Flux-Periodicity Crossover from hc/e in Normal Metallic to hc/2e in Superconducting Loops

The periodic response of a metallic or a superconducting ring to an external magnetic flux is one of the most evident manifestations of quantum mechanics. It is generally understood that the oscillation period hc/2e in the superconducting state is half the period hc/e in the metallic state, because the supercurrent is carried by Cooper pairs with a charge 2e. On the basis of the Bardeen-Cooper-Schrieffer theory we discuss, in which cases this simple interpretation is valid and when a more careful analysis is needed. In fact, the knowledge of the oscillation period of the current in the ring provides information on the electron interactions. In particular, we analyze the crossover from the hc/e periodic normal current to the hc/2e periodic supercurrent upon turning on a pairing interaction in a metal ring. Further, we elaborate on the periodicity crossover when cooling a metallic loop through the superconducting transition temperature Tc.Comment: To be bublished in "Superconductors", InTech (Rijeka), 2012 (ISBN 979-953-307-798-6

Supercurrent as a Probe for Topological Superconductivity in Magnetic Adatom Chains

A magnetic adatom chain, proximity coupled to a conventional superconductor with spin-orbit coupling, exhibits locally an odd-parity, spin-triplet pairing amplitude. We show that the singlet-triplet junction, thus formed, leads to a net spin accumulation in the near vicinity of the chain. The accumulated spins are polarized along the direction of the local $\mathbf{d}$-vector for triplet pairing and generate an enhanced persistent current flowing around the chain. The spin polarization and the "supercurrent" reverse their directions beyond a critical exchange coupling strength at which the singlet superconducting order changes its sign on the chain. The current is strongly enhanced in the topological superconducting regime where Majorana bound states appear at the chain ends. The current and the spin profile offer alternative routes to characterize the topological superconducting state in adatom chains and islands.Comment: 5 pages, 3 figures, 5 pages of supplemental material

Superconductivity with Finite-Momentum Pairing in Zero Magnetic Field

In the BCS theory of superconductivity, one assumes that all Cooper pairs have the same center of mass momentum. This is indeed enforced by self consistency, if the pairing interaction is momentum independent. Here, we show that for an attractive nearest neighbor interaction, this is different. In this case, stable solutions with pairs with momenta q and -q coexist and, for a sufficiently strong interaction, one of these states becomes the groundstate of the superconductor. This finite-momentum pairing state is accompanied by a charge order with wave vector 2q. For a weak pairing interaction, the groundstate is a d-wave superconductor

Fractional Flux Quantization in Loops of Unconventional Superconductors

The magnetic flux threading a conventional superconducting ring is typically quantized in units of $\Phi_0=hc/2e$. The factor 2 in the denominator of $\Phi_0$ originates from the existence of two different types of pairing states with minima of the free energy at even and odd multiples of $\Phi_0$. Here we show that spatially modulated pairing states exist with energy minima at fractional flux values, in particular at multiples of $\Phi_0/2$. In such states condensates with different center-of-mass momenta of the Cooper pairs coexist. The proposed mechanism for fractional flux quantization is discussed in the context of cuprate superconductors, where $hc/4e$ flux periodicities as well as uniaxially modulated superconducting states were observed.Comment: 5 pages, 3 figure

Momentum-Space Spin Texture in a Topological Superconductor

A conventional superconductor with spin-orbit coupling turns into a topological superconductor beyond a critical strength of the Zeeman energy. The spin-expectation values $\mathbf{S}(\mathbf{k})$ in momentum space trace this transition via a characteristic change in the topological character of the spin texture within the Brillouin zone. At the transition the skyrmion counting number switches from 0 to 1/2 identifying the topological superconductor via its meron-like spin texture. The change in the skyrmion counting number is crucially controlled by singular points of the map $\mathbf{S}(\mathbf{k})/|\mathbf{S}(\mathbf{k})|$ from the Brillouin zone, i.e. a torus, to the unit sphere. The complexity of this spin-map is discussed at zero temperature as well as for the extension to finite temperatures.Comment: 16 pages, 9 figure

Entropic gravity, minimum temperature, and modified Newtonian dynamics

Verlinde's heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of freedom on the holographic screen. With the simplest possible setup, the resulting gravitational acceleration felt by a test mass m from a point mass M at a distance R is found to be of the form of the modified Newtonian dynamics (MOND) as suggested by Milgrom. The corresponding MOND-type acceleration constant is proportional to the minimum temperature, which can be interpreted as the Unruh temperature of an emerging de-Sitter space. This provides a possible explanation of the connection between local MOND-type two-body systems and cosmology.Comment: 12 pages, v6: published versio

The treatment of missing data when estimating student growth with pre-post educational accountability data

To ensure program quality and meet accountability mandates, it is becoming increasingly important for educational institutions to show “value-added” for attending students. Value-added is often evidenced by some form of pre-post assessment, where a change in scores on a construct of interest is considered indicative of student growth. Although missing data is a common problem for these pre-post designs, missingness is rarely addressed and cases with missing data are often listwise deleted. The current study examined the mechanism underlying, and bias resulting from, missingness due to posttest nonattendance in a higher-education accountability testing context. Although data were missing for some students due to posttest nonattendance, these initially missing data were subsequently collected via makeup testing sessions, thus allowing for the empirical examination of the mechanism underlying the missingness and the biasing effects of the missingness. Parameter estimates and standard errors were compared between the “complete” (i.e., including makeup) data and a number of different missing data techniques. These comparisons were completed across varying percentages of missingness and across noncognitive (i.e., developmental) and cognitive (i.e., knowledge-based) measures. For both noncognitive and cognitive measures, posttest data was found to be missing-not-at-random (MNAR), indicating that bias should occur when utilizing any missing data handling technique. As expected, the inclusion of auxiliary variables (i.e., variables related to missingness, the variable with missing values, or both) decreased the conditional relationship between the posttest noncognitive measure scores and posttest attendance (i.e., missingness); however, it increased the conditional relationship between posttest cognitive measure scores and posttest attendance. Thus, utilizing advanced missing data handling with auxiliary variables resulted in reduced parameter bias and reduced standard error inflation for the noncognitive measure, but increased parameter bias for some parameters (posttest mean and pre-post mean change) for the cognitive measure. These effects became more exaggerated as missingness percentages increased. With respect to future research, additional examination of bias-inducing effects when employing missing data techniques is needed. With respect to testing practice, assessment practitioners are advised to avoid missingness if possible through well-designed assessment methods, and to attempt to thoroughly understand the missingness mechanism when missingness is unavoidable

Two experiments for the price of one? -- The role of the second oscillation maximum in long baseline neutrino experiments

We investigate the quantitative impact that data from the second oscillation maximum has on the performance of wide band beam neutrino oscillation experiments. We present results for the physics sensitivities to standard three flavor oscillation, as well as results for the sensitivity to non-standard interactions. The quantitative study is performed using an experimental setup similar to the Fermilab to DUSEL Long Baseline Neutrino Experiment (LBNE). We find that, with the single exception of sensitivity to the mass hierarchy, the second maximum plays only a marginal role due to the experimental difficulties to obtain a statistically significant and sufficiently background-free event sample at low energies. This conclusion is valid for both water Cherenkov and liquid argon detectors. Moreover, we confirm that non-standard neutrino interactions are very hard to distinguish experimentally from standard three-flavor effects and can lead to a considerable loss of sensitivity to \theta_{13}, the mass hierarchy and CP violation.Comment: RevTex 4.1, 23 pages, 10 figures; v2: Typos corrected, very minor clarifications; matches published version; v3: Fixed a typo in the first equation in sec. III