A study of possible superconducting phases of graphene has been constructed in detail. A realistic tight binding model, fit to ab initio calculations, accounts for the Lidecoration of graphene with broken lattice symmetry, and includes
The shape of 3
 Award ID(s):
 2145080
 Publication Date:
 NSFPAR ID:
 10376187
 Journal Name:
 Nature Communications
 Volume:
 13
 Issue:
 1
 ISSN:
 20411723
 Publisher:
 Nature Publishing Group
 Sponsoring Org:
 National Science Foundation
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Abstract s andd symmetry Bloch character that influences the gap symmetries that can arise. The resulting seven hybridized LiC orbitals that support nine possible bond pairing amplitudes. The gap equation is solved for all possible gap symmetries. One band is weakly dispersive near the Fermi energy along Γ →M where its Bloch wave function has linear combination of and$${d}_{{x}^{2}{y}^{2}}$$ ${d}_{{x}^{2}{y}^{2}}$d _{xy}character, and is responsible for and$${d}_{{x}^{2}{y}^{2}}$$ ${d}_{{x}^{2}{y}^{2}}$d _{xy}pairing with lowest pairing energy in our model. These symmetries almost preserve properties from a two band model of pristine graphene. Another part of this band, alongK → Γ, is nearly degenerate with uppers band that favors extendeds wave pairing which is not found in two band model. Upon electron doping to a critical chemical potentialμ _{1} = 0.22eV the pairing potential decreases, then increases until a second critical valueμ _{2} = 1.3 eV at which a phase transition to a distorteds wave occurs. The distortion ofd  or swave phases are a consequence of decoration which is not appear in two band pristine model. In the pristine graphene these phases convert to usuald wave or extendeds wave pairing. 
Abstract It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.
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Abstract Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultralow Reynolds numbers
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Abstract We present a toy model for the thermal optical/UV/Xray emission from tidal disruption events (TDEs). Motivated by recent hydrodynamical simulations, we assume that the debris streams promptly and rapidly circularize (on the orbital period of the most tightly bound debris), generating a hot quasispherical pressuresupported envelope of radius
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Abstract We perform pathintegral molecular dynamics (PIMD), ringpolymer MD (RPMD), and classical MD simulations of H
O and D$$_2$$ ${}_{2}$ O using the qTIP4P/F water model over a wide range of temperatures and pressures. The density$$_2$$ ${}_{2}$ , isothermal compressibility$$\rho (T)$$ $\rho \left(T\right)$ , and selfdiffusion coefficients$$\kappa _T(T)$$ ${\kappa}_{T}\left(T\right)$D (T ) of H O and D$$_2$$ ${}_{2}$ O are in excellent agreement with available experimental data; the isobaric heat capacity$$_2$$ ${}_{2}$ obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$C_P(T)$$ ${C}_{P}\left(T\right)$ O and D$$_2$$ ${}_{2}$ O exhibit a liquidliquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$ ${}_{2}$ O and D$$_2$$ ${}_{2}$ O can be fitted remarkably well using the TwoStateEquationofState (TSEOS). Using the TSEOS, we estimate that the LLCP for qTIP4P/F H$$_2$$ ${}_{2}$ O, from PIMD simulations, is located at$$_2$$ ${}_{2}$ MPa,$$P_c = 167 \pm 9$$ ${P}_{c}=167\pm 9$ K, and$$T_c = 159 \pm 6$$ ${T}_{c}=159\pm 6$ g/cm$$\rho _c = 1.02 \pm 0.01$$ ${\rho}_{c}=1.02\pm 0.01$ . Isotope substitution effects are important; the LLCP location in qTIP4P/F D$$^3$$ ${}^{3}$ O is estimated to be$$_2$$ ${}_{2}$ MPa,$$P_c = 176 \pm 4$$ ${P}_{c}=176\pm 4$ K, and$$T_c = 177 \pm 2$$ ${T}_{c}=177\pm 2$ g/cm$$\rho _c = 1.13 \pm 0.01$$ ${\rho}_{c}=1.13\pm 0.01$ . Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effectsmore »$$^3$$ ${}^{3}$