Noise- and microwave experiments in moving CDW, Wigner crystals and vortex lattice

Transcription

1 Carcassonne, France (9/26, 2002) Noise- and microwave experiments in moving CDW, Wigner crystals and vortex lattice Atsutaka MAEDA Dep. Basic Science, The Univ. Tokyo Outline 1) Dynamic Phase diagram of driven vortices In high-t c superconductors 2) Comparison between vortices and CDW spectrum dynamical coherence volume 3) Collective charge excitation in spin ladder (Sr,Ca) 1-x Cu 24 O 41 : CDW or Wigner crystal?

2 Collaborators Dynamic Phase diagram of driven vortices Y. Togawa Dep. Basic Science, UT (now at Tonomura group) H. Kitano Dep. Basic Science, UT T. Tsuboi Dep. Basic Science, UT (now at Agilent Technology) T. Hanaguri Dep. Adv. Material Res., UT Experiments in the spin ladder R. Inoue Dep. Basic Science, UT H. Kitano Dep. Basic Science, UT N. Motoyama Dep. Adv. Material Res., UT K. Kojima Dep. Adv. Material Res., UT S. Uchida Dep. Adv. Material Res., UT

3 <New concepts proposed in driven vortex system> f (=J B) plasticity dynamic reordering static channels reordered phase pinned lattice (Bragg glass) f c etc. KV transition A.E.Koshelev & V.M.Vinokur, PRL 73, 3580 (1994). phase transition f t or crossover Tpt f t PF 1 T T pt moving fluid phase [creep regime] T [plastic flow (PF)] H.J.Jensen et al., PRL 60, 1676 (1988). v exp 1 F 0 k B T F T.Nattermann & S.Scheidl, Adv. Phys. 49, 607 (2000). µ [moving-braggglass phase] [smectic phase] P.Le Doussal & T.Giamarchi, PRB 57, (1998). L. Balents et al., PRB 57, 7705 (1998). K. Moon et al., PRL 77, 2778 (1996).

4 KV transition in NbSe2 dynamic phase diagram of conventional type-ii SC (NbSe 2 ) S. Bhattacharya et al., PRL 70, 2617 (1993). I - V dv/di noise, pulse responce etc. plastic flow elastic flow KV transition 1 f t Tpt T pinned state Z. Xiao et al., PRL 85, 3265 (2000). KV transition coherent flow plastic flow pinned state HTSC (Bi2212, H // c) plastic flow local density noise (spatial correlation) T. Tsuboi et al., PRL 80, 4550 (1998). Lorentz microscopy A. Tonomura et al., Nature 397, 308(1999). coherent flow conduction noise (washboard noise) Y. Togawa et al., PRL 85, 3716 (2000).

5 <Experimental approach> monitoring temporal order of driven vortices 1. Noise measurement (I) conduction noise (CN) (II) local density noise (LDN) Sensitivity : V/ Hz 100 H // c-axis I + V + V FFT analyzer HP-35670A Bi 2 Sr 2 CaCu 2 O y 100 2DEG Hall probe array 2. Ac-dc interference study Sensitivity : G / Hz 500 I + I + I H // c-axis V + V Bi 2 Sr 2 CaCu 2 O y SRS 830 Lock-In Amplifier V V rf V ac Driving Force: I dc + I rf sin(w rf t) + I ac sin(w ac t) (I dc, I rf >> I ac )

6 << Significance of simultaneous noise measurements >> Local density noise : δb = φ 0 δn W.J.Yeh and Y.H. Kao, PRB 44, 360(1991). T.Tsuboi et al., PRL 80, 4550(1998). [ Driven vortex system ] density fluctuations (δn) & velocity fluctuations (δv) δv δe dl = (δb v + B δv) dl Conduction noise : J.R.Clem, Phys. Rep. 75, 1(1981). S.Bhattacharya & M.J.Higgins, PRL 70, 2617(1993). A.C.Marley et al., PRL 74, 3029(1995). G.D'Anna et al., PRL 75, 3521(1995). H.Safar et al., PRB 52, 6211(1995).

7 BB-δ n (µg 2 /Hz) (V 2 /Hz) J dc (A/cm 2 ) J dc (A/cm 2 ) H (Oe) J dc = 394 A/cm 2 J dc = 394 A/cm 2 f = 10 Hz T = 80 K Bi 2 Sr 2 CaCu 2 O y BB-δ n G 2 /Hz BB-δ n G 2 /Hz G 2 /Hz f = 10 Hz T = 80 K Bi 2 Sr 2 CaCu 2 O y V /Hz V 2 /Hz V 2 /Hz ρ onset 10-9 Ωcm V 2 /Hz BB-δ n V 2 /Hz H (Oe) H = 50.2 Oe (V 2 /Hz) velocity 80 K noise contour map H - swept 1.0 m/s F = J B J - swept Boundary of noise is independent of how to sweep in J-H plane H pt (0 A/cm 2 ) = 60 Oe Broadband noise appeared in vortex-solid regime and BB-δ n appeared in different field region Each BBN corresponds to different kind of vortex motion

8 BB-δ n noise power spectral density contour map T.Tsuboi et al., PRL 80, 4550 (1998). A.Maeda et al., PRB 65, (2002). H 2pk ρ 10-9 Ω cm H 2pk H pt BB-δ n appeared near resistivity onset BB-δ n appeares even in low-t regime where 2nd peak effect occurs. BB-δ n spatial correlation method channel-like plastic flow

9 Ac-dc Interference Effect of Vortices another technique to detect developement of temporal order H <v> Driving Force: I dc + I ac sin(w ac t) p f ac = q f w = q 1 a ρ j B = q 3 2 E φ 0 B 15 ma 100 A/cm 2 Bi 2 Sr 2 CaCu 2 O y 10 µω 21 ma Bi 2 Sr 2 CaCu 2 O y 10 µω I ac = 21 ma 18 ma 15 ma 18 ma 12 ma 9 ma dv / di (a.u.) 15 ma 12 ma 9 ma dv / di (a.u.) 1 3/2 2 5/2 3 5/2 3 6 ma 3 ma 0 ma 6 ma 3 ma f ac = 100 khz 1/2 f ac = 100 khz 0 ma H = 50.2 Oe T = 80 K H = 50.2 Oe T = 80 K I dc (ma) V (µv) temporal order of driven vortices develops in a certain field region in vortex-solid regime

10 BB-δ n (µg 2 /Hz) (V 2 /Hz) J dc (A/cm 2 ) J dc = 263 A/cm 2 J dc = 263 A/cm 2 Interference effect BB-δ n f = 10 Hz G 2 /Hz BB-δ n f = 10 Hz V 2 /Hz K noise contour map with appearence region of interference effect H = 50.2 Oe J dc = 263 A/cm 2 J ac = 98.5 A/cm (V 2 /Hz) 1000 khz dv/di (a.u.) 0 T = 80 K Bi 2 Sr 2 CaCu 2 O y ρ 10-9 Ω cm H pt 100 khz J ac = 0 A/cm 2 Interference effect H (Oe)

11 J dc (A/cm 2 ) J dc (A/cm 2 ) J dc (A/cm 2 ) Interference effect BB-δ n G 2 /Hz f = 10 Hz Bragg glass T = 80 K Bi 2 Sr 2 CaCu 2 O y ρ 10-9 Ω cm V 2 /Hz f = 10 Hz H (Oe) ρ 10-9 Ω cm Bragg glass T = 70 K Bi 2 Sr 2 CaCu 2 O y moving vortex fluid H (Oe) ρ 10-9 Ω cm Bragg glass T = 60 K Bi 2 Sr 2 CaCu 2 O y H pt BB- δ v f = 10 Hz V 2 /Hz Interference effec t Interference effec t H (Oe) moving vortex fluid H p t f = 10 Hz V 2 /Hz moving vortex fluid H pt 80 K 70 K 60 K J H T J - H plane, including results of noise contour, interference effect, resistivity, H pt (vortex-lattice phase transition field) With decreasing T, BB-δv becomes to appear after disappearance of interference effects BB-δv seems to appear when temporal order of coherent flow decreases.

12 H (Oe) H 2pk ρ 10-9 Ω cm H pt Bi 2 Sr 2 CaCu 2 O y J dc = 131 A/cm 2 moving vortex fluid J H T Bragg glass Interference effect T (K) T c 131 A/cm 2 <static phase diagram> H (Oe) H 2pk ρ 10-9 Ω cm Bragg glass H pt Interference effect Bi 2 Sr 2 CaCu 2 O y J dc = 263 A/cm 2 moving vortex fluid T (K) T c H (Oe) H 2pk 263 A/cm 2 Bragg glass Bi 2 Sr 2 CaCu 2 O y (#h4) vortex fluid H pt T c T (K) 400 H 2pk Bi 2 Sr 2 CaCu 2 O y J dc = 394 A/cm 2 H (Oe) ρ 10-9 Ω cm Bragg glass H pt moving vortex fluid Interference effect 394 A/cm T (K) T c

13 J dc (A/cm 2 ) J dc (A/cm 2 ) Bi 2 Sr 2 CaCu 2 O y H = 60 Oe Bragg glass T (K) ρ 10-9 Ω cm Bragg glass moving vortex fluid T (K) small Interference effect BB-δ n ρ onset ρ 10-9 Ω cm Interference effect 60 Oe Bi 2 Sr 2 CaCu 2 O y H = 100 Oe T pt moving vortex fluid T pt 100 Oe Interference effect J dc (A/cm 2 ) driving force J Bragg glass Interference Interference eff ect ρ 10-9 Ω cm H T 200 Oe Bi 2 Sr 2 CaCu 2 O y H = 200 Oe BB- δ v moving vortex fluid T pt T (K) large just below T pt plastic flow Bragg glass coherent flow flow with less coherence flow with almost no coherence moving vortex fluid

14 Dynamic phase diagram of driven vortices Bi decrease of coherent temporal order J Bi 2 Sr 2 CaCu 2 O y H = 100 Oe H J dc (A/cm 2 ) Ω cm ρ coherent flow plastic flow moving vortex fluid T Bragg glass Interference effect Simulation <Weak pinning> T pt T (K) C. J. Olson et al., PRL 81, 3757 (1998). private communication Driving current f d / f 0 transeversesolid flow coherent flow pinned state smectic flow Temperature plastic flow A v = 1

15 Dynamic phase diagram of driven vortices Bi decrease of coherent temporal order Bi 2 Sr 2 CaCu 2 O y H = 100 Oe J H J dc (A/cm 2 ) Ω cm ρ coherent flow plastic flow moving vortex fluid T NbSe 2 Bragg glass Interference effect T pt T (K) Z. Xiao et al., PRL 85, 3265 (2000). J dc (A/cm 2 ) coherent flow smectic J t J p plastic flow J c NbSe 2 H = 1.8 T moving vortex fluid KV transition 1 f t Tpt T 0 pinned state J * T m T (K) Phase boundary corresponding to KV transition is not found in the dynamic phase diagram of Bi2212.

16 Dynamic phase diagram of driven vortices P. Le Doussal &T. Giamarchi, PRB57, 11356(1998). present study H H?

17 Vortices in SC (2D) vs CDW (1D) Similarity vs difference 1) Coherent motion (washboard motion) in the so-called creep regime --elementary process of sliding motion-- 2) Deterioration of coherence with increasing driving force

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28 Deterioration of the coherence of dc driven vortices Contrary to theoretical predictions Similar phenomena in a CDW system, m-tas 3 (semiconducting) (Maeda et al. J. Phys. Soc. Jpn (1985) ) Also contrary to (a) Experiment in another CDW system NbSe 3 (metallic) (Thorne et al.) (b) Numerical simulation for 1dim CDW (Matsukawa et al.) --did not take account of plastic deformation Importance of plastic deformation for realistic description of the phenomena

29 [Driven Vortices] 2D driven sytem YBa 2 Cu 3 O y Bi 2 Sr 2 CaCu 2 O y Bi 2 Sr 2 CaCu 2 O y H = 50.2 O e T = 80 K w rf = 100 khz I rf = 21 ma 18 m A 15 m A E (µv/mm) J.M.Harris et al.,prl 74, 3684 (1995). [Sliding CDW] 1/2 1D driven system 1 3/2 2 5/ V (µv) 3 12 m A 9 m A 6 m A 3 m A 0 m A 10 µω main peak & harmonics sub-harmonics (1/2 series) 1/ /3 1/3 NbSe main peak & harmonics (perfect mode-locking) sub-harmonics (many series) R.P.Hall and A.Zettel,PRB 30, 2279 (1984).

30 Vortices in SC (2D) vs CDW (1D) Similarity vs difference 1) Coherent motion (washboard motion) in the so-called creep regime common to vortex and CDW --elementary process of sliding motion stick-slip like motion of phase kinks 2) Deterioration of coherence with increasing driving force Vortices in SC is less coherent than CDW difference in dimensionality?

31 Spin Ladder Sr 14-x Ca x Cu 24 O 41 Carrier doping in spin ladder structure expect superconductivity (E. Dagotto and T. M. Rice: PRB45 (1992) 5744) Sr substitution by isovalent Ca Insulator metallic (N. Motoyama et al.: PRB 55, R3386 (1997)) superconductivity in heavily doped crystal (M. Uehara et al.: JPSJ 65 (1996) 2764.) chains ladders Role Ca : charge transfer from chain to ladder (T. Osafune et al.: PRL 78, 1980 (1997))

32 Ohmic conductivity T (K) ( -1 cm -1 ) x(ca) = 12, c-axis x(ca) = 1, c-axis x(ca) = 0, c-axis x(ca) = 0, a-axis / T (1/K)

33 ladder / NLC in the ladder- and rung directions of Sr 14 Cu 24 O 41 rung Sr 14 Cu 24 O K 120 K 140 K 160 K c-axis E (V/cm) K 140 K 160 K Sr 14 Cu 24 O K 120 K 140 K 160 K a - axis ' / K 120 K 140 K 160 K / Electric Field (V/cm) Small increase ( σ ~ 3% at 10 V/cm) NLC starts between V/cm σ(e)/σ 0 was almost independent of T Electric Field (V/cm) Large increase ( σ ~ 20% at 5 V/cm) The existence of characteristic field is less clear σ(e)/σ 0 strongly depends on T The NLC was quite different between the two directions

34 Extra conductivity at microwaves Large dielectric constants at microwaves

35 5-500 µsec Duty 1/10-1/ msec a boxcar averager (SRS-SR250) and a digital oscilloscope (TDS420A) Local maximum around at 50 GHz (10 K) observed up to ~150 K single-particle resonance :unlikely (ω 0 <<T) collective

36 5 4 ( & ' % # "!.-*, The collective charge excitation in the ladder planes of Sr 14 Cu 24 O 41 (1) NQR (2) MW and nonlinear dc conductivity W & $ % 6 T (K) s s W a -1-1 ( cm ) 1 Conductivity ( -1 cm -1 ) 10 1 T = 10K / K 150 K 190 K E (Vcm -1 ) M. Takigawa et al. PRB 57, 1124 (1998). (3) Optical Response also nonlinear σ(e) ) *+ 321 * / Frequency (GHz) H. Kitano et al. EPL 56, 434 (2001). (4) Low-ω Dielectric Response also switching, Ramman sct. B. Gorshunov et al. cond-mat/ v2. G. Blumberg et al. Science 297, 584 (2002).

37 (1)A peak in σ 1 (ω) at ω 0 ω 0 <<T : collective origin (2) Nonlinear conduction (>E0) charge orderded state without lattice distortion (3) σ(e), σ(ω) only in the ladder direction * ee 2 0 m 0 (4) σ(e) : characteristic of low doped materials E V / cm / 2 50GHz 0 d Cu Cu m * m0 a collective mode characteristic of low dimensional correlated systems 4k F -CDW Wigner crystal

38 Conclusion (A) Experimental determination of dynamic phase diagram of driven vortices in a high-t c, BSCCO by a coupled study of density- and conduction noise, and ac-dc interference effect 1) Bragg glass plastic flow coherent flow less coherent flow incoherent flow moving vortex liquid 2) Different dynamic phase diagram from that of conventional NbSe 2 3) Different from expectation of numerical simulation 4) No phase boundary, corresponding to the K-V transition 5) characteristic: decrease of coherent temporal order in the high driving force region (B) Vortices and CDW: 2D vs 1D 1) dynamical coherence: better developed in the CDW 2) Similar elementary process (similarity in the spetctra) (C) Collective charge dynamics in the spin ladder 1) Scaling in the nonlinear conduction 2) Very small oscillator strength: similar to the SDW suggesting moving Wigner crystal in 1D