theoretical approach to physical properties of atom-inserted c 60 crystals...
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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 LabKawashima 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 crystalsConventional unit cell of a FCC C60 Crystal
Superconductivity found in 1990s.
Insulator (Band gap 1.2ev)≒
SC
SC
Insulator
Insulator
MetalMetal
Insulator
The main object to study from now on - Cs3C60 crystal
Cs3C60 Crystal(A15 structure) Interesting points
・ Transition from Mott insulator ( モット絶縁体 ) to metal, andsuperconducting 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 atom-inserted C60 crystals.
In 2008, superconductivity in Cs3C60 crystal was found by Takabayashi group.
Cs atom
Pressure dependence of Tc of Cs3C60 crystalLow pressure region
Ref: ALEXEY Y. GANIN et al. Nature Mat., Vol. 7(2008)
Superconductors have perfect anti-magnetism( 完全反磁性 ).
Below about 47K, Cs3C60 is Mott insulator.
Under more than 3kbar, Cs3C60 is superconductor.
Anti-ferro magnetism
Electron pair
Mott insulator – Superconductor transition
Ref:
Metal
AFI : Anti-ferro insulator (Mott insulator )SC : Superconductor
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.
A copper-oxide crystal
Phase diagram of Cs3C60
Hole density per Cu atom
Way to study ― Theoretical approach to physical properties( 物性 ) by computational simulations
Numerical calculations of the physical properties using computers
(Parallel calculation)
Experimental facts
Input data of a material
Resulting output data
Comparison
Calculations by other groups
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 DFT( 密度汎関数理論 ) within LDA( 局所密度近似 )
In first principles method, you begin with Schrödinger eigen equation, and analyze physical properties of materials theoretically.
Schrödinger eigen equation in a crystal
at r.
Band structures of C60-based crystalsC60(FCC) - Insulator K3C60(FCC) - Metal Ba6C60(BCC) - Semimetal
Unoccupiedstates
Occupiedstates
Fermi energy
Ref: O. Gunnarsson, Reviews of Modern Physics, Vol. 68, No. 3, 575-606(1996)・ Steven C. Erwin, Phys. Rev. B, Vol. 47 No.21, 14657-14660(1993)
Wave vector space
Band gap
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 structure4. Density of states (DOS)
1. Optimize the atomic positions
Parts of an input data Initial values
&controlcalculation='relax'
&systemibrav=2 celldm(1)=26.79 nat=60 ntyp=1
ATOMIC_POSITIONS (angstrom)C -0.707 0.000 3.455C -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 constantParts of input data Total energy vs lattice constantlista=’26.55 26.60 26.65 26.70 .....'for a in $listado&control
calculation=‘scf'
&systemibrav=2 celldm(1)=$a nat=60 ntyp=1
ATOMIC_POSITIONS (angstrom)C -0.713 0.000 3.485C -1.437 1.174 3.031
・・
C 2.303 -2.601 0.734
done
Experimental value26.79 Bohr
26.63 Bohr
誤差約 0.6%
3. Band structure
Ref: O. Gunnarsson, Reviews of Modern Physics, Vol. 68, No. 3, 575-606(1996)
Band gapBand gap
By O.Gunnarsson group By me
Experimental band gap of C60 crystal is about 1.2 ev.
4. Density of states (DOS)
D(ε) [states/ev ・cell]
ε [ev]
Band gap
Band gap
D(ε) shows the number of electronic quantum states per unit cell existing between ε and ε+Δε.
Numerical applications of DOS Some physical properties of electron system can be
estimated from one electron energy and DOS.Total energy of electronic system
Low-temperature Specific heat of electronic system
Fermi distribution function
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
Crystal structure
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!
・ Band structure・ Density of states・ Fermi surface
・ Atomic positions・ lattice constant
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 methodYou 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.