Understanding the I-V Characteristics of CDW Conductors

2. A Brief History of LinesThe I-V Characteristics of CDW Conductors

3. A Brief History of LinesThe I-V Characteristics of CDW Conductors Robert Thorne Cornell University

4. Conclusions • The humble I-V measurement is an extremely powerful probe of CDW physics. But . . .

5. Conclusions • The humble I-V measurement is an extremely powerful probe of CDW physics. But . . . • Measuring the intrinsic properties of the collective sliding state is much harder than in single-particle transport systems.

6. Conclusions • The humble I-V measurement is an extremely powerful probe of CDW physics. But . . . • Measuring the intrinsic properties of the collective sliding state is much harder than in single-particle transport systems. • Many interesting ideas have been proposed by theorists to explain CDW I-V characteristics. But . . .

7. Conclusions • The humble I-V measurement is an extremely powerful probe of CDW physics. But . . . • Measuring the intrinsic properties of the collective sliding state is much harder than in single-particle transport systems. • Many interesting ideas have been proposed by theorists to explain CDW I-V characteristics. But . . . • None of these theories reproduce even the most basic experimental features.

10. Monceau, Ong, Portis, Meerschaut & Rouxel, 1976 Gcdw(E) = G exp (-E0/E)

11. Ong, Brill, Eckert, Savage, Khanna & Somoano, 1979 E0  RRR-2  ni2

12. Fleming & Grimes, 1979

14. GCDW(E) = G[(E-ET)/E] exp (-E0/E), E>ET

15. Modified Zener form provides excellent fit but: • E0 ~ 2 ET for all T • E/E0 ~ 1 100 for E/ET ~ 2  200 • exp (-E0/E) ~ 0.37 to 0.99  Tunneling probability is always close to 1 in region where fit works !! ??

16. Asymptotic behavior of G(E) as E? Sneddon, Cross & Fisher 1982 FLR model: GCDW (E) = G – CE-1/2

17. SCF: GCDW(E) = G – CE-1/2 Zener: GCDW(E) = G – C/E SCF

18. Behavior as EET? • Depinning of an elastic CDW is a dynamic critical phenomenon. • CDW correlation length diverges as reduced field f = (E- ET) /ET  0 ICDW(f)  vCDW(f) = f, =3/2 (Mean field)

19. Monceau, Renard, Richard, Saint Lager, Wang, 1985:  = 1.3 – 2.3 in TaS3Gill, 1985:  ~ 1.5 in NbSe3  >2 in TaS3

20.  =1.24 in TaS3  =1.16 in 3D

21. Are You Measuring the CDW’s Intrinsic Behavior? • CDW current is longitudinally inhomogeneous due to phase slip at current contacts • Perform measurements with large current contact separation, at T where phase slip length is short. Adelman 1995 Lemay 1998

22. Borodin, Nad, Savitskaja, Zaitsev-Zotov, 1996 Yetman & Gill, 1987 ET ET  A-1/2 Cross-section A

23. McCarten et al., 1989 ET 1/thickness in ordinary size NbSe3 crystals

24. v2 v1 2 1 CDW current is transversely inhomogeneous due to (a) current injection from side contacts or(b) CDW shear from thickness steps and inhomo- geneous pinning Maher et al., 1992

25. dV/dI E dV/dI E Behavior of “perfect” samples: = 1.09

26. Problems with “Critical” Interpretation of I-V Exponent = 1.09 in cleanest measurements Fits from f = 0.1 to 10 • How wide is critical regime? (For ordinary critical phenomena, f << 0.1) • What is the role of finite size effects?

27.  = 5/6 = 0.83 3D 2/3 = 0.66 2D 1/2 = 0.5 1D • Middleton, Myers (Ph.D. Theses) (1992): • Bulk critical regime extends only to f ~ 0.1 • In experimental sample sizes, scaling eliminated • or limited to < 1 decade.

28. Simulation: Experiment:

29. Balents and M. Fisher (1995) • convective term added to FLR • Plastic to elastic transition Marchetti, Balents, Radzihovski, Middleton, Natterman, Vinokur . . . (1996-2005) • plasticity, thermal creep and visco-elastic behavior (One) Predicted Phase Diagram for Driven CDWs:

30. Balents and M. Fisher (1995) • convective term added to FLR • Plastic to elastic transition Marchetti, Balents, Radzihovski, Middleton, Natterman, Vinokur (1996-2000) • plasticity, thermal creep and viscoelastic behavior (One) Predicted Phase Diagram for Driven CDWs:

31. The Elephant Under the Carpet: Zettl & Gruner, 1982 Fleming et al., 1986 I 1/T

32. The Elephant Under the Carpet: Mihaly et. al,, 1987 Itkis & Nad, 1991 ET ET* Littlewood, 1988, 1989: Due to freeze-out of single particles

33. The Elephant Under the Carpet: Adelman et al., 1993Metallic NbSe3 shows the same behavior! ET, ET*  1/thickness

34. The Elephant Under the Carpet: • In all sliding CDW & SDW materials (partially and fully gapped): • For T>2TP/3: • CDW depins at ET, ICDW(E>ET) increases smoothly • ET = collective pinning threshold • thermal rounding negligible except near TP; • fully coherent collective response above ET •  negligible plasticity • For T< 2TP/3: • ET evolves smoothly, but conduction above ET freezes out • For T<TP/2: • ET still well defined, but abrupt transition appears at ET*

35. The Elephant Under the Carpet: In all sliding CDW & SDW materials (partially and fully gapped): The zero-temperature classical elastic models studied to date only “reproduce” the most qualitative features of the CDW I-V characteristic at high temperatures. Finite temperature and plastic models do not predict the measured behavior at any T. (Except perhaps within 1K of TP?)

36. “A New Kind of Science” by Stephen Wolfram Reviewed by Steven Weinberg, New York Review of Books “Wolfram himself is a lapsed elementary particle physicist, and I suppose he can't resist trying to apply his experience with digital computer programs to the laws of nature. This has led him to the view . . . that nature is discrete rather than continuous. . . . he concludes that the universe itself would then be an automaton, like a giant computer.” “It's possible, but I can't see any motivation for these speculations, except that this is the sort of system that Wolfram and others have become used to in their work on computers. So might a carpenter, looking at the moon, suppose that it is made of wood.”

37. ICDW(E) v(E) between ET and ET* Lemay et al., 1999 Creep-like conduction exists in a regime where narrow-band “noise” is highly coherent.  creep is coherent and collective Fits: v(E,T) = 0(E-ET) exp[-T0/T] exp[(E-ET)/T]

38. Coherent Creep between ET and ET* in Pure, Ta and Ti-Doped NbSe3 Cicak et al., 2002 Fit: v(E) = v0 (E-ET) exp [-T0/T ] exp[ (E-ET)/T] T0 =54060 K =1.3  single-particle barrier

39. Eb Explaining the Elephant Larkin and Brazovskii 1994-1996; Abe 1984; Zaitsev-Zotov 1997; FLR 1979; Zawadowski 1985; Tucker 1988; Baldea 1996 Two types of pinning: 1. Local pinning (strong) • Impurity interaction energy vs CDW phase hysteretic; produces finite average force per impurity as CDW phase advances • ETlocal, strong ni,strong • Energy scale ~ , length scale ~ 

40. Explaining the Elephant Two types of pinning: 1. Local pinning ETlocal, strong ni,strong Energy scale ~ , length scale ~  2. Collective pinning ETcol ni2 (3d) Energy scale ~ 105, length scale ~ 10 m (~ 104 )

41. At high temperatures (2TP/3 < T < TP): • Local pinning barriers easily overcome • Elastic collective pinning theory should describe observed v(E), I(V) At low temperatures (T < TP/2): • strong local pinning barriers become important • v(E,T) exhibits creep-like field dependence • characteristic activation energies ~ DW gap 

42. Phase diagram for driven screened DW T T=0: coherent collective sliding pinned E ETcollective  ni2 (3D)  ni/t (2D) ETtot = f(local, collective pinning)

43. Finite, Low T: T Incoherent collective creep L ~ L Epincol ~ 106 ~ 108 T glassy, diverging barriers vcreep < 10-5Å/s E ETcollective ETtot

44. Finite, Low T: T Incoherent collective creep L ~ L~ 10 m Ebcol ~ 106 ~ 108 T diverging barriers vcreep < 10-5Å/s Coherent collective “creep” coherent sliding limited by thermal activation over local pinning barriers L ~ hvF/ ~ 10Å Ebloc ~  finite barriers vcreep ~ 103Å/s E ETcollective ETtot

45. Finite, Low T: T Incoherent collective creep L ~ Llarkin ~ 1 m Ebcol ~ 106 ~ 108 T diverging barriers vcreep < 10-5Å/s Coherent collective “creep” coherent sliding limited by thermal activation over local barriers L ~ hvF/ ~ 10Å Ebloc ~  finite barriers vcreep < 104Å/s coherent collective sliding v >108Å/s E ETcollective ETtot

46. Finite, Low T: T First order dynamic transition Incoherent collective creep Coherent collective sliding Coherent collective motion limited by local creep E ETcollective ETtot

47. T<TP T Incoherent collective creep Coherent collective sliding Critical point Coherent collective sliding Coherent collective “creep” E ETcollective ETtot

48. Conclusions • The humble I-V measurement is an extremely powerful probe of CDW physics. But . . . • Measuring the intrinsic properties of the collective sliding state is much harder than in single-particle transport systems. • Many interesting ideas have been proposed by theorists to explain CDW I-V characteristics. But . . . • None of these theories reproduce even the most basic experimental features.

49. Questions • How general is detailed behavior observed in NbSe3? • Can experiments observe any signatures of dynamic critical behavior • What is the correct explanation for the asymptotic high-field behavior? • What is the correct explanation of v(E,T) in the coherent creep region? • What are the relevant local barriers? • What is the nature of the transition atET*? • What is the role of descreening in fully gapped density wave materials? Effect of descreening on critical behavior?