharp quasiparticle peak as well as a pseudogap at the Fermi level in the triple-layered compound. Comparison among three compounds has revealed a universal rule that the characteristic energies of superconducting and pseudogap behaviors are scaled with the maximum {\it T$_c$}.Comment: 4 pages, 4 figure

Proposal for an Experiment to Test a Theory of High Temperature Superconductors

A theory for the phenomena observed in Copper-Oxide based high temperature superconducting materials derives an elusive time-reversal and rotational symmetry breaking order parameter for the observed pseudogap phase ending at a quantum-critical point near the composition for the highest $T_c$. An experiment is proposed to observe such a symmetry breaking. It is shown that Angle-resolved Photoemission yields a current density which is different for left and right circularly polarized photons. The magnitude of the effect and its momentum dependence is estimated. Barring the presence of domains of the predicted phase an asymmetry of about 0.1 is predicted at low temperatures in moderately underdoped samples.Comment: latex, 2 figure

Detecting fractions of electrons in the high-TcT_c cuprates

We propose several tests of the idea that the electron is fractionalized in the underdoped and undoped cuprates. These include the ac Josephson effect, and tunneling into small superconducting grains in the Coulomb blockade regime. In both cases, we argue that the results are qualitatively modified from the conventional ones if the insulating tunnel barrier is fractionalized. These experiments directly detect the possible existence of the chargon - a charge $e$ spinless boson - in the insulator. The effects described in this paper provide a means to probing whether the undoped cuprate (despite it's magnetism) is fractionalized. Thus, the experiments discussed here are complementary to the flux-trapping experiment we proposed in our earlier work(cond-mat/0006481).Comment: 7 pages, 5 figure

The electronic specific heat in the pairing pseudogap regime

When pairing correlations in a quasi two dimensional electron system induce a pseudogap in the single particle density of states, the specific heat must also contain a sizeable pair contribution. The theoretically calculated specific heat for such a system is compared to the experimental results of Loram and his collaborators for underdoped YBa_2Cu_3O_{6+x} and La_{2-x}Sr_{x}CuO_4 samples. The size and doping dependence of the extracted pseudogap energy scale for both materials is comparable to the values obtained from a variety of other experiments.Comment: 4 pages, 5 eps figure

Superconducting properties of the attractive Hubbard model

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.Comment: RevTeX format, 8 figures. Accepted for publication in Z.Phys.