The “normal” state of layered
dichalcogenides
Arghya Taraphder
Department of Physics and Centre for Theoretical Studies
Indian Institute of Technology
Kharagpur
Workshop @ Harish Chandra Research Institute, November 12-14, 2010
Salient Features
 Transition metal dichalcogenide – TM atoms
separated by two layers of chalcogen atoms
TM atoms form 2D triangular lattice
 CDW & Superconductivity (likely to be anisotropic)
 Partially filled TM d band or chalcogen p band:[]d1/0
 1T and 2H type lattice structure
 Both I and C CDW at moderate temperature
 Normal to SC transition with pressure/doping
 Normal transport unusual (cf. HTSC)
Dichalcogenides: crystal structure
Glossary
Typical Phase diagram
2H-TaSe2
1T-TiSe2
D.B. Mcwhan, et al. PRL 45,269(1980)(2HTaSe2)
A. F. Kusmartseva, et al. PRL 103, 236401(2009) (1TTiSe2)
B. Sipos, et al. Nat. mater. 7, 960 (2008) (IT-TaS2)
1T-TaS2
Cava et al.
2H-TaS2
Phase diagram of 1T-TiSe2 : doping and pressure
Quantum critical?
Castro-Neto, loc cit
Cava, PRL (2008)
DC Resistivities
Aebi, loc cit
Resistivity of TMDs: 1T and 2H
Y. Ueda, et al. Journal of Physical Society
of Japan 56 2471-2476, (1987).
P. Aebi, et al. Journal of Electron
Spectroscopy and Related Phenomena
117–118 (2001)
2H-TaSe2
Vescoli et al, PRL 81, 453 (1998)
R C Dynes, et al., EPJB 33, 15 (2003)
Optical conductivity
(0.04 < E < 5 eV range)
Features of dc transport and Re σ (ω)
•“Drude-like” peak at ω=0 for both systems along both ab and
C-directions, narrowing at low T, indicating freezing of
scattering of charge carriers at low energy
•Tccdw does not affect transport at all, in fact thermodynamics
is also unaffected
•Broad conductivity upto large energies (~0.5 eV)
Dynes loc cit
Spectral weight distribution
•Spectral weight is non-zero even upto 5 eV and
beyond – “recovery” of total n uncertain
•Shifts progressively towards FIR as T is lowered condensation at lower frequency
• Nothing abrupt happens as T_CDW is crossed
Transport scattering rate
ab-plane
Transport scattering rate
c-axis
Scattering rate from transport
• Strongly
frequency dependent. Rapid suppression
of both Γab and Γc below characteristic freq. ~ 500 /cm
Possible “pseudogap” in 20K curve
•High and low T Γab cross each other for TaSe2
at some frequency
•No saturation of Γab upto 0.6 eV
•Both Γab and Γc are above Γ= ω line upto 2000 /cm and
nearly linear in ω
“QP” Scattering
Rate & SE from ARPES
Valla, PRL 85, 4759 (2000)
Fit with momentum-indep. SE
Valla, loc. cit..
Electronic structure
Aebi, JES 117, 433 (2001)
Self-energy from ARPES
•Local - no k-dependence
•Re Σ peaks at 65 meV, Im Σ drops there –
characteristic of a photo-hole scattering off a
collective ‘mode’ ~ 65 mev (too large for all phonons
in TaSe2)
•Im Σ(0) matches excellently with transport Γ(0) in
its T-dependence
Band structure
2H-TaSe2
Aebi, JES 117, 433 (2001)
H.E. Brauer,et al. J. Phys. Cond.
Matter 13, 9879 (2001)
Tight Binding Description
N V Smith, et al. J. Phys. C:Solid State Phys. 18
(1985) 3175-3189
Tight binding fit near FL for 2H-TaSe2
N V Smith, et al. J. Phys. C:
Solid State Phys. 18 (1985) 3175-3189.
Fermi surface map for the TB bands
2H-TaSe2
1T-TaS2
Liu, PRL 80, 5762 (1998)
ARPES - 2H-TaSe2
Liu, PRL 80, 5762 (1998)
Valla et al, PRL 85, 4759 (2000)
CDW Gap ? Castro_Neto, PRL 86, 4382 (2001)
)Pseudogap in 2H-TaSe2, Borisenko et al, PRL 100, 196402 (2008)
Fermi surface and ARPES - 2H type
S V Borisenko, et al.
Phys. Rev. Lett. 100, 196402 (2008)
N V Smith, et al. J. Phys. C: Solid State Phys.
18 (1985) 3175-3189.
Fermi surface and ARPES - 1T type
F.Clerc, et al. Physica B 351
245-249, (2004)
N V Smith, et al. J. Phys. C:
Solid State Phys. 18 (1985) 3175-3189.
Fermi surface of 1T-TiSe2
P. Aebi, et al. Phys.Rev.B 61 16213, (2000)
Superlattice & BZ in the CDW phase
of Dichalcogenides
2H-TaSe2
1T-TaS2
N V Smith, et al. J. Phys. C:Solid State Phys. 18 (1985)
3175-3189.
Our Work: LDA - tight binding fit near FL for 2H-TaSe2
N V Smith, et al. J. Phys. C:
Solid State Phys. 18 (1985) 3175-3189.
Fermi surface map for the TB bands
2H-TaSe2
1T-TaS2
Spectral Function for 2H-TaSe2
Before DMFT
After DMFT
Evolution of Spectral Function and fitting ARPES
Conductivity and resistivity from DMFT
DMFT with inter-orbital hopping for 2H-TaSe2
Opening of gap with increase in
temperature
Pressure dependence of Fermi Surface
Change in spectral function with pressure
Temperature dependent Spectral function
at different pressure
Change in resistivity at different pressure
Conclusion
• DMFT Spectral function is broadened.
• With application of Inter-orbital coulomb interaction
the system goes to insulator.
• With application of Inter-orbital hopping DMFT orbital
occupation changes from LDA.
• There is a opening of gap with increasing temperature
up-to 140K.
• With decreasing pressure hole pockets in the Fermi
surface disappear.
• With increasing pressure the gap formed at the Fermi
surface decreases.