1. The “normal” state of layered dichalcogenides Arghya Taraphder Indian Institute of Technology Kharagpur Department of Physics and Centre for Theoretical Studies Workshop @ Harish Chandra Research Institute, November 12-14, 2010

2. 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:[]d 1/0 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)

3. Dichalcogenides: crystal structure

4. Glossary

5. Typical Phase diagram D.B. Mcwhan, et al. PRL 45,269(1980)(2H- TaSe2) A. F. Kusmartseva, et al. PRL 103, 236401(2009) (1T- TiSe2) B. Sipos, et al. Nat. mater. 7, 960 (2008) (IT-TaS2) 2H-TaSe2 1T-TiSe2 1T-TaS2

6. 2H-TaS2 Cava et al.

7. Phase diagram of 1T-TiSe2 : doping and pressure

8. Quantum critical? Castro-Neto, loc cit Cava, PRL (2008)

9. DC Resistivities Aebi, loc cit

10. 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)

11. Vescoli et al, PRL 81, 453 (1998) 2H-TaSe2

12. Optical conductivity (0.04 < E < 5 eV range) R C Dynes, et al., EPJB 33, 15 (2003)

13. 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)

14. Dynes loc cit

15. 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

16. Transport scattering rate ab-plane

17. Transport scattering rate c-axis

18. 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

19. “QP” Scattering Rate & SE from ARPES Valla, PRL 85, 4759 (2000)

20. Valla, loc. cit.. Fit with momentum-indep. SE

21. Aebi, JES 117, 433 (2001) Electronic structure

22. 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

23. 2H-TaSe2 H.E. Brauer,et al. J. Phys. Cond. Matter 13, 9879 (2001) Band structure Aebi, JES 117, 433 (2001)

24. Tight Binding Description N V Smith, et al. J. Phys. C:Solid State Phys. 18 (1985) 3175-3189

25. Tight binding fit near FL for 2H-TaSe 2 N V Smith, et al. J. Phys. C: Solid State Phys. 18 (1985) 3175-3189.

26. Fermi surface map for the TB bands 2H-TaSe 2 1T-TaS 2

27. ARPES - 2H-TaSe2 Liu, PRL 80, 5762 (1998)

29. Valla et al, PRL 85, 4759 (2000)

30. CDW Gap ? Castro_Neto, PRL 86, 4382 (2001)

31. )Pseudogap in 2H-TaSe2, Borisenko et al, PRL 100, 196402 (2008)

32. Fermi surface and ARPES - 2H type N V Smith, et al. J. Phys. C: Solid State Phys. 18 (1985) 3175-3189. S V Borisenko, et al. Phys. Rev. Lett. 100, 196402 (2008)

33. Fermi surface and ARPES - 1T type N V Smith, et al. J. Phys. C: Solid State Phys. 18 (1985) 3175-3189. F.Clerc, et al. Physica B 351 245-249, (2004)

34. Fermi surface of 1T-TiSe 2 P. Aebi, et al. Phys.Rev.B 61 16213, (2000)

35. Superlattice & BZ in the CDW phase of Dichalcogenides N V Smith, et al. J. Phys. C:Solid State Phys. 18 (1985) 3175-3189. 2H-TaSe 2 1T-TaS 2

36. Our Work: LDA - tight binding fit near FL for 2H-TaSe 2 N V Smith, et al. J. Phys. C: Solid State Phys. 18 (1985) 3175-3189.

37. Fermi surface map for the TB bands 2H-TaSe 2 1T-TaS 2

38. Spectral Function for 2H-TaSe 2 Before DMFT After DMFT

39. Evolution of Spectral Function and fitting ARPES

40. Conductivity and resistivity from DMFT

41. DMFT with inter-orbital hopping for 2H-TaSe 2

42. Opening of gap with increase in temperature

43. Pressure dependence of Fermi Surface

44. Change in spectral function with pressure

45. Temperature dependent Spectral function at different pressure

46. Change in resistivity at different pressure

47. 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.