Charge density wave and superconductivity in transition metal dichalcogenides

kitefleaUrban and Civil

Nov 15, 2013 (3 years and 4 months ago)

63 views

C
harge density wave

and superconductivity

in

transition metal dichalcogenides

Donglai Feng

Dept. of Physics and Advanced Materials Laboratory,
Fudan University

KITPC, 2007

Outline


Introduction


Rich physics in transition metal
dichalcogenides


Angle resolved photoemission spectroscopy
(ARPES)


2H
-
Na
x
TaS
2


2H
-
NbSe
2



1T
-
Cu
x
TiSe
2

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 A

Space group

P
6/mmc

a=3.364 A c=5.897 A

Space group:

P
3m1

Charge Density Wave in TMD

1T
-
TaS
2
, 1T
-
TaSe
2
, 2H
-
TaS
2
, 2H
-
TaSe
2

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
(
13
13
2
TaSe
T


2H family 3*3

1T
-
TaSe2 Sqrt(13)*Sqrt(13)

1T
-
VSe2 2*2

1T
-
TiSe2 2*2*2

1T
-
TiTe2 no cdw

……



Saddle band points

scattering



Fermi Surface
nesting

Q
0

All 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).

TaSe
2

TaS
2

NbSe
2

NbS
2

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: Cu
x
TiSe
2

Mott
-
insulator transitions in other TMD

s

control U/t by pressure in NiS
2

, and by Se substitution in
Ni(S
1
-
x
Se
x
)
2



Photoemission intensity
:
I(k,
w
)=I
0

|M(k,
w
)|
2
f(
w
)
A(k,
w)


Single
-
particle spectral function

Angle
-
Resolved Photoemission Spectroscopy

Energy Conservation

E
B
= h
n


E
kin



F

Momentum Conservation

K
||


=
k
|
|
+ G
||

Angle
-
Resolved Photoemission Spectroscopy

0.1
°

2
-
10

now

2
°

20
-
40

past

Dq

D
E (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)

Energy (eV)

E
nergy

d
istribution

c
urves (
EDC
)


Complex lineshapes and
background


Fermi function cut
-
off

PEAK POSITION

Dispersion


PEAK WIDTH

1/
t

獣慴s敲楮朠牡瑥

Momentum

M
omentum

d
istribution

c
urves (
MDC
)


Good fit with Lorentzian shape


No Fermi function complications

EDC and MDC

ARPES 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 in

2H
-
Structured TMD

s



Saddle band points

scattering



Fermi Surface
nesting

Q
0

Scattering between several saddle

band points, where a singularity in

density of state to causes an anomaly

in 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 wavevectors


Nesting of FS
: no gaps open near FS.
(T. Valla
et al
),



FS varies in different systems


Saddle points
: energy too far from E
F
, 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
-
TaS
2
:

CDW transition@70K


SC transition@0.8K





Na
0.33
TaS
2
’s Tc
sc

is 4.7K




Na
0.33
TaS
2
•1.3H
2
O ‘s Tc
sc

is as


large as 5.5K,


which is reminiscent


of

Na
x
CoO
2
•yH
2
O


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

Na doing


Na
x
TaS
2

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
Na
0.1
TaS
2
Na
0.05
TaS
2
Na
x
TaS
2
(x<0.05)
Na
x
TaS
2
(x<0.05)


AC response (10
- 4
Am
2
/g)
T (K)
0
20
40
60
80
100
0.0
0.2
0.4
0.6
0.8
1.0
T
c
= 4.4 K

2H-TaS
2

Na
0.1
TaS
2




(Normalized to 90 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 E
F

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)

Collective

mode

Electronic band

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

Strong and anisotropic ‘Kinks’ in NbSe
2

A sign of strong electron
-
phonon interaction.

Na
x
TaS
2
, x=0.1, Tc=3.8K, T
CDW
=0, very weak

Na
x
TaS
2
, x<0.05, Tc<1K, T
CDW
=70K, show up

Doping dependence of “kink” in Na
x
TaS
2

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

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
-
NbSe
2

n(k)’s vs. E
B
, 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 Q
cdw
?


While the autocorrelation peaks at Q
cdw
?!

Scattering between asymmetrically gapped regions

CDW gap vs. total density of states

New mechanism

1.
Do not involve FS

2.
Not just involve single saddle point

3.
but involve the entire Brillouin zone, where there is a
large fraction of spectral weight at E
F

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
-

Cu
x
TiSe
2

CuxTiSe
2
: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 Cu
x
TiSe
2

For 21.2eV photon energy,
electrons with k
z

ranges from
3
p
/2c to 5
p
/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
0.0
E-E
F
(eV)
20K
-1.2
-0.8
-0.4
0.0
E-E
F
(eV)
60K
-1.2
-0.8
-0.4
0.0
E-E
F
(eV)
100K
-1.2
-0.8
-0.4
0.0
E-E
F
(eV)
140K
-1.2
-0.8
-0.4
0.0
E-E
F
(eV)
200K
-1.2
-0.8
-0.4
0.0
E-E
F
(eV)
230K
Intensity (arb. units)

A

L

Temperature dependence of
the A
-
L cut of TiSe
2

L

L’

A

20K

100K

60K

200K

140K

230K

CDW occurs at 220K

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 E
f

Intensity (arb. units)

Intensity (arb. units)

A closer look of A & L

band folding

Edge 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~0.11)


“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
-
E
f

Intensity (arb. units)

-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

G

L

G

Temperature dependence of EDC

s @ L


How CDW disappear

x=0

x=0.065

1.
Charge neutrality is fulfilled

2.
Correlation plays an important role

3.
x=0.065 data make possible low temperature, and more precise picture

4.
100 meV raise of chemical potential

Se bands well below EF, while the
exciton binding energy is estimated before to be 17 meV

Conclusion

1T
-
TiSe
2

Excitonic CDW

Cu doping
increases.

Chemical Potential shift

Exciton formation costly

CDW opens gap at valence band not E
f


Copper doping increase carrier density

AT 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
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

灯楮琬 楴⁩猠
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