CCharge density waveharge density wave and superconductivity and superconductivity in in transition metal dichalcogenidestransition metal dichalcogenides

Donglai FengDept. of Physics and Advanced Materials

Laboratory, Fudan University

KITPC, 2007

Outline

• Introduction– Rich physics in transition metal

dichalcogenides– Angle resolved photoemission

spectroscopy (ARPES)

•2H-NaxTaS2

•2H-NbSe2 •1T-CuxTiSe2

Transition metal Dichalcogenides (TMD)

From Hai-Hu Wen The first and still mysterious 2D CDW material discovered in `74

a=3.314 A, c=12.090 ASpace group P6/mmc

a=3.364 A c=5.897 ASpace group: P3m1

Charge Density Wave in TMD

1T-TaS2, 1T-TaSe2, 2H-TaS2, 2H-TaSe2 in-plane resistivity

Advance in Physics, 50, 1171(2001).

Structure transition of in 2H TMD

From Hai-Hu Wen

The Zoo of CDW

3*3 (2H family))1(1313 2TaSeT

2H family 3*31T-TaSe2 Sqrt(13)*Sqrt(13)1T-VSe2 2*21T-TiSe2 2*2*21T-TiTe2 no cdw……

Saddle band points scattering Fermi Surface nesting

Q0All conventional CDW mechanism failed to work ?!

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).

TaSe2 TaS2NbSe2

NbS2

Superconductivity and its Competition with CDW

From Hai-Hu Wen How CDW and SC compete ？

E. Morosan et al., Nature Physics 2, 544 (2006)

First 1T-TMD superconductor: CuxTiSe2

Mott-insulator transitions in other TMD’s

control U/t by pressure in NiS2 , and by Se substitution in Ni(S1-xSex)2

Photoemission intensity: I(k,)=I0 |M(k,)|2f() A(k,

Single-particle spectral function

Angle-Resolved Photoemission Spectroscopy

Energy ConservationEB= hEkin

Momentum Conservation

K|| = k||+ G||

Angle-Resolved Photoemission Spectroscopy

0.1°2-10now

2°20-40past

E (meV)

Improved energy resolution Improved momentum resolution Improved data-acquisition efficiency

Parallel multi-angle recordingM

omen

tum

Energy

A. Damascelli et al., PRL 85, 5194 (2000)

Energy (eV)Energy (eV)

Mom

en

tum

(A

Mom

en

tum

(A

-1-1))

Energy distribution curves (EDC)

mom

entu

m

Complex lineshapes and background

Fermi function cut-off

PEAK POSITIONDispersion

PEAK WIDTH1/ scattering rate

Energ

yEnerg

y

MomentuMomentumm

Momentum distribution curves (MDC)

Good fit with Lorentzian shape No Fermi function

complications

EDC and MDC

ARPES in FudanARPES in Fudan

• High flux Helium lamp

• High angular resolution analyzer: R4000

• Low temperature (10K)

•5meV total resolution

ARPES system at Fudan

The electronic origin of CDW in2H-Structured TMD’s

Saddle band points scattering Fermi Surface nesting

Q0

Scattering between several saddle band points, where a singularity in density of state to causes an anomalyin response function.

Particular topology of FS leads to a divergent response to an external perturbation, and then induces the divergence in response function.

Both nesting of Fermi surface or saddle points have caveats. mismatch of nesting and CDW wavevectorsNesting 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)

Two existing mechanisms of CDW proposed for 2H compounds

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?

• 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

Lerf et al, Mat. Res. Bull. 9, 1597 (1974); 14, 797 (1979); Johnston , ibid. 17, 13 (1982)

Na doing – NaxTaS2

1 2 3 4 5 6 7 8-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

Na0.1

TaS2

Na0.05

TaS2

NaxTaS

2 (x<0.05)

NaxTaS

2 (x<0.05)

AC

res

po

nse

(10

- 4 A

m2 /g

)

T (K)

0 20 40 60 80 100

0.0

0.2

0.4

0.6

0.8

1.0

Tc= 4.4 K

2H-TaS2

Na0.1

TaS2

(N

orm

aliz

ed t

o 9

0 K

)

T (K)

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

Single-particle spectral function

Eschrig, Norman, PRB 67, 144503 (2003) Hengsberger et al., PRL 83, 592 (1999) Valla et al., PRL 83, 2085 (1999)

Be(0001) Mo(110)

Collectivemode

Electronic band

Study many body effects with ARPES: e--phonon Coupling

Strong and anisotropic ‘Kinks’ in NbSe2

A sign of strong electron -phonon interaction.

NaxTaS2, x=0.1, Tc=3.8K, TCDW=0, very weak

NaxTaS2, x<0.05, Tc<1K, TCDW=70K, show up

Doping dependence of “kink” in NaxTaS2

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

bc d

Why 3×3 ?

Auto correlation analysis

Chatterjee et al, PRL 06.

Hoffman et al. Science 02

Vershinin et al Science 05

Autocorrelation map of NaxTaS2

How about NbSe2 ?

Spectral weight distribution and suppression in NbSe2

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

•Similarity to the saddle point scenario•Gapped region does Not exactly match Qcdw ?•While the autocorrelation peaks at Qcdw ?!

Scattering between asymmetrically gapped regions

CDW gap vs. total density of states

New mechanism

1. Do not involve FS2. Not just involve single saddle point3. 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 mechani

sm 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

E. Morosan et al., Nature Physics 2, 544 (2006)

High temperature superconductor

Heavy Fermion superconductor

E. Dagotto, Science 309 (2005)257.

1T CuxTiSe2

For 21.2eV photon energy, electrons with kz ranges from 3/2c to 5/2c.

J. of Electron Spectro. Related Phenom. 117–118 (2001) 433

Brillouin zone and nature of the states

From N. L. Wang

Open questions in the phase-diagram

1. Semimetal or Semiconductor?

2. What is the mechanism of (2x2x2) CDW?

3. Why Copper doping would weaken the CDW?

4. Why superconductivity emerges?

5. What is the reason for the suppression of superconductivity at high doping range?

6. Do CDW and SC really compete?

7. Why SC only discovered in this single 1T compound so far?

-1. 2 -0. 8 -0. 4 0. 0E-EF (eV)

20K

-1. 2 -0. 8 -0. 4 0. 0E-EF (eV)

60K

-1. 2 -0. 8 -0. 4 0. 0E-EF (eV)

100K

-1. 2 -0. 8 -0. 4 0. 0E-EF (eV)

140K

-1. 2 -0. 8 -0. 4 0. 0E-EF (eV)

200K

-1. 2 -0. 8 -0. 4 0. 0E-EF (eV)

230K

Inte

nsi

ty (

arb

. u

nit

s)

A

L

Temperature dependence of the A-L cut of TiSe2

L

L’

A

20K 100K60K 200K140K 230K

CDW occurs at 220K

CDW opens a gap of 66 meV near A at the valence band.

CDW folds features to L, and the EDC also suggests Ti 3d band is above Ef

Inte

nsi

ty (

arb

. u

nit

s)

Inte

nsi

ty (

arb

. u

nit

s)

A closer look of A & L

band foldingEdge shift

TiSe2

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~0.1

1) “Normal” R-T curve Inelastic scattering enhanced?

G.Wu, X.H.Chen et al.

-1.2 -0.8 -0.4 0.0

x=0.11

E-Ef

Inte

nsity

(arb

. uni

ts)

-1.2 -0.8 -0.4 0.0

x=0.065

Fine structure of EDC’s

Correlated metal + band-picture semiconductor

Shift of Chemical potential

L

Temperature dependence of EDC’s @ L’

How CDW disappear

x=0 x=0.065

1. Charge neutrality is fulfilled2. Correlation plays an important role3. x=0.065 data make possible low temperature, and more precise picture4. 100 meV raise of chemical potential Se bands well below EF, while the excito

n binding energy is estimated before to be 17 meV

Conclusion 1T-TiSe2

Excitonic CDW

Cu doping increases.

Chemical Potential shift

Exciton formation costly

CDW opens gap at valence band not Ef

Copper doping increase carrier densityAT high doping range,

Inelastic scattering enhanced

CDW suppressed

Superconductivity

rises

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 W

ang (IOP) and many others

• Funding Support

Thank you !

Excitonic scenario & the CDW transition

The new peak originates from the Se 4p band at 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