The c axis optical conductivity of layered systems in the superconducting state

In this paper, we discuss the c axis optical conductivity Re [sigma_c(omega)] in the high T_c superconductors, in the superconducting state. The basic premise of this work is that electrons travelling along the c axis between adjacent CuO_2 layers must pass through several intervening layers. In earlier work we found that, for weak inter-layer coupling, it is preferable for electrons to travel along the c axis by making a series of interband transitions rather than to stay within a single (and very narrow) band. Moreover, we found that many of the properties of the normal state optical conductivity, including the pseudogap could be explained by interband transitions. In this work we examine the effect of superconductivity on the interband conductivity. We find that, while the onset of superconductivity is clearly evident in the spectrum, there is no clear signature of the symmetry of the superconducting order parameter.Comment: 6 pages, 4 figure

Effect of nonlocal interactions on the disorder-induced zero-bias anomaly in the Anderson-Hubbard model

To expand the framework available for interpreting experiments on disordered strongly correlated systems, and in particular to explore further the strong-coupling zero-bias anomaly found in the Anderson-Hubbard model, we ask how this anomaly responds to the addition of nonlocal electron-electron interactions. We use exact diagonalization to calculate the single-particle density of states of the extended Anderson-Hubbard model. We find that for weak nonlocal interactions the form of the zero-bias anomaly is qualitatively unchanged. The energy scale of the anomaly continues to be set by an effective hopping amplitude renormalized by the nonlocal interaction. At larger values of the nonlocal interaction strength, however, hopping ceases to be a relevant energy scale and higher energy features associated with charge correlations dominate the density of states.Comment: 9 pages, 7 figure

Antimatter, Lorentz Symmetry, and Gravity

A brief introduction to the Standard-Model Extension (SME) approach to testing CPT and Lorentz symmetry is provided. Recent proposals for tests with antimatter are summarized, including gravitational and spectroscopic tests.Comment: Presented at the 12th International Conference on Low Energy Antiproton Physics, Kanazawa Japan, March 6-11, 2016, Accepted for publication in JPS Conference Proceeding

Extinction of impurity resonances in large-gap regions of inhomogeneous d-wave superconductors

Impurity resonances observed by scanning tunneling spectroscopy in the superconducting state have been used to deduce properties of the underlying pure state. Here we study a longstanding puzzle associated with these measurements, the apparent extinction of these resonances for Ni and Zn impurities in large-gap regions of the inhomogeneous BSCCO superconductor. We calculate the effect of order parameter and hopping suppression near the impurity site, and find that these two effects are sufficient to explain the missing resonances in the case of Ni. There are several possible scenarios for the extinction of the Zn resonances, which we discuss in turn; in addition, we propose measurements which could distinguish among them.Comment: 10 pages, 8 figure

Disorder and chain superconductivity in YBa_2Cu_3O_{7-\delta}

The effects of chain disorder on superconductivity in YBa_2Cu_3O_{7-\delta} are discussed within the context of a proximity model. Chain disorder causes both pair-breaking and localization. The hybridization of chain and plane wavefunctions reduces the importance of localization, so that the transport anisotropy remains large in the presence of a finite fraction $\delta$ of oxygen vacancies. Penetration depth and specific heat measurements probe the pair-breaking effects of chain disorder, and are discussed in detail at the level of the self-consistent T-matrix approximation. Quantitative agreement with these experiments is found when chain disorder is present.Comment: 4 pages, 2 figures, submitted to PRB rapid communication

Effect of Interband Transitions on the c axis Penetration Depth of Layered Superconductors

The electromagnetic response of a system with two planes per unit cell involves, in addition to the usual intraband contribution, an added interband term. These transitions affect the temperature dependence and the magnitude of the zero temperature c-axis penetration depth. When the interplane hopping is sufficiently small, the interband transitions dominate the low temperature behaviour of the penetration depth which then does not reflect the linear temperature dependence of the intraband term and in comparison becomes quite flat even for a d-wave gap. It is in this regime that the pseudogap was found in our previous normal state calculations of the c-axis conductivity, and the effects are connected.Comment: 8 pages, 5 figure

Infrared divergence in QED3_3 at finite temperature

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour $QED_{3}$ at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artefact of taking into account only the leading order term in the $1 \over N$ expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger-Dyson equation we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio $r=2*Mass(T=0)/critical temperature$ is approximately 6, consistently with previous calculations which neglected the transverse photon contribution.Comment: 37 pages, 12 figures, typos corrected, references added, Introduction rewritte

Effect of Proximity Coupling of Chains and Planes on the Penetration Depth Anisotropy in Y_1Ba_2Cu_3O_7

We calculate the penetration depth $\lambda$ in the $a$, $b$ and $c$ directions for a simple model of YBa$_2$Cu$_3$O$_7$. In this model there are two layers---representing a CuO$_2$ plane and a CuO chain---per unit cell. There is a BCS--like pairing (both $s$ wave and $d$ wave are considered) interaction localised in the CuO$_2$ planes. The CuO chains become superconducting at temperatures lower than $T_c$ because of their proximity to the planes, and there is an induced gap in the chains. Since the temperature dependence of the penetration depth in the $b$ direction (along the chains) is sensitive to the size of the induced gap, the difference between the shapes of the penetration depth curves in the $a$ and $b$ directions reveals a great deal about the nature of the condensate in the chains. We find that in our proximity model there are always regions of the chain Fermi surface on which the induced gap is much smaller than $T_c$, so that the temperature dependence of $\lambda_b$ is always different than that of $\lambda_a$. Experimental observations of the of the $ab$ anisotropy show nearly identical temperature dependences. The main result of our paper, then, is that a simple proximity model in which the pairing interaction is localized to the planes, and the planes are coherently coupled to the chains cannot account for the superfluid on the chains.Comment: 24 Pages, Submitted to Phys. Rev.

An "Accidental" Symmetry Operator for the Dirac Equation in the Coulomb Potential

On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is intimately connected to the familiar Laplace-Runge-Lenz vector. Our approach guarantees not only derivation of Johnson-Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian follows.Comment: 6 page