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

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

Transition metal Dichalcogenides (TMD) a=3.314 A, c=12.090 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

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

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 ?!

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

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

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

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

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

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

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

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

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)

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?

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)

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

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

Comparison of CDW0K and CDW65K

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)

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

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, 144503 (2003)

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

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

Gap analysis at M: doping and T-dependence

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

Gap analysis

Gap analysis: doping and T-dependence

Momentum dependence a b c d

Why 3×3 ?

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

Autocorrelation map of NaxTaS2

How about NbSe2 ?

Spectral weight distribution and suppression in NbSe2 34

Spectral weight suppression in the CDW state of NbSe2

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)

T-dependence of auto-correlation

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

CDW gap vs. total density of states

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.

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

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.

Understanding the phase diagram of 1T - CuxTiSe2

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.

1T CuxTiSe2

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

From N. L. Wang

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?

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

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

Fermi patch, and Fermi surface

Doping dependence of EDC

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.

Fine structure of EDC’s

Correlated metal + band-picture semiconductor

Shift of Chemical potential G L G

Temperature dependence of EDC’s @ L’

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

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!

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

Thank you !

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) 1839