1. Hall effect in pinned and sliding states of NbSe 3 A. Sinchenko, R. Chernikov, A. Ivanov MEPhI, Moscow P. Monceau, Th. Crozes Institut Neel, CNRS, Grenoble

2. Outline 1.Hall effect in CDW compounds. Motivation of studying of NbSe 3. 2.Hall effect in NbSe 3 at low longitudinal electric field E<E t. Comparison with magnetoresistance. Two band model problems. 3.Hall effect in NbSe 3 in sliding state of CDW. Hole and electron pockets: what is the difference? 4.Conclusion

3. Hall effect in NbSe 3 (E<E t ) NbSe 3 in the Pierlse state –– semimetal ground state because small electron and hole pockets in the Fermi surface main contribution to the Hall effect from pockets carriers Hall voltage is quite unusual in NbSe 3 below T p2 =59 K - strong non-linear magnetic field dependence which drives the Hall voltage through a negative minimum and then positive at higher fields. -Monceau and Ong (1978) reported that the zero-field-limit Hall constant 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 difference in population (n p -n n )= 310 18 cm -3 below T p2. R.V. Coleman, et al, PRB, 1990 What is correct?

4. Hall effect in the compounds with a CDW. (E>E t ) Does CDW give contribution to the Hall voltage? TaS 3 S. Artemenko, et al, JETP Lett., 1984 K 0.3 MoO 3 L. Forro, et. al, PRB, 1986 CDW itself does not give contribution to the Hall voltage. Non linear Hall voltage is result of normal metal Explanation – CDW itself does not give contribution to the Hall voltage. Non linear Hall voltage is result of normal metal “back-flow” (S. Artemenko and F. Kruglov, (Sov. Phys. Solid State, 1984)

5. Hall effect in NbSe 3 (E>E t ) NbSe 3 – G.X. Tesseme and N.P. Ong – CDW motion gives no visible contribution to the Hall effect. (PRB, 1981) Where is back-flow? “Back-flow” model predicts reduction of V H also in NbSe 3 especially at the temperatures close to T p.

6. Experimental 1.Evaporation of gold contacts to the opposite faces of crystal 2. Preparation of Hall probes from the crystal itself Two types of structure: In both cases the change in voltage on the Hall pairs of contacts [V 1,3 (+B)-V 1,3 (-B)]/2 or [V 2,4 (+B)-V 2,4 (-B)]/2 was taken to be equal to the Hall voltage, V H, and the sum [V 1,3 (+B)+V 1,3 (-B)]/2 or [V 2,4 (+B)+V 2,4 (-B)]/2 was taken as a longitudinal drop of voltage.

7. Experimental results (E<E t ) At low electric field (E<<E t ) the Hall voltage is linear function of current. CDW does not give the contribution to the electric transport. R H =V H /I R H is strongly magnetic field dependent and demonstrates the reversal of the Hall constant sign at all temperatures 5K 35K

8. Comparison with magnetoresistance maximum dR/dB at B=B 0 B<B 0 MR ~ B 2 B>B 0 MR ~ B

9. Comparison with magnetoresistance B 0 =B zc ? Electron and hole pockets demonstrate quite different behavior in magnetic field: electrons: MR~B 2 holes: MR~B

10. MR~B 2 - usual MR~B - unusual Quantum linear magnetoresistance ? Conditions (Abrikosov, 1999): In the case NbSe 3 n ~10 17 cm -3 and m*~ 10 -2 m e Two band model: n ~10 18 cm -3 and m*=0.24m e heavy electrons Correlation with ARPES data (J. Schafer et al, PRL, 2003) NbSe 3 – 3 types of chains 1 – high -T CDW 2 - low - T CDW 3 - ? + small hole pockets because non-perfect nesting of low-T CDW (m*~ 10 -2 m e )

11. Experimental results (E>E t ) A first step – what is the E t (B) dependence? Threshold electric field is practically Independent on magnetic field at T>25 K. 30 K Experimental results – above 25 K

12. 30 K First type of Hall contacts (evaporated) Second type of Hall contacts (litography) 1. Field generation model – CDW generates normal carriers 2. 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.

13. To make this effect more pronounce, we determine the difference δV H =V H -V lin The last term is the linear Hall voltage dependence observed at low electric field below the threshold. 30 K Below E t – visible deviation of the Hall voltage from linear dependence. Position of this deviations coincides with corresponding singularities in IV-curve. Most probably – this effect is attributed by the local CDW deformations.

14. Temperarure evolution Deviation of the Hall voltage from linear `dependence decreases with the temperature increase. δ V H =A·exp(-T/T 0 ) T 0 =3.4 K

15. conclusion 1. Hall voltage, V H, changes sign in a wide temperature range and the magnetic field for which V H 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 T p2, 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 E t. Thanks to S. Brazovskii and Yu. Latyshev Thanks to S. Brazovskii and Yu. Latyshev