“Quantization” of The q-Vectors in Microcrystals of K0.3MoO3 and NbSe3.

S.G. ZybtsevV.Ya. Pokrovskii (pok@cplire.ru)S.V. Zaitsev-Zotov

The prehistory.

From: Borodin, D. V., Zaitsev-Zotov, S. V. & Nad’, F. Ya. Coherence of a charge density wave and phase slip in small samples of a quasi-one-dimensional conductor TaS3. Zh. Eksp. Teor. Fiz.

93, 1394-1409 (1987).

Temperature dependence of resistance for a TaS3 sample with dimensions 24 m×0.02 m2.

q(T) single PS events between discrete states of the CDW. The steps height correspond, on average, with the creation or annihilation of 2 electrons per conducting chain, as should be the case for a PS event. BUT no discrete states that varied regularly with temperature were observed; in addition, the steps varied in height.

eq

L L

Lack of coherence?Of tight boundary conditions?

K0.3MoO3 – the blue bronze. More coherent?

Microphotograhs of three BB samples with gold film ablated over it (the upper is the representative one). The scale-bar (common) corresponds to 20 m

Current dependence of differential resistance under RF irradiation for the representative sample. The peaks are the Shapiro stepsdemonstrating complete synchronization of the CDW sliding.

20 m

The hysteresis loop: regular discrete states.

S.G. Zybtsev, V.Ya. Pokrovskii & S.V. Zaitsev-Zotov. ‘ Quantized ’ states of the charge-density wave in microcrystals of K 0.3 MoO 3 . Nature. Commun. x:x doi: 10.1038/ ncomms1087 (2010).

Fragments of the temperature dependences of conduction for different samples. The sample dimensions are: 21×5×0.3 m3 (the representative one), 50×7×0.3 m3 (σ is multiplied by 1.5) and 10×5 m2 (σ is divided by 1.5).

Not just only fine pictures!

Counting and summing steps vs. T

One PS event: δq = 2π/L q(T)

Five steps are added to m as a fitting parameter

The q(T) dependence reconstructed from the steps distribution in T.

The wave vector variation in BB. δq/q change for the representative sample calculated from σ(T) ‘+’ – cooling in a wide temperature range, ‘*’ and ‘o’ – cooling and heating in the narrow temperature range. Inset: the Arrhenius plot of the same data together with the diffraction results [1] (‘squares’); the error-bars are also from [1].

1. Girault, S., Moudden, A. H., Pouget, J. P., & Godard, J. M. X-ray study of

vanadium-doped blue bronze. Phys. Rev. B 38, 7980-7984 (1988).

Relation between the steps’ position and height.

δq/(q − q(0)) = (δ/)coth2(ζ/T) ≈ δ/.Note that ( q − q (0)) / δ q is just the number of steps, m.m(T) = (σ/δσ)tanh2(ζ/T) ≈ σ/δσ.

δq/(q − q(0)) ≈ δ/.

The mobility found from the steps height: topical for NbSe3.

δσs=eδn =(2/L)e /s0

BB:Hall: at ~90 K  = 13 cm2/Vs [Forró, L et al., Phys. Rev. B 34, 9047-9050 (1986)] From δσs:  = 10 cm2/Vs – nice agreement

NbSe3: complex chain and band structure.Hall effect, transverse magnetoresistance,… - with 6 fitting parameters, 2-band

model. Large growth of carriers’ mobilities on type-I chains: at L-He >105 cm2/Vs

[N. P. Ong, Phys. Rev. B 18, 5272–5279 (1978)]. Nearly no progress since 1978 !

The principle advantage of the single-PS approach:Particular-band carriers are created or annihilated.

A.A. Sinchenko, R.V. Chernikov, A.A. Ivanov, P. Monceau, Th. Crozes, and S. Brazovskii, J. Phys.: Condens. Matter 21, 435601 (2009).

Characterisation of NbSe3

microsamples.

0.52 m× 0.055 m

E. Slot, M.A. Holst, H. S. J. van der Zant, and S. V. Zaitsev-Zotov, Phys. Rev. Lett. 93, 176602 (2004).

Et=56 mV/cm (120 K) 6 mV/cm (47 K)

ET=3 V/cmOptimal: 30–60 m × (24)10-2 m2

R(T) for NbSe3 microsamples.

The R(T) dependence for the Sample No 1 at low temperatures (L=35 m, R300=5.11 kΩ )

Example of (T) after subtracting a polynomial (sample No 5, L=33 m, R300=3.2 kΩ). The inset shows a similar presentation for the sample No 1.

The states fan out (diverge) at low temperatures δσ grows grows

typically 30 m × (24) 10-2 m2

R(T) for NbSe3 microsamples – “fans”.

20 25 30 35 40 45 50

-5

0

5

10

15

x 10-5

T (K)

-

P(T

) (

-1)

20 25 30 35 40 45 50-6

-4

-2

0

2

4

x 10-5

T (K)

-

P(T

) (

-1)

25 30 35 40 45 50 55

-1

-0.5

0

0.5

1

1.5x 10

-4

T (K)

-

P( T

) (

-1)

30 35 40 45

-8

-6

-4

-2

0

2

x 10-5

T (K)

T (

K)

Mobility of type-I carriers in NbSe3 .

0.01 0.02 0.03 0.04

10-5

10-4

10-3

10-2

1/T (K-1)

q/q

(0)-

1

q1(T) [1]

q2(T)

36 40 44 48

0

0.5

1

1.5

2

T (K)

q/q

q2(T) for NbSe3 .

q2(T) reconstructed from the steps distribution sample No 1 (). q1(T) from [1] (o). Inset: a fragment of q2(T) loop. [1]. A. H. Moudden et al., PRL 65, 223 (1990)

No diffraction data on q2(T) are available!

(T) found from δσ (6 samples are processed) and according to the Ong’s model (gray).

Surprisingly nice agreement!

The total q2 change is only ~10-4 in the range 20-50 K!

The upper CDW of NbSe3 - type III chains.

Normalized changes of in the range of the upper CDW state. Polynomials approximating the heating part of (T) are subtracted. The samples are: a) No 1, b) No 7 (L=50 m, R300=6.4 kΩ), c) No 8 (L=32 m, R300=4.2 kΩ).

Δσ/σ~10-3 Hysteresis~510-3

The upper CDW of NbSe3 - type III chains –the mobility

The heights of the jumps of conductivity (the left scale) and the corresponding values of mobility (the right scale) for the samples presented above.

The mobility is 400–600 cm2/Vs for all the 3 samples, with a tendency to grow with decreasing T

The q1 change is ~ 3–6×10-4. This appears several times smaller than the value reported in [A. H. Moudden, J. D. Axe, P. Monceau, and F. Levy, Phys. Rev. Lett. 65, 223 (1990).]. Why?...

Conclusions1.) BB shows jumps of conduction, regular in temperature – single PS events. The jumps correspond with transitions between discrete states of the CDW and reveal quantization of electrons’ wave vectors near the Fermi-vector.

2) Similar jumps of conduction can be resolved for NbSe3 for the lower CDW state; for the upper – near the limit of resolution.

3) Distribution of the jumps in T allows reconstruction of the q(T) dependences and its hysteresis. The resolution is comparable or exceeds that of the up-to-date diffraction techniques. For BB change of q down to 65 K and its hysteresis is observed. For NbSe3 the q2(T) dependence is found.

4) The value of δσ at a single PS gives for the quasiparticles created or annihilated. For BB is in agreement with the Hall-effect result. For NbSe3 δσ provides the only direct way for the measurement of . The fast growth at low T agrees with the Ong’s model (the pocket holes) and is even faster.

5) Further prospects: studies of fine effects in q change and mobilities of many-band Peierls conductors. Other-type compounds? SDW in Cr: rearrangements of the antiferromagnetic domain walls

Thank you! Merci!