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Kusakabe Lab Kawashima Kei

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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 Lab

KawashimaKei

Contents

- Introduction
- Crystal structuresof atom-inserted C60crystals(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

Conventional unit cell of a FCC C60 Crystal

Insulator

Insulator

SC

Superconductivity found in 1990s.

Metal

Metal

Insulator

SC

Insulator (Band gap≒1.2ev)

The main object to study from now on －Cs3C60 crystal

In 2008, superconductivity in Cs3C60 crystal was found by Takabayashi group.

Cs3C60Crystal

(A15 structure)

Interesting points

・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 Tcamong atom-inserted C60crystals.

Cs atom

Pressure dependence of Tc of Cs3C60 crystal

Low pressure region

Superconductors have perfect anti-magnetism(完全反磁性).

Ref: ALEXEY Y. GANINet 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 analyzecorrectly systems such as strongly correlated electron systems(強相関電子系)and high-temperature superconductors(高温超伝導体).

First principlesmethod

In first principles method, you begin with Schrödinger eigenequation, 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, 14657-14660(1993)

Wave vector space

Current study― Theoretical simulations for C60 Crystal

- Optimize the atomic positions(60 C atoms in a unit cell)
- Obtain the optimum lattice constant (length of the one edge of FCC conventional unit cell)
- Band structure
- Density of states (DOS)

1. Optimize the atomic positions

Initial values

Parts of an input data

To obtain the optimized atomic positions, you set the values of the initial lattice constant and the initial atomic potions

to the experimental values.

- &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

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

By me

Band gap

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 εand 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 Cs3C60under higher pressures(1Gpa, 10Gpa, 100Gpa etc.)

・Band structure

・Density of states

・Fermi surface

・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 objectfrom now on ― Cs3C60 crystalBelow 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.

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