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Unadulterated spectral function of low-energy quasiparticles Evtushinsky Daniil Institute of Metal Physics, Kiev, Ukraine Moscow Institute of Physics and Technology
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### Transcript of Unadulterated spectral function of low-energy quasiparticles

Microsoft PowerPoint - Dan_CORPES_final.pptEvtushinsky Daniil
• Is quasiparticle approach valid ?
• Offset at ω → 0 and at T → 0 ?
• Behavior near TC ?
• Evolution with doping?
Problems
R-?
Σ"int=Σ"-Σ"imp
• RA – Analyzer • Remains constant • Easy to measure
• RS – Sample Surface • Varies with space and time • Difficult to measure
R=RA ⊗ RS
bare dispersion
In te
ns ity
L G
- 0.01 eV
- 0.1 eV
We measure I(k, ω) We are interested in A(k, ω) We need to remove R(k, ω)
Nodal Direction
No gap
Momentum Resolution
( )( ) 2 0
2 max
0 0 ))((
)(1),()( ω
ω π
ω Σ ′′+−⋅
Real MDC is a convolution between pure signal and resolution:
κκκ dRkLRLkMDC ⋅⋅−=⊗= ∫ )()()(
Σ(k,ω)=Σ(ω) M(k)=const ε(k) linear
Real MDC = Pure MDC (Lorentzian)
Real MDC = Pure MDC ⊗ Resolution (Lorentzian) (Gaussian)
Lorentzian ⊗ Gaussian = Voigt profile
What is Voigt Profile?
Lorentzian ⊗ Gaussian = Voigt profile
Voigt Profile
κκκ dGkLGLkV ⋅⋅−=⊗= ∫ )()()(
2 2
G LL
V WWWW ++≈
Where L is a lorentzian, and G is gaussian. HWHM WL and WG
)/)2ln(exp( )2ln(
G L
error< 1.2 %
L, G: 1. Offset 2. Max position 3. Amplitude 4. Width
Lorentz, Gauss 10
Lorentz, Gauss
0.500.400.30 k, 1/A
MDC Shape
0.500.450.40 k, A-1
2 I n t e n s i t y
0.500.450.40
Σ(ω) from Voigt Fit
Resolution: WG=const
Overall width, WV
Intrinsic width, WL
• BSCCO • x=0.21 • x=0.16 • x=0.12
• YBCO • Temperature dependence • Comparison to high-resolution data
Examples on BSCCO
ω , e V
x=0.21, T = 100 K x=0.16, T = 40 K x=0.12, Low T
Voigt Fit in application to YBCO
0.550.500.450.400.350.30 1/A
Image1,24 K
Image2,24 K
20
15
10
5
20
15
10
5
Comparison to the low-energy high- resolution data
0.03
0.02
0.01
0.00
W (
a
R∼(hν−φ)-1/2
B. ω-dependence: WG(ω)=const
C. YBCO: different images give same result while exposed to Voigt Fit procedure
D. T-dependence: while WG exhibits almost random and strange behavior, WL(T) always increases with temperature
E. Purified by Voigt Fit data coincides with high-resolution data (Koralek PRL 2006)
Justification of Voigt Fit procedure
-0.2
0.0
0.2
0.500.450.40 k, A-1
0.500.450.40
B. ω-dependence: WG(ω)=const
C. YBCO: different images give same result while exposed to Voigt Fit procedure
D. T-dependence: while WG exhibits almost random and strange behavior, WL(T) always increases with temperature
E. Purified by Voigt Fit data coincides with high-resolution data (Koralek PRL 2006)
Justification of Voigt Fit procedure
60
50
40
30
20
10
0
A. MDC Lineshape
B. ω-dependence: WG(ω)=const
C. YBCO: different images give same result while exposed to Voigt Fit procedure
D. T-dependence: while WG exhibits almost random and strange behavior, WL(T) always increases with temperature
E. Purified by Voigt Fit data coincides with high-resolution data (Koralek PRL 2006)
Justification of Voigt Fit procedure
0.04
0.02
0.00
A. MDC Lineshape
B. ω-dependence: WG(ω)=const
C. YBCO: different images give same result while exposed to Voigt Fit procedure
D. T-dependence: while WG exhibits almost random and strange behavior, WL(T) always increases with temperature
E. Purified by Voigt Fit data coincides with high-resolution data (Koralek PRL 2006)
Justification of Voigt Fit procedure
20
15
10
5
B. ω-dependence: WG(ω)=const
C. YBCO: different images give same result while exposed to Voigt Fit procedure
D. T-dependence: while WG exhibits almost random and strange behavior, WL(T) always increases with temperature
E. Purified by Voigt Fit data coincides with high-resolution data (Koralek PRL 2006)
Justification of Voigt Fit procedure
0.03
0.02
0.01
0.00
W (
a
A. MDC Lineshape
B. ω-dependence: WG(ω)=const
C. YBCO: different images give same result while exposed to Voigt Fit procedure
D. T-dependence: while WG exhibits almost random and strange behavior, WL(T) always increases with temperature
E. Purified by Voigt Fit data coincides with high-resolution data (Koralek PRL 2006)
Most interesting part
Fermi-level
0.03
0.02
0.01
0.00
-0.15-0.10-0.050.00 ω (eV)
OP 89 K, T = 30 K OP 89 K, T = 110–135 K OD 75 K, T = 80–130 K
b
Reduced self-energy function
Σ” ∼ ω2
T.Valla Physical Review B, 2006 T. Yamasaki et al., cond-mat/0603006
ARPES vs.
MDC Width: 0.030 vs 0.004 1/Å
Yoshida’s MDC used to calculate resistivity. HWHM=0.03 1/Å Compare to result, obtained by Voigt-fit procedure: 0.004 1/Å.
Yoshida Physica B 2004
Yos hid
from ARPES (Σ''~20 meV) isotropic part (Σ''=2 meV)
20 meV
ARPES: τ-1= τI-1+τf-1
2 meV
from ARPES (Σ''~20 meV) isotropic part (Σ''=2 meV)
20 meV
2 meV
2
m ne τσ =Simple Drude formula: Note that m* is calculated from
renormalized dispersion. n=(1-x)
How resistivity changes if we take in to account some extra features?
Two kinds of scattering: R↓ ARPES: τ-1= τI-1+τf-1
Transport: τ-1= τI-1+ α·τf-1 , α<<1 Forward, τf Isotropic, τI
Inhomogeneity: R↑ n ~ (1-Vm) nd + Vm nm Vm – metallic phase volume
Conclusions
• Non-zero Σ"(T=0) ≈ 16 meV • No drop at TC
• Σ“ depends rather on dopants than on x • To compare to transport we need to
disentangle isotropic and forward contributions
Conclusions
• Non-zero Σ"(T=0) ≈ 16 meV • No drop at TC
• Σ“ depends rather on dopants than on x • To compare to transport we need to
disentangle isotropic and forward contributions
Conclusions
• Non-zero Σ"(T=0) ≈ 16 meV • No drop at TC
• Σ“ depends rather on dopants than on x • To compare to transport we need to
disentangle isotropic and forward contributions
Conclusions
• Non-zero Σ"(T=0) ≈ 16 meV • No drop at TC
• Σ“ depends rather on dopants than on x • To compare to transport we need to
disentangle isotropic and forward contributions
Forward
Isotropic
0.10
0.08
0.06
0.04
0.02
0.00
Σ″ (ω , T=95..125 K) (ω -dep for average image)
Σ″ (ω =0, T)
Σ"(ω,T)= S(ω)+S(πT) → 0.14
OP (KEI) Y-doped (YDLY)
0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.000
M D C , 1 / A
300250200150100500 T, K
x w[0] + w[1]*T + w[2]*T^2 0.21 {0.0045, 1.90e-05, 7.2e-08} 0.16 {0.0052, 1.02e-05, 8.9e-08} 0.16(Ni){0.0054,-3.84e-06, 9.4e-08} 0.16(Zn){0.0093, 2.64e-05, 8.7e-09} 0.11 {0.0116,-1.44e-06, 1.7e-07} 0.12(Y) {0.0052, 2.41e-05, 2.1e-07}
Energy resolution in Foigt fit
I(k, ω) ∝ A(k, ω) ⊗R(k, ω) R(k, ω)= Rk⊗ Rω
Energy resolution has almost the same effect on the MDC shape as momentum resolution, so both Rω and Rk are taken into account by Voigt-fit procedure.
Pure MDC – Lorentzian Real MDC = pure MDC ⊗ Resolution - Voigt
6
4
2
0.500.450.40
Σ“imp(ω) ~ ω , T<TC
Gap → DOS → Σ“ opening change change
)()()()(
212121 '' ωωωωωωωω −−∝Σ ∫∫ DOSDOSDOSddin
Σ“in(ω) ~ ω2, T>TC Σ“in(ω) ~ ωn, n≥3, T<TC
( ) Ω⋅Ω⋅Ω−∝Σ ∫ dNDOS impimp )()(''
:impuritieson Scattering