Hall effect in pinned and Hall effect in pinned and sliding states of NbSesliding states of NbSe33

A. A. SinchenkoSinchenko, , R.R. ChernikovChernikov, A. Ivanov, A. IvanovMEPhI, MoscowMEPhI, Moscow

P. Monceau, Th. CrozesP. Monceau, Th. CrozesInstitut Neel, CNRS, GrenobleInstitut Neel, CNRS, Grenoble

OutlineOutline1.1. Hall effect in CDW compounds. Motivation of studying Hall effect in CDW compounds. Motivation of studying

of NbSeof NbSe33..

2.2. Hall effect in NbSeHall effect in NbSe33 at low longitudinal electric field at low longitudinal electric field EE<<EEtt. Comparison with magnetoresistance. Two band . Comparison with magnetoresistance. Two band model problems.model problems.

3.3. Hall effect in NbSeHall effect in NbSe3 3 in sliding state of CDW. Hole and in sliding state of CDW. Hole and electron pockets: what is the difference?electron pockets: what is the difference?

4.4. ConclusionConclusion

Hall effect in NbSeHall effect in NbSe33 ( (EE<<EEtt))NbSeNbSe33 in the Pierlse state –– semimetal ground state because small electron in the Pierlse state –– semimetal ground state because small electron andand hole pockets in the Fermi surface main contribution to the Hall hole pockets in the Fermi surface main contribution to the Hall

effect from pockets carrierseffect from pockets carriersHall voltage is quite unusual in NbSeHall voltage is quite unusual in NbSe33 below T below Tp2p2=59 K=59 K - strong non-linear magnetic field dependence which drives the Hall voltage - strong non-linear magnetic field dependence which drives the Hall voltage

through a negative minimum and then positive at higher fields.through a negative minimum and then positive at higher fields. - Monceau and Ong (1978) reported that the zero-field-limit Hall constant Monceau and Ong (1978) reported that the zero-field-limit Hall constant

changes sign from n-type to p-type at 15 K. changes sign from n-type to p-type at 15 K. - Explanation in the frame of a two-band model (Ong 1978) in which the Explanation in the frame of a two-band model (Ong 1978) in which the

difference in population (ndifference in population (npp-n-nnn)= 310)= 3101818 cm cm-3-3 below T below Tp2p2..

R.V. Coleman, et al, PRB, 1990

What is correct?

Hall effect in the compounds with a CDW.Hall effect in the compounds with a CDW. ( (EE>>EEtt))

Does CDW give contribution to the Hall voltage?Does CDW give contribution to the Hall voltage?

TaS3

S. Artemenko, et al, JETP Lett., 1984

K0.3MoO3

L. Forro, et. al, PRB, 1986

Explanation – CDW itself does not give contribution to the Hall voltage. CDW itself does not give contribution to the Hall voltage. Non linear Hall voltage is result of normal metal Non linear Hall voltage is result of normal metal “back-flow” (S. Artemenko and F. Kruglov, (Sov. Phys. Solid State, 1984)

Hall effect in NbSeHall effect in NbSe33

( (EE>>EEtt))

NbSeNbSe33 – G.X. Tesseme and N.P. Ong – CDW motion gives – G.X. Tesseme and N.P. Ong – CDW motion gives

no visible contribution to the Hall effect. (PRB, 1981)no visible contribution to the Hall effect. (PRB, 1981)

Where is back-flow?

“Back-flow” model predictsreduction of VH also in NbSe3 especially at the temperatures close to Tp.

ExperimentalExperimental

1. Evaporation of gold contactsto the opposite faces of crystal

2. Preparation of Hall probesfrom the crystal itself

Two types of structure:

In both cases the change in voltage on the Hall pairs of contacts[V1,3(+B)-V1,3(-B)]/2 or [V2,4(+B)-V2,4(-B)]/2 wastaken to be equal to the Hall voltage, VH, and the sum[V1,3(+B)+V1,3(-B)]/2 or [V2,4(+B)+V2,4(-B)]/2 wastaken as a longitudinal drop of voltage.

Experimental results (Experimental results (EE<<EEtt))

At low electric field (E<<Et) the Hall voltage is linear function of current.CDW does not give the contribution to theelectric transport. RH=VH/I

RH is strongly magnetic field dependent and demonstrates the reversal of the Hallconstant sign at all temperatures

5K

35K

Comparison with magnetoresistanceComparison with magnetoresistance

maximum dR/dB

at B=B0

B<B0 MR ~ B2

B>B0 MR ~ B

Comparison with magnetoresistanceComparison with magnetoresistance

B0=Bzc ?

Electron and hole pockets demonstrate quite different behavior in magnetic field:

electrons: MR~B2

holes: MR~B

MR~B2 - usualMR~B - unusual Quantum linear magnetoresistance ?

2/3

c

eHne cm

eHT

*

Conditions (Abrikosov, 1999):

In the case NbSe3 n ~1017cm-3 and m*~ 10-2me

Two band model: n ~1018cm-3 and m*=0.24me

heavy electrons

Correlation with ARPES data(J. Schafer et al, PRL, 2003)

NbSe3 – 3 types of chains1 – high -T CDW2 - low - T CDW3 - ?

+ small hole pockets because non-perfect nesting oflow-T CDW (m*~ 10-2me)

Experimental results (Experimental results (EE>>EEtt))

A first step – what is the Et(B) dependence?

Threshold electric field is practicallyIndependent on magnetic field at T>25 K.

30 K

Experimental results – above 25 K

30 K

First type of Hall contacts(evaporated)

Second type of Hall contacts(litography)

1. Field generation model – CDW generates normal carriers2. CDW motion deforms electron or hole pockets.3. “back-flow” model if CDW interacts with one type of carriers only (with light holes?).

Three possibility to explain:

In both cases – strong influence of CDW motion on the Hall voltage.

To make this effect more pronounce, we determine the difference

δVH=VH-Vlin

The last term is the linear Hall voltage dependence observed at low electric field below the threshold.

30 K

Below Et – visible deviation of the Hall voltage from linear dependence.Position of this deviations coincides with corresponding singularities inIV-curve. Most probably – this effect is attributed by the local CDW deformations.

Temperarure evolutionTemperarure evolution

Deviation of the Hall voltage from linear `dependence decreases with the temperature increase.

δ VH=A·exp(-T/T0)

T0=3.4 K

conclusionconclusion1. Hall voltage, VH, changes sign in a wide temperature range and the magnetic field for which VH crosses zero is temperature dependent. The two band model needs corrections.2. Electron and hole pockets demonstrate qualitatively different magnetoresistance behavior. 3. in high magnetic field the CDW motion changes significantly the Hall voltage at all temperatures below Tp2, that can not be explained in the frame of "back-flow" model. 4. Our results indicate that the CDW in the sliding state interacts differently with electrons and holes leading strong change in the normal carriers concentration at Et.

Thanks to S. Brazovskii and Yu. LatyshevThanks to S. Brazovskii and Yu. Latyshev