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Calculation of superconducting critical temperature of hole-doped CuAlO 2 and CuAlS 2. Yoshida lab Hiroki Uede. 10/02 M1 colloquium. Index. Introduction - Electron-phonon superconductivity - - Allen-Dynes formula - P revious work - Delafossite structure CuAlO 2 - M y work

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calculation of superconducting critical temperature of hole doped cualo 2 and cuals 2

Calculation of superconducting critical temperature of hole-doped CuAlO2 and CuAlS2

Yoshida lab

Hiroki Uede

10/02

M1 colloquium

index
Index
  • Introduction

- Electron-phonon superconductivity -

- Allen-Dynes formula -

  • Previous work

- Delafossite structure CuAlO2 -

  • My work

- Chalcopyrite structure CuAlS2 -

  • Summary
  • Future plan
e lectron phonon interaction
Electron-phonon interaction

If attractive interaction between electrons exist, electrons near the Fermi surface form Cooper pair, and fall into lower energy.

The attraction is attributed to an “electron-phonon interaction”

+

Cooper pair

slide5

The Allen-Dynes formula

λ : electron-phonon interaction

ωlog : the logarithmic averaged phonon frequency

μ* : screened Coulomb interaction

assumed

α2F(ω) : Eliashberg function

N(εF) : electronic density of states at the Fermi level εF

ωνq and εk : phonon and electron energies

: the electron-phonon matrix elements

P. B. Allen and R. C. Dynes: Phys. Rev. B 12 (1975) 905.

previous work
Previous work

Akitaka Nakanishi , Hiroshi Katayama-Yoshida:Solid State Commun. 152 (2012) 24–27

crystal structure of cualo 2
Crystal structure of CuAlO2
  • Delafossite structure

hexagonal

  • p-type transparent semiconductor

Cu

Al

O

rigid band model
Rigid band model

doped-system

non-doped system

the number of valence electrons reduce

Fermi energy εF

number of electrons at Fermi energy N(εF)

band structure

phonon dispersion

not change

eigenvalue εk

phonon frequency

electron-phonon matrix

electron-phonon interaction λ

the logarithmic averaged phonon frequency ωlog

superconducting critical temperature TC

assumed

results1
Results1

Density of State(DOS)

Band dispersion

CuAlO2 has flat band near Fermi level, and this band is Cu- and the O-2pz anti-bonding π-band

results2
Results2

Tc and λvs. Nh

TC

Electron–phonon interaction λ and logarithmic averaged

phonon frequencies ωlog. Tc has max and minatNh = 0.3, 1.0.

Nh

λ increase → TC increase

at Nh=0.3

results3

O

O

O

O

Results3

phonon dispersion

Nh=0.3()

Nh=1.0()

phonon mode that stretches the O–Cu–O dumbbell has a strong interaction with electrons of the flat band in Cu-and the O-2pz anti-bonding π-band

Phonon dispersions and electron-phonon interactions of hole-doped CuAlO2. The radius of circle represents the strength of partial electron-phonon interaction .

Note that many are very small and their circles are no longer invisible.

(a) The number of holes Nh = 1.0. (b) Nh = 0.3.

Cu

Cu

motivation
Motivation

CuAlO2

(Delafossite structure)

CuAlS2TC= ? [K]

(chalcopyrite structure)

valence electron

O:2p

    ↓

S:3p

purpose
Purpose
  • Calculate electron-phonon interaction λ and superconducting critical temperatureTCof CuAlS2 based on rigid band model and Allen-Dynes formula
  • Compare delafossite structure (two dimensional) CuAlO2 with chalcopyrite structure (three dimensional) CuAlS2
crystal structure of cuals 2
Crystal structure of CuAlS2
  • Chalcopyrite structure
  • tetrahedral coordination
  • semiconductor

Cu

Al

S

c omputational m ethod electric structure phonon dispersion
Computational method-electric structure & phonon dispersion-
  • Quantum-Espresso code
  • Based on Density Functional Theory (DFT)
  • Generalized Gradient Approximation (GGA)
  • Ultra-soft pseudo potential
  • 8×8×8 k-point grid (electron)

8×8×8 q-point grid (phonon)

  • Cut-off energy for wave function is 40 [Ry]
  • Cut-off energy for charge density is 320 [Ry]
b and dispersion
Band dispersion

Energy = 0 is

Valence Band Maximum (VBM)

Eg=1.65 [eV]

Γ

Γ

*U.P. Verma , Per Jensen , Monika Sharma , Poonam Singh: Computational and Theoretical Chemistry 975 (2011) 122–127

**J.E. Jaffe, A. Zunger, Phys. Rev. B 28 (1983) 5822

d ensity of states dos
Density of states (DOS)

Energy zero is the top of the valence band Maximum (VBM).

d ensity of states dos1
Density of states (DOS)

anti-bonding state

(Cu 3dεand S 3p)

bonding state

(Cu 3dεand S3p)

non bonding state

(Cu3dγ)

Energy zero is the top of the valence band Maximum (VBM).

p honon dispersion1
Phonon dispersion

CuAlO2 (Delafossite structure)

CuAlS2 (Chalcopyrite structure)

Γ

Γ

S atom is heavier than O atom

→ Max phonon frequency of CuAlS2 lower than that of CuAlO2

summary
Summary
  • I introduce Allen-Dynes formula.
  • I introduce previous work. CuAlO2 has based on rigid band model.
  • I show results of band dispersion ,DOS ,and phonon dispersion of CuAlS2
f uture plan
Future plan
  • I will calculate TC vs. number of holes about CuAlS2
  • I will consider difference of dimensionality and Tc
  • I will calculate other chalcopyrite structures.

CuAlS2

CuGaS2

AgAlS2

AuAlS2

CuInS2