Melted discommensuration in charge density waves

T. Matsuura1, J. Hara1, K. Inagaki2, M. Tsubota1, T. Hosokawa1, and S. Tanda1

1Hokkaido University, Sapporo, Japan

2Asahikawa Medical University, Asahikawa, Japan

Ecrys2014, 21st August

arXiv:1410.8689 [cond-mat.mes-hall]

http://arxiv.org/abs/1410.8689

Charge density wave in o-TaS3 systems

1. Aharonov-Bohm oscillation with current switching in CDW ring, M. Tsubota, et al., Europhys. Lett. 97, 57011 (2012).

2. Coexistence of incommensurate and commensurate CDWs, K. Inagaki, et al., J. Phys. Soc. Jpn. 77, 093708 (2008).

a = 36.804 Å b = 15.173 Å c = 3.34 Å

Orthorhombic unit cell of TaS3

C. Roucau, el al., Phys. Stat. Solidi A (1980)

• Peierls gap is fully opened at TP (218 K)

• Commensurate CDW (commensurability M = 4)

(Qc= 0.5a*, 0.125b*, 0.25c*)

A. H. Thompson, et al., PRB (1981)

Typical CDW

Introduction

con

du

ctiv

ity

1000/T

218 K

Synchrotron X-ray diffraction experiment for o-TaS3 crystal

0 200 400

0

0.05

0 200 400

50

100

0.96 1 1.040

10

20

30

0.96 1 1.04

d = 5c

z / c

d/d

z

d = 7c (ra

d)

kz / Qc

Fo

uri

er

Ma

g. (a

.u.)

Qc QicQc

2d / c

(a) (b)

(c) (d)

z

Edc < Eth

Edc > Eth

dc soliton flow(e)

Random DC

Regular DC

dc CDW bulk flow

Ith

K. Inagaki, et al., J. Phys. Soc. Jpn. 77, 093708 (2008).

Discommensurate CDW is hidden

Pinning state Sliding state

c-CDW

ic-CDW

c ic c ic

0.25c* 0.255c*

1. Coexisting of commensurate(c) and incommensurate(ic) CDWs 2. CDW current enhances ic-CDW

c-CDW

ic-CDW

Model

ic-CDW ⇒ Discommensurate CDW

Ith

Sliding state Pinning state

Qc= 0.25c*

Qic= 0.255c*

Sliding state Pinning state

Quantum interference of 2e charge soliton

M. Tsubota, et al., Europhys. Lett. 97, 57011 (2012).

M. Tsubota, et al., Physica B, 404, 416 (2009).

Aharonov-Bohm oscillation in CDW ring

o-TaS3 ring

h/2e oscillation

Purpose: To reexamine CDW dynamics on o-TaS3

Results: New-type spectrum was observed

Discussions: Soliton liquid model is proposed

Experiment: Ac-dc interference measurement on o-TaS3

Ac-dc interference measurement

Zettel, Gruner Solid. State. Commnun (1983) O. Hoffmann, et al., Phys. Rev. B9 3746(1974)

impurity

r = r 0 + rCDW sin(2kF x + )

V = Vdc + VRF sin(2pfRFt) V

The internal degrees of CDW must affect ac-dc interference spectrum

po

ten

tial

E=0

EET

Pinning

Sliding

one-particle model

a strong evidence of an electronic crystal sliding

Shapiro steps at ICDW = NefRF

Vdc

Dif

fere

nti

al r

esis

tan

ce d

V/d

I

−0.1 0 0.1 0.20

0.005

0.01

0.015

−1 0 10.005

0.01

0.015

Idc (mA)

dI/d

V (

S)

−0.2 0 0.20

0.005

0.01

0.015

−1 0 10.005

0.01

0.015

Idc(mA)

dI/

dV

(S

)

−1/1−2/1

1/12/1

fRF = 1 MHz

0 mV50 mV100 mV120 mV140 mV160 mV180 mV200 mV

Differential conductance under ac+dc voltages VRF dependence

Some samples show strange ac-dc interference peaks!

1st Shapiro

? ?

Temperature dependence

• Two probe measurement with gold film contacts

• Cross section: 16 x 7 μm2 • Length: 110 μm

• dI/dV was measured using Lock-in

Amplifier technique with low-frequency ac current of 13 Hz.

o-TaS3 whisker sample

Results 1

−0.4 −0.2 0 0.2 0.4

0 100 2000

0.2

0.4

0 2 4

Idc (mA)

dI/

dV

[r

ela

tive]

5MHz3.5MHz2.7MHz2.1MHz1MHz

VRF = 200 mV

50 mS

Ha

lf o

f cu

rre

nt in

terv

al

be

twe

en

pe

aks (

mA

)

VRF (mV) fRF (MHz)

(a)

(b) (c)

−1/11/1

new peak

1/1 Shapiro peak

new peak1/1 Shapiro peak

Frequency (fRF) dependence

integer): chains, ofnumber the:(

2RFNBN

CDW

nN

nffeN

I↑ (Black) peaks

New ac-dc interference effects! ↑ (Red) peaks

⇒Normal Shapiro peaks

0 100 2000

0.1

0.2

0 2 4

(I(+

)C

DW

− I

(−)

CD

W)/

2 (

mA

)

VRF (mV) fRF (MHz)

(a) (b)

new peak

1st Shapiro peak

new peak

1st Shapiro peak

Differential conductance under ac+dc voltages Results 2

T-dependence of the ac –dc interference

0.48

0.5

0.52

0.54

0.16

0.18

0.03

0.04

−2e−05 0 2e−050.006

0.007

0.008

0.009

dI/d

V (

mS

)Idc (A)

VRF = 600 mV, fRF = 1 MHz

T = 150 K

T = 100 K

T = 80 K

T = 60 K

Different sample

Inhomogeneous CDW current?

Inhomogeneous CDW current may make split of threshold field and Shapiro peaks… • However, they must follow the Shapiro step

manners. • No dip of differential conductance on the zero

bias peak.

New ac-dc interference peaks must originate from hidden internal degrees of freedom of CDW!!

Yu. I. Latyshev, et al., JETP Lett. 46, 10 (1987)

v1

v2

Discussions

Inhomogeneous current is not the origin of new ac-dc interference peaks!

1st Shapiro

Mixed Density Wave Model

CDW

SDW

r

r

r

r

totr

totr

CDW+SDW

mSDW ~ m0

mCDW ~ 1000 m0

CDW+SDW

State

CDW State CDW State

mSDW < mMDW < mCDW

c-CDW

ic-CDW

Pinning state Sliding state

Return to discommensuration model

0 100 2000

0.2

0.4

30

40

50

60

−1

0

1

Position z

r(z

,(z

))

(z

)

d/d

z

),(sin),( 0 tzzQtz C rr *25.0 cQC

Pinning state Sliding state

c-CDW

ic-CDW

c ic c ic

0.25c* 0.255c*

ic-CDW ⇒ Discommensurate CDW

K. Inagaki, et al., J. Phys. Soc. Jpn. 77, 093708 (2008).

Soliton solution

Phase dynamics equation (sine-Gordon equation)

Fourier transform reproduce the split diffraction??

2p/M

0 200 400

0

0.05

0 200 400

50

100

0.96 1 1.040

10

20

30

0.96 1 1.04

d = 5c

z / c

d/d

z

d = 7c (ra

d)

kz / Qc

Fo

uri

er

Ma

g. (a

.u.)

Qc QicQc

2d / c

(a) (b)

(c) (d)

z

Edc < Eth

Edc > Eth

dc soliton flow(e)

Random DC

Regular DC

dc CDW bulk flow

Soliton lattice

Solitons liquid ←Peaks appear at

Fourier transform of Soliton lattice

A 2p soliton exists in 50 CDW

K. Inagaki, JPSJ (2008).

ΔQ

C=2p/QC : wavelength of c-CDW

←Peaks appear at

Qic+nΔQ [ΔQ = M(Qic-Qc)]

Mph / gMvd

Qic

ΔQ

0 200 400

0

0.05

0 200 400

50

100

0.96 1 1.040

10

20

30

0.96 1 1.04

d = 5c

z / c

d/d

z

d = 7c (ra

d)

kz / Qc

Fo

uri

er

Ma

g. (a

.u.)

Qc QicQc

2d / c

(a) (b)

(c) (d)

z

Edc < Eth

Edc > Eth

dc soliton flow(e)

Random DC

Regular DC

dc CDW bulk flow

2p soliton liquid reproduces the ic-c CDWs diffraction peaks

Soliton lattice

Solitons liquid ←Peaks appear at

←Qic and Qc peaks remain, if M = 1

Fourier transform of Soliton liquid

A 2p soliton exists in 50 CDW

K. Inagaki, JPSJ (2008).

ΔQ

C=2p/QC : wavelength of c-CDW

Mph / gMvd

←Peaks appear at

Qic+nΔQ [ΔQ = M(Qic-Qc)]

ΔQ

Reinterpretation of CDW in o-TaS3 K. Inagaki, et al., J. Phys. Soc. Jpn. 77, 093708 (2008).

• A 2p soliton exists in 50 C • Randomness ∝ d-1

0 200 400

0

2

4

0.95 1 1.05

0

2

4

d/d

z

FF

T m

ag

nitu

de

z/C kz/QC

c ic

Ic-CDW to c-CDW ⇒ Decreasing of Soliton width d [ d=vph/gM

0.5 and gM∝ r0 ]

Sliding of 2p solitons in o-TaS3 Numerical calculation with solitons

M = 1

A 2p soliton exists in 50 C

Ith

K. Inagaki, et al., J. Phys. Soc. Jpn. 77, 093708 (2008).

K. Inagaki, et al., (2008).

The one-dimensional soliton liquid model reproduces the current-induced enhancement of ic-CDW!

• Soliton width d decreases when CDW sliding current increases ⇒ ic-CDW

Ith

Sliding state Pinning state

… So the soliton liquid model can explain the new ac-dc interference peaks?

1st Shapiro

? ?

1st Shapiro

? ?

IV characteristics is calculated from the SG equation

)(),(sin impCPimp zztzzQgF M = 1 Local impurity potential

0 100 2000

0.2

0.4

30

40

50

60

−1

0

1

Position z

r(z

,(z

))

(z

)

d/d

z

Effects of solitons and impurities are investigated

E=Edc E=Edc+ERF sin(2pfRFt)

ERF=2

IV characteristics with/without solitons and impurities

No soliton No impurity

No soliton With impurities

With solitons No impurity

With solitons With impurities

)(),(sin impCPimp zztzzQgF M = 1 Local impurity potential

Soliton flow state under RF voltage

• Pinning state (Edc < ES1): Both soliton and CDW do not contribute dc conduction

• Soliton flow state (ES1 < Edc < ES2) : Solitons are depinned and contribute dc conduction

• Sliding state (ES2 < Edc ) : Soliton and CDW contribute dc conduction

With solitons With impurities

E=Edc+ERF sin(2pfRFt) ERF=2

Conclusion

• New type of ac-dc interference peaks is observed in o-TaS3 whiskers.

• One-dimensional soliton liquid model provides a possible explanation of the experimental results.

Thank you for your attention!

Also the model is consistent with the AB oscillation in CDW rings