Predicting the Superconducting Transition Temperature for LiBC

IntroductionTransition Temperature, TcHigh Transition Temperature of MgB2, 39KSimilarity in Structure of MgB2 and LiBCLack of Success in Formulating Superconducting LiBC

BCS Theory of SuperconductivityBardeen, Cooper, and Schrieffer (1972)Effect of Phonon Vibrational Modes on ElectronsElectrons as Fermions: Half Spin (1/2, 3/2, etc.)Coupled Electrons as Bosons: Integral SpinAllen-Dynes Equation: Tc : ln ,

Electron Band StructureHybridization of Atomic Energy Levels from BondingPicture of Allowed Levels but not ProbabilitiesMultiple Locations with Same Energy LevelSlope of BandsDensity of States (DOS)

Electron Band StructureHybridization of Atomic Energy Levels from BondingPicture of Allowed Levels but not ProbabilitiesMultiple Locations with Same Energy LevelSlope of BandsDensity of States (DOS)

Phonon DispersionGraphs Similar to Electron Band and DOS PlotsVibrational Frequencies for Energy Levels

ComputationsBICON CEDiTMartin Brndle, Ruedi Rytz, and Gion Calzaferri, Department of Chemistry and Biochemistry, Univeristy of BerneElectron Band StructureUnisoftP. Elter and G. Eckold, Institut for Physical Chemistry, University of GttingenPhonon Dispersion Curve

Determination of Spring ConstantsBICON CEDiT for Total EnergyDisplacements along Lines between Atom PairsEquation from Classical Mechanics: E = k x2InaccuracyOther Atoms in StructureABINIT a common project of the Universit Catholique de Louvain, Corning Incorporated,and other contributors (http://www.abinit.org)

Figures

Calculations and ResultsHigh and Low Values of (Doping)The Effect of Doping ( = 0.5 and 1.0)DOS Peak near Fermi LevelLogarithmically Averaged Frequency, lnValues of Tc: 16 K and 45.4 K

Calculations and ResultsHigh and Low Values of (Doping)The Effect of Doping ( = 0.5 and 1.0)DOS Peak near Fermi LevelLogarithmically Averaged Frequency, lnValues of Tc: 16 K and 45.4 K

ConclusionsTc Lower than ExpectedEffect of Doping on lnAnharmonicityRange Still High