1. Charge density wave and superconductivity in
transition metal dichalcogenides
Donglai Feng
Dept. of Physics and Advanced Materials Laboratory, Fudan University
Title:Charge density waveand superconductivtyin transition metaldichalcogenides
Abstract: Charge density wave, or CDW, is usually associated with Fermi surfaces nesting. Transition metal dichalcogenides are the first 2D CDW materials, where superconductivity and CDW coexists. We here report a new CDW mechanism discovered in a 2H-structured transition metal dichalcogenide NaxTaS2, where the two essential ingredients of CDW are realized in very anomalous ways due to the strong-coupling nature of the electronic structure. Namely, the CDW gap is only partially open, and charge density wavevector match is fulfilled through participation of states of the large Fermi patch, while the straight FS sections have secondary or negligible contributions. We illustrate that the competition and coexistence of superconductivity are realized uniquely in this system. For 1T-CuxTiSe2, the newly discovered first 1T-structured transition metal dichalcogenide superconductor, there appears to be competition between CDW and superconductivity. We found that Cu doping significantly enhances the density of states around the Fermi energy, while strong scattering is observed at the solubility limit (x~0.11), which is consistent with the non-monotonic doping dependence of the superconductivity. Furthermore, the raise of the chemical potential also explain the suppression of the charge density wave based on an excitonic mechanism proposed before. Our results suggest that the competition might be merely a coincidence.
KITPC, 2007

2. Introduction 2H-NaxTaS2 2H-NbSe2 1T-CuxTiSe2
Outline
Introduction
Rich physics in transition metal dichalcogenides
Angle resolved photoemission spectroscopy (ARPES)
2H-NaxTaS2
2H-NbSe2
1T-CuxTiSe2

3. Transition metal Dichalcogenides (TMD)
a=3.314 A, c= A
Space group P6/mmc
a=3.364 A c=5.897 A
Space group: P3m1
From Hai-Hu Wen
The first and still mysterious 2D CDW material discovered in `74

4. Charge Density Wave in TMD
Structure transition of in 2H TMD
1T-TaS2, 1T-TaSe2, 2H-TaS2, 2H-TaSe2 in-plane resistivity
Advance in Physics, 50, 1171(2001).
From Hai-Hu Wen

5. The Zoo of CDW 2H family 3*3 1T-TaSe2 Sqrt(13)*Sqrt(13) 1T-VSe2 2*2
1T-TiSe2 2*2*2
1T-TiTe2 no cdw ……
3*3 (2H family)
Fermi Surface nesting
Saddle band points scattering Q0
All conventional CDW mechanism failed to work ?!

6. Superconductivity and its Competition with CDW
NbS2
NbSe2
TaSe2
TaS2
Studying the competitions among many degrees of freedom in materials is one focal pointin condensed matter physics.
D. Jerome, C. Berthier, P. MoliniZe, J. Rouxel, J. Phys. (Paris) Colloq. 4 (37) (1976) C125.
A. H. Castro Neto, Phys. Rev. Lett.86, 4382(2001).
How CDW and SC compete ？
From Hai-Hu Wen

7. First 1T-TMD superconductor: CuxTiSe2
E. Morosan et al., Nature Physics 2, 544 (2006)

8. Mott-insulator transitions in other TMD’s
control U/t by pressure in NiS2 , and by Se substitution in Ni(S1-xSex)2

9. Angle-Resolved Photoemission Spectroscopy
Energy Conservation
EB= hn - Ekin - F
Momentum Conservation
K|| = k||+ G||
Photoemission intensity: I(k,w)=I0 |M(k,w)|2f(w) A(k,w)
Single-particle spectral function

10. Angle-Resolved Photoemission Spectroscopy
0.1°
2-10
now 2°
20-40
past Dq
DE (meV)
Improved energy resolution
Improved momentum resolution
Improved data-acquisition efficiency
Parallel multi-angle recording
Momentum
Energy
A. Damascelli et al., PRL 85, 5194 (2000)
Light source

11. EDC and MDC Energy (eV) Momentum (A-1) Energy distribution
curves (EDC)
momentum
Complex lineshapes and background
Fermi function cut-off
Energy
Momentum
distribution
curves (MDC)
Good fit with Lorentzian shape
No Fermi function complications
PEAK POSITION
Dispersion
PEAK WIDTH
1/t scattering rate

12. ARPES system at Fudan ARPES in Fudan High flux Helium lamp
SSRL: As low as 5K; energy resolution is ~10meV; angle resolution is better than 0.3 degree. 22.7eV photo energy,
Ours: 10K (closed-circle He cryostat); energy resolution is better than 8meV; angle resolution is ~0.3 degree.
High flux Helium lamp
High angular resolution analyzer: R4000
Low temperature (10K)
5meV total resolution

13. The electronic origin of CDW in 2H-Structured TMD’s

14. Two existing mechanisms of CDW proposed for 2H compounds
Fermi Surface nesting
Saddle band points scattering Q0
Particular topology of FS leads to a divergent response to an external
perturbation, and then induces the divergence in response function.
Scattering between several saddle
band points, where a singularity in
density of state to causes an anomaly
in response function.
Here I would like to reports some experimental evidence of a new mechanism in ARPES data from our systemic study for several doping level 2H-NaxTaS2.
Firstly, let me give a concise introduction of the former two popular mechanisms for this system.
Here, we propose our understanding for the system.
Both nesting of Fermi surface or saddle points have caveats.
mismatch of nesting and CDW wavevectors
Nesting of FS: no gaps open near FS. (T. Valla et al),
FS varies in different systems
Saddle points: energy too far from EF, tiny effect;
no gaps open near saddle points, etc. (Th.Straub et al)

15. Open issues in 2H-TMD systems
CDW
Non-observation of the CDW gap
Nesting Fermi surface vector does not match the CDW ordering vector.
The resistivity drop in 2H-TMD upon forming CDW
How CDW and Superconductivity competes?

16. Na doing – NaxTaS2 2H-TaS2: CDW transition@70K SC transition@0.8K ；
Na0.33TaS2’s Tcsc is 4.7K
Na0.33TaS2•1.3H2O ‘s Tcsc is as
large as 5.5K,
which is reminiscent
of NaxCoO2•yH2O
Hydrated cobalt oxides
Lerf et al, Mat. Res. Bull. 9, 1597 (1974); 14, 797 (1979); Johnston , ibid. 17, 13 (1982)

17. Fermi surface and spectra
Extended flat band region around M in this system

18. Luttinger theorem and Fermi patch
This is opposite to the rigid band picture

19. Comparison of CDW0K and CDW65K

20. Strong coupling regime
Anomalous electronic properties
Incoherent spectrum
Broad linewidth ~ dispersion
Finite weight at EF even the centroid is far away
Clear dispersion
Well defined Fermi surface
All signs point to that the system is in strong coupling regime.
here between electron and lattice (i.e. polaronic system)

21. Examples of strongly interacting system
Blue bronze KMO
Bi2201
B. P. Xie et al. PRL 07

22. Study many body effects with ARPES: e--phonon Coupling
Single-particle spectral function
Hengsberger et al., PRL 83, 592 (1999)
Valla et al., PRL 83, 2085 (1999)
Be(0001)
Mo(110)
Electronic band
Collective
mode
Eschrig, Norman, PRB 67, (2003)

23. Strong and anisotropic ‘Kinks’ in NbSe2
A sign of strong electron -phonon interaction.

24. Doping dependence of “kink” in NaxTaS2
NaxTaS2, x=0.1, Tc=3.8K, TCDW=0, very weak
NaxTaS2, x<0.05, Tc<1K, TCDW=70K, show up

25. Gap analysis at M: doping and T-dependence

26. A new theoretical approach resolving the gap issue
Demler et al PRL 2006

27. Gap analysis

28. Gap analysis: doping and T-dependence

29. Momentum dependence a b c d

30. Why 3×3 ?

31. Auto correlation analysis
Hoffman et al. Science 02
Vershinin et al Science 05
Chatterjee et al, PRL 06.

32. Autocorrelation map of NaxTaS2

33. How about NbSe2 ?

34. Spectral weight distribution and suppression in NbSe234

35. Spectral weight suppression in the CDW state of NbSe2

36. 2H-NbSe2 n(k)’s vs. EB, and autocorrelation
the CDW wave vector is 1/3 a* regardless of doping, or element (S, Se, Ti, Ta, or Nb)

37. T-dependence of auto-correlation

38. Scattering between asymmetrically gapped regions
Similarity to the saddle point scenario
Gapped region does Not exactly match Qcdw ?
While the autocorrelation peaks at Qcdw ?!

39. CDW gap vs. total density of states

40. New mechanism Do not involve FS Not just involve single saddle point
but involve the entire Brillouin zone, where there is a large fraction of spectral weight at EF due to strong coupling/polaronic effects
Q fulfills the CDW condition
Gap identified
Phase space is consistent with CDW strength
May well applies to CDW instabilities in many other strong-coupling systems.

41. CDW/Superconductivity competition
Yokoya et al. Science,294, 2518(2001)
K pocket is CDW- gapped, therefore less spectral weight available for SC.

42. Summary for the CDW in 2H compounds
Polaronic electronic structure, providing the playground of the unconventional CDW and SC.
Identification of the CDW gap over extended regions in the Brillouin zone, resolving all the issues of CDW condition
Gap size
CDW wave-vector matching
Different system may vary in details even though the CDW is always 3*3 for the 2H compounds.
The new mechanism is possibly a general CDW mechanism for strong-coupling systems, and may well be applied to CDW (instabilities) in many strongly correlated systems, such as the high Tc superconductors.

43. Understanding the phase diagram of 1T - CuxTiSe2

44. CuxTiSe2:SC and CDW competition in 1T-TMD’s Ubiquitous phase diagram of superconductors
High temperature superconductor
Heavy Fermion superconductor
E. Morosan et al., Nature Physics 2, 544 (2006)
E. Dagotto, Science 309 (2005)257.

45. 1T CuxTiSe2

46. Brillouin zone and nature of the states
For 21.2eV photon energy, electrons with kz ranges from 3p/2c to 5p/2c.
J. of Electron Spectro. Related Phenom. 117–118 (2001) 433

47. From N. L. Wang

48. Open questions in the phase-diagram
Semimetal or Semiconductor?
What is the mechanism of (2x2x2) CDW?
Why Copper doping would weaken the CDW?
Why superconductivity emerges?
What is the reason for the suppression of superconductivity at high doping range?
Do CDW and SC really compete?
Why SC only discovered in this single 1T compound so far?

49. Temperature dependence of the A-L cut of TiSe2
CDW occurs at 220K
20K
60K
100K
140K
200K
230K A
Intensity (arb. units) L

50. A closer look of A & L Edge shift band folding TiSe2
Intensity (arb. units)
Intensity (arb. units)
CDW opens a gap of 66 meV near A at the valence band.
CDW folds G features to L, and the EDC also suggests Ti 3d band is above Ef

51. Fermi patch, and Fermi surface

52. Doping dependence of EDC

53. How superconductivity being suppressed?
Tc increases with doping, due to the spectral weight enhance at EF
Tc drop in the overdoping regime
Large background at high doping (x~0.11)
“Normal” R-T curve
Inelastic scattering enhanced?
Intensity (arb. units)
E-Ef
G.Wu, X.H.Chen et al.

54. Fine structure of EDC’s

55. Correlated metal + band-picture semiconductor

56. Shift of Chemical potentialG L G

57. Temperature dependence of EDC’s @ L’

58. How CDW disappear x=0 x=0.065 Charge neutrality is fulfilled
Correlation plays an important role
x=0.065 data make possible low temperature, and more precise picture
100 meV raise of chemical potential Se bands well below EF, while the exciton binding energy is estimated before to be 17 meV

59. Conclusion A ubiquitous and intriguing phase diagram by accident!
1T-TiSe2
Excitonic CDW
Chemical Potential shift
Exciton formation costly
CDW suppressed
Cu doping increases.
Superconductivity
rises
CDW opens gap at valence band not Ef
Copper doping increase carrier density
AT high doping range,
Inelastic scattering enhanced
Superconductivity
suppressed
A ubiquitous and intriguing phase diagram by accident!

60. Acknowledgement Fudan Group
Dawei Shen, Jiafeng Zhao, Binping Xie, Hongwei Ou, Jia Wei, Lexian Yang, Jinkui Dong, Yan Zhang
Synchrotron work
D. H. Lu, R. H. He (SSRL), S. Qiao, M. Arita (HiSOR)
Single Crystals
Prof. Haihu Wen(IOP),
Prof. Xianhui Chen (USTC)
Prof. Jin Shi (U. of Wuhan)
Discussions
Zhengyu Weng(Tsinghua), Dunghai Lee (UCB), Nanlin Wang (IOP) and many others
Funding Support

61. Thank you !

62. Excitonic scenario & the CDW transition
The new peak originates from the Se 4p band at G point, it is folded to the L point when 2x2x2 CDW is happened. This is quite similar to what Kohn has proposed in 1967
Alex Zunger , A. J. Freeman , Phys. Rev. B (17)