The possibility of measuring intrinsic electronic correlations in graphene using a d-wave contact Josephson junction

While not widely recognized, electronic correlations might play an important role in graphene. Indeed, Pauling's resonance valence bond (RVB) theory for the pp-bonded planar organic molecules, of which graphene is the infinite extension, already established the importance of the nearest neighbor spin-singlet bond (SB) state in these materials. However, despite the recent growth of interest in graphene, there is still no quantitative estimate of the effects of Coulomb repulsion in either undoped or doped graphene. Here we use a tight-binding Bogoliubov-de Gennes (TB BdG) formalism to show that in unconventional d-wave contact graphene Josephson junctions the intrinsic SB correlations are strongly enhanced. We show on a striking effect of the SB correlations in both proximity effect and Josephson current as well as establishing a 1/(T-T_c) functional dependence for the superconducting decay length. Here T_c is the superconducting transition temperature for the intrinsic SB correlations, which depends on both the effects of Coulomb repulsion and the doping level. We therefore propose that d-wave contact graphene Josephson junctions will provide a promising experimental system for the measurement of the effective strength of intrinsic SB correlations in graphene.Comment: 4 pages, 4 figure

The effect of nearest neighbor spin-singlet correlations in conventional graphene SNS Josephson junctions

Using the self-consistent tight-binding Bogoliubov-de Gennes formalism we have studied the effect of nearest neighbor spin-singlet bond (SB) correlations on Josephson coupling and proximity effect in graphene SNS Josephson junctions with conventional s-wave superconducting contacts. Despite the s-wave superconducting state in the contacts, the SB pairing state inside the junction has d-wave symmetry and clean, sharp interface junctions resemble a 'bulk-meets-bulk' situation with very little interaction between the two different superconducting states. In fact, due to a finite-size suppression of the superconducting state, a stronger SB coupling constant than in the bulk is needed in order to achieve SB pairing in a junction. For both short clean zigzag and armchair junctions a d-wave state that has a zero Josephson coupling to the s-wave state is chosen and therefore the Josephson current decreases when a SB pairing state develops in these junctions. In more realistic junctions, with smoother doping profiles and atomic scale disorder at the interfaces, it is possible to achieve some coupling between the contact s-wave state and the SB d-wave states. In addition, by breaking the appropriate lattice symmetry at the interface in order to induce another d-wave state, a non-zero Josephson coupling can be achieved which leads to a substantial increase in the Josephson current. We also report on the LDOS of the junctions and on a lack of zero energy states at interfaces despite the unconventional order parameters, which we attribute to the near degeneracy of the two d-wave solutions and their mixing at a general interface.Comment: 13 pages, 9 figures. Typos correcte

Josephson current in graphene: the role of unconventional pairing symmetries

We investigate the Josephson current in a graphene superconductor/normal/superconductor junction, where superconductivity is induced by means of the proximity effect from external contacts. We take into account the possibility of anisotropic pairing by also including singlet nearest-neighbor interactions, and investigate how the transport properties are affected by the symmetry of the superconducting order parameter. This corresponds to an extension of the usual on-site interaction assumption, which yields an isotropic s-wave order parameter near the Dirac points. Here, we employ a full numerical solution as well as an analytical treatment, and show how the proximity effect may induce exotic types of superconducting states near the Dirac points, e.g. $p_x$- and $p_y$-wave pairing or a combination of s-wave and p+\i p-wave pairing. We find that the Josephson current exhibits a weakly-damped, oscillatory dependence on the length of the junction when the graphene sheet is strongly doped. The analytical and numerical treatments are found to agree well with each other in the s-wave case when calculating the critical current and current-phase relationship. For the scenarios with anisotropic superconducting pairing, there is a deviation between the two treatments, especially for the effective $p_x$-wave order parameter near the Dirac cones which features zero-energy states at the interfaces. This indicates that a numerical, self-consistent approach becomes necessary when treating anisotropic superconducting pairing in graphene.Comment: 15 pages, 12 figure

Self-consistent solution for proximity effect and Josephson current in ballistic graphene SNS Josephson junctions

We use a tight-binding Bogoliubov-de Gennes (BdG) formalism to self-consistently calculate the proximity effect, Josephson current, and local density of states in ballistic graphene SNS Josephson junctions. Both short and long junctions, with respect to the superconducting coherence length, are considered, as well as different doping levels of the graphene. We show that self-consistency does not notably change the current-phase relationship derived earlier for short junctions using the non-selfconsistent Dirac-BdG formalism but predict a significantly increased critical current with a stronger junction length dependence. In addition, we show that in junctions with no Fermi level mismatch between the N and S regions superconductivity persists even in the longest junctions we can investigate, indicating a diverging Ginzburg-Landau superconducting coherence length in the normal region.Comment: 8 pages, 6 figure

Leverage-induced systemic risk under Basle II and other credit risk policies

We use a simple agent based model of value investors in financial markets to test three credit regulation policies. The first is the unregulated case, which only imposes limits on maximum leverage. The second is Basle II and the third is a hypothetical alternative in which banks perfectly hedge all of their leverage-induced risk with options. When compared to the unregulated case both Basle II and the perfect hedge policy reduce the risk of default when leverage is low but increase it when leverage is high. This is because both regulation policies increase the amount of synchronized buying and selling needed to achieve deleveraging, which can destabilize the market. None of these policies are optimal for everyone: Risk neutral investors prefer the unregulated case with low maximum leverage, banks prefer the perfect hedge policy, and fund managers prefer the unregulated case with high maximum leverage. No one prefers Basle II.Comment: 27 pages, 8 figure

The impact of across-slope forest strips on hillslope subsurface hydrological dynamics

Forest cover has a significant effect on hillslope hydrological processes through its influence on the water balance and flow paths. However, knowledge of how spatial patterns of forest plots control hillslope hydrological dynamics is still poor. The aim of this study was to examine the impact of an across-slope forest strip on sub-surface soil moisture and groundwater dynamics, to give insights into how the structure and orientation of forest cover influences hillslope hydrology. Soil moisture and groundwater dynamics were compared on two transects spanning the same elevation on a 9° hillslope in a temperate UK upland catchment. One transect was located on improved grassland; the other was also on improved grassland but included a 14 m wide strip of 27-year-old mixed forest. Sub-surface moisture dynamics were investigated upslope, underneath and downslope of the forest over 2 years at seasonal and rainfall event timescales. Continuous data from point-based soil moisture sensors and piezometers installed at 0.15, 0.6 and 2.5 m depth were combined with seasonal (~bi-monthly) time-lapse electrical resistivity tomography (ERT) surveys. Significant differences were identified in sub-surface moisture dynamics underneath the forest strip over seasonal timescales: drying of the forest soils was greater, and extended deeper and for longer into the autumn compared to the adjacent grassland soils. Water table levels were also persistently lower in the forest and the forest soils responded less frequently to rainfall events. Downslope of the forest, soil moisture dynamics were similar to those in other grassland areas and no significant differences were observed beyond 15 m downslope, suggesting minimal impact of the forest at shallow depths downslope. Groundwater levels were lower downslope of the forest compared to other grassland areas, but during the wettest conditions there was evidence of upslope-downslope water table connectivity beneath the forest. The results indicate that forest strips in this environment provide only limited additional sub-surface storage of rainfall inputs in flood events after dry conditions in this temperate catchment setting