Theoretical approach to physical properties of atom-inserted C60 crystals 原子を挿入されたフラーレン結晶の 物性への理論的アプローチ Kusakabe Lab Kawashima Kei Contents • Introduction – Crystal structures of atom-inserted C60 crystals (Objects of my study) – Cs3C60 crystal (The main object to study from now on) • Mott insulator-superconductor transition of Cs3C60 • Way to study ― Theoretical approach to physical properties by computational simulations ― First principles calculation in DFT within LDA • Current studies ― Computational simulations for C60 Crystal • Future works ― Computational simulations for Cs3C60 crystal • Summary Crystal structures of atom-inserted C60 crystals Insulator Conventional unit cell of a FCC C60 Crystal SC Insulator Superconductivity found in 1990s. Metal Metal Insulator Insulator (Band gap≒1.2ev) SC The main object to study from now on －Cs3C60 crystal In 2008, superconductivity in Cs C 3 60 Cs3C60 Crystal (A15 structure) Cs atom crystal was found by Takabayashi group. ・Transition from Mott insulator (モット絶縁体) to metal, and superconducting transition (超伝導転移) at low temperatures under appropriate pressure. The phase diagram is similar to that of cupper oxide high-temperature superconductors(銅酸化物高温超 伝導体). ・The maximum Tc is about 38K, that is the highest Tc among atominserted C60 crystals. Pressure dependence of Tc of Cs3C60 crystal Low pressure region Superconductors have perfect anti-magnetism(完全反磁性). Ref: ALEXEY Y. GANIN et al. Nature Mat., Vol. 7(2008) Mott insulator – Superconductor transition Below about 47K, Cs3C60 is Mott insulator. Anti-ferro magnetism Under more than 3kbar, Cs3C60 is superconductor. Electron pair Phase diagram of Cs3C60 AFI : Anti-ferro insulator (Mott insulator ) SC : Superconductor A copper-oxide crystal Metal Hole density per Cu atom TN is the temperature at which the zero-field magnetization begins to increase. Tc is the temperature at which the zero-field magnetization begins to decrease. Ref: Way to study ― Theoretical approach to physical properties(物性) by computational simulations Input data of a material Experimental facts Calculations by other groups Comparison Numerical calculations of the physical properties using computers (Parallel calculation) Resulting output data Advantages and disadvantages of computational simulations • Advantages – You can estimate physical properties of materials easily using only computers. – You can analyze unknown materials. – You can perform accurate calculations of elastic properties(弾性) and phonon dispersion etc. • Disadvantages – Sometimes estimated physical properties of materials do not agree with experimental facts. – It is not so easy to analyze correctly systems such as strongly correlated electron systems(強相関電子系) and high-temperature superconductors(高温超伝導体). First principles method In first principles method, you begin with Schrödinger eigen equation, and analyze physical properties of materials theoretically. Schrödinger eigen equation in a crystal In DFT(密度汎関数理論) within LDA(局所密度近似) at r. Band structures of C60-based crystals C60(FCC) - Insulator K3C60(FCC) - Metal Ba6C60(BCC) - Semimetal Unoccupied states Band gap Fermi energy Occupied states Ref: O. Gunnarsson, Reviews of Modern Physics, Vol. 68, No. 3, 575-606(1996) ・Steven C. Erwin, Phys. Rev. B, Vol. 47 No.21, 14657- Wave vector space Current study ― Theoretical simulations for C60 Crystal 1. Optimize the atomic positions (60 C atoms in a unit cell) 2. Obtain the optimum lattice constant (length of the one edge of FCC conventional unit cell) 3. Band structure 4. Density of states (DOS) 1. Optimize the atomic positions Initial values Parts of an input data &control calculation='relax' &system ibrav=2 celldm(1)=26.79 nat=60 ntyp=1 ATOMIC_POSITIONS (angstrom) C -0.707 0.000 3.455 C -1.425 1.164 3.005 ・ ・ C 2.285 -2.579 0.728 To obtain the optimized atomic positions, you set the values of the initial lattice constant and the initial atomic potions to the experimental values. Optimized atomic positions 2. Get the optimum lattice constant Parts of input data Total energy vs lattice constant lista=’26.55 26.60 26.65 26.70 .....' for a in $lista do &control calculation=‘scf' &system ibrav=2 celldm(1)=$a nat=60 ntyp=1 ATOMIC_POSITIONS (angstrom) C -0.713 0.000 3.485 C -1.437 1.174 3.031 ・ ・ C 2.303 -2.601 0.734 done Experimental value 26.79 Bohr 誤差約0.6% 26.63 Bohr 3. Band structure By O.Gunnarsson group Band gap By me Band gap Experimental band gap of C60 crystal is about 1.2 ev. Ref: O. Gunnarsson, Reviews of Modern Physics, Vol. 68, No. 3, 575-606(1996) 4. Density of states (DOS) D(ε) shows the number of electronic quantum states per unit cell existing between ε and ε+Δε. D(ε) [states/ev・cell] Band gap Band gap ε [ev] Numerical applications of DOS Some physical properties of electron system can be estimated from one electron energy and DOS. Total energy of electronic system Fermi distribution function Low-temperature Specific heat of electronic system Superconductive transition temperature by McMillan’s formula Electron-Phonon Coupling Constant Electron-Electron Coulomb Interaction (μ=D(εF)Vc) Future works ― Calculations for Cs3C60 under higher pressures(1Gpa, 10Gpa, 100Gpa etc.) Electronic structure ・Band structure ・Density of states ・Fermi surface Crystal structure ・Atomic positions ・lattice constant Electron-phonon coupling (電子-フォノン結合) → important in Superconductivity based on BCS theory. Very stable crystal structure is needed for phonon calculations! Summary • The main studying object from now on ― Cs3C60 crystal Below about 47K under ambient pressure, it is an insulator called Mott insulator. By applying pressure, it transfers to a superconductor at low temperatures. I’ll try to study superconductive mechanism of Cs3C60 under higher pressure by calculating electronic structure and electron-phonon coupling. • Theoretical simulations based on first principles method You can estimate various physical properties of crystals using only computers. ― Crystal structure optimization, band structure, density of states, and phonon structure etc. • What I learned from my studies up to now I’ve got familiar with parallel calculation for many-electrons system. I’ve learned that DFT within LDA has good calculation accuracy for some C60-based crystals. I’ve got prepared for future works by calculating physical properties of C60 crystal.
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