Symmetry of superconducting correlations in displaced bilayers of graphene

Using a Green's function approach, we study phonon-mediated superconducting pairing symmetries that may arise in bilayer graphene where the monolayers are displaced in-plane with respect to each other. We consider a generic coupling potential between the displaced graphene monolayers, which is applicable to both shifted and commensurate twisted graphene layers; study intralayer and interlayer phonon-mediated BCS pairings; and investigate AA and AB(AC) stacking orders. Our findings demonstrate that at the charge neutrality point, the dominant pairings in both AA and AB stackings with intralayer and interlayer electron-electron couplings can have even-parity $s$-wave class and odd-parity $p$-wave class of symmetries with the possibility of invoking equal-pseudospin and odd-frequency pair correlations. At a finite doping, however, the AB (and equivalently AC) stacking can develop pseudospin-singlet and pseudospin-triplet $d$-wave symmetry, in addition to $s$-wave, $p$-wave, $f$-wave, and their combinations, while the AA stacking order, similar to the undoped case, is unable to host the $d$-wave symmetry. When we introduce a generic coupling potential, applicable to commensurate twisted and shifted bilayers of graphene, $d$-wave symmetry can also appear at the charge neutrality point. Inspired by a recent experiment where two phonon modes were observed in a twisted bilayer graphene, we also discuss the possibility of the existence of two-gap superconductivity, where the intralayer and interlayer phonon-mediated BCS picture is responsible for superconductivity. These analyses may provide a useful tool in determining the superconducting pairing symmetries and mechanism in bilayer graphene systems

Theory of phase segregation in DNA assemblies containing two different base pair sequence types

Spontaneous pairing of homologous DNA sequences – a challenging subject in molecular biophysics, often referred to as ‘homology recognition’ – ha s been observed in vitro for several DNA system s a . One of th e se experiments involved liquid crystalline quasi - columnar phases formed by a mixture of two kinds of oligo mer of double stranded DNA . Both oligomer types were of the same length and identical stoichiometric base - pair composition , but the base - pairs followed a different order . Phase segregation of the two DNA types was observed in the experiments , wit h the formation of boundaries between domai ns rich in molecules of one type (order) of base pair sequence . We formulate here a modified ‘ X - Y model ’ for phase segregation in such assemblies , obtain approximate solutions of the model , compare analytical results to Monte Carlo simulations, and rationalize past experimental observations . This study, furthermore , reveals the factors that affect the degree of segregat ion . Such information c ould be used in planning new versions of similar segregation experiments , needed for deepen i ng our understanding of forces that might be involved , e.g., in gene - gene recognition

Intransitive aggregated preferences

An impossibility theorem for preference aggretating rules is discussed. In this theorem no transitivity condition or acyclicity condition is imposed on the preferences: neither on the individual level nor on the aggregated level. Under the conditions that aggregation is non-dictatorial, Pareto-optimal, neutral and independent of irrelevant alternatives, it follows that the aggregated preferences are much more complex and therefore less ordered than the individual preferences.mathematical economics and econometrics ;

Magnetic-crystallographic phase diagram of superconducting parent compound Fe1+x_{1+x}Te

hrough neutron diffraction experiments, including spin-polarized measurements, we find a collinear incommensurate spin-density wave with propagation vector $\mathbf k =$ ($0.4481(4) \, \,0 \, \, \frac1 2$) at base temperature in the superconducting parent compound Fe$_{1+x}$Te. This critical concentration of interstitial iron corresponds to $x \approx 12$ and leads crystallographic phase separation at base temperature. The spin-density wave is short-range ordered with a correlation length of 22(3) \AA, and as the ordering temperature is approached its propagation vector decreases linearly in the H-direction and becomes long-range ordered. Upon further populating the interstitial iron site, the spin-density wave gives way to an incommensurate helical ordering with propagation vector $\mathbf k =$ ($0.3855(2) \, \,0 \, \, \frac1 2$) at base temperature. For a sample with $x \approx 9(1)$, we also find an incommensurate spin-density wave that competes with the bicollinear commensurate ordering close to the N\'eel point. The shifting of spectral weight between competing magnetic orderings observed in several samples is supporting evidence for the phase separation being electronic in nature, and hence leads to crystallographic phase separation around the critical interstitial iron concentration of 12%. With results from both powder and single crystal samples, we construct a magnetic-crystallographic phase diagram of Fe$_{1+x}$Te for $ 5% < x <17%