Magnetic-field-tuned superconductor-insulator transition in underdoped La 2-x Sr x CuO 4

Transcription

1 Magnetic-field-tuned superconductor-insulator transition in underdoped La 2-x Sr x CuO 4 Dragana Popović National High Magnetic Field Laboratory Florida State University, Tallahassee, FL, USA Collaborators at NHMFL: X. Shi (now at Sandia National Labs, USA) P.V. Lin V. Dobrosavljević Samples: A. Bollinger & I. Božović (Brookhaven Nat l Lab, USA) T. Sasagawa (Tokyo Institute of Technology, Japan) Funding: NSF grants (DMR ; DMR ) NHMFL (NSF and the State of Florida)

2 Effects of magnetic field in cuprates Questions: o Zero-temperature H-field-driven superconductor-insulator transition (SIT) in 2D? Quantum criticality? (scaling) o o (See Conductor-Insulator Quantum Phase Transitions, ed. by Dobrosavljević, Trivedi, Valles; Oxford University Press, 2012, for review and open questions) Nature of the field-induced resistive state? Interplay of quantum criticality and vortex matter physics? Experiments: o Magnetoresistance over a wide range of H and T (down to 0.09 K) o Low-T c La 2-x Sr x CuO 4 samples grown using different methods Conclusions: o Three distinct phases as T 0: H-field-driven SIT not direct

3 Temperature dependence of the in-plane resistivity in underdoped La 2-x Sr x CuO 4 (mid-point) T c =20 K ρ ab vs. T; down to 0.7 K [Y. Ando et al., Phys. Rev. Lett. 75, 4662 (1995); also, Steiner et al., Phys. Rev. Lett. 94, (2005)]

4 Type II superconductors in a magnetic field Reviews: Blatter et al., Rev. Mod. Phys. 66, 1125 (1994); Rosenstein et al., Rev. Mod. Phys. 82, 109 (2010); LeDoussal, Int. J. Mod. Phys. B 24, 3855 (2010) Mean-field picture: With disorder (M.P.A. Fisher etc.) Thermal fluctuations: vortex glass Vortex glass (VG): T g =0; superconductor only at T=0

5 H-T phase diagram of vortex matter Bi 2 Sr 2 CaCu 2 O 8+δ Vortex glass: topologically disordered, amorphous Bragg glass: a distorted, but topologically ordered lattice; many metastable states [Beidenkopf et al., Phys. Rev. Lett. 98, (2007)]

6 H-T phase diagram of vortex matter La 1.9 Sr 0.1 CuO 4 (mid-point T c =29 K) [Divakar et al., PRL 92, (2004)] Superconductor-insulator transition: VG insulator at high H M.P.A. Fisher, PRL 1990; etc.: Quantum phase transition in disordered 2D superconductors: driven by delocalization and Bose condensation of field-induced vortices Scaling: ρ(t,h)=ρ c f(t/t*) Also in conventional superconductors, e.g. NbSe 2 [G. Li et al., Phys. Rev. Lett. 96, (2006)]

7 a) MBE-grown film (100 nm) x=0.07 (Δx=0.01) Zero-resistance T c (H=0) = (3.8±0.1) K 1000Å LSCO film c axis LaSrAlO substrate Our La 2-x Sr x CuO 4 samples Ohmic regime, current densities as low as ( ) A/cm 2 Four different cryostats/magnets (up to 35 T); extremely slow sweep rates: T/min b) single crystal - x=0.06 (La 2-x Sr x CuO 4+y ) - bar shaped 3.02 x 0.42 x 0.34 mm 3 for in-plane ρ measurements Zero-resistance T c (H=0) = (5.2±0.1) K

8 In-plane ρ(t) in x=0.07 LSCO film for different H c T max (H) R =ρ/d, R /layer =ρ/l, d sample thickness; d = nl ; n - # of layers; l = 6.6 Å thickness of one layer Decrease of T c with H: T c (H) 0 for H 4 T T c (H) 0 pinning of vortices by disorder

9 Determination of the zero-resistance T c (H) in x=0.07 LSCO film T max T c (H) Zero-resistance field at a given T: the field where the resistivity is smaller than the noise floor T c (H) Phenomenological fits: H(T)=H 0 exp(-t/t 0 ) T c (H)=0 for µ 0 H 0 = (4.4±0.5) T T max (H)=0 for µ 0 H 0 = (13.4±0.7) T

10 In-plane ρ(t) in x=0.07 LSCO film for different H c T max (H) R =ρ/d, R /layer =ρ/l, d sample thickness; d = nl ; n - # of layers; l = 6.6 Å thickness of one layer Decrease of T c with H: T c 0 for H 4 T T max 0 for H 13.5 T For T < T max, ρ(t 0) 0

11 Low-T, intermediate H (~ 6-13 T) regime Measured down to 0.09 K Solid lines power-law fit: ρ(t) = ρ 0 (H)T α(h) ρ(t=0) = 0 (superconductor) Power-law ρ(t) expected in a vortex liquid above the glass transition at T g =0. (M.P.A. Fisher et al.; ) α 0 at H~13.5 T

12 In-plane ρ(t) in x=0.07 LSCO film for different H c T max (H) R =ρ/d, R /layer =ρ/l, d sample thickness; d = nl ; n - # of layers; l = 6.6 Å thickness of one layer ρ(t, H) exhibit a change of sign of dρ/dt as a function of H at high T > 5 K

13 Scaling analysis in the high-t (T > T max ) regime µ 0 H 1 *=3.63 T ρ(t,h)=ρ 1 * f 1 (T/T 1 *) Film: ρ 1 *=1.15 mω cm (R /layer 17.4 kω) Crystal: µ 0 H 1 *=6.68 T ρ 1 *=1.19 mω cm (R /layer 18.0 kω)

14 Scaling analysis in the high-t (T > T max ) regime Scaling parameter T 1 * T 1 * ~ δ zν, zν ~ 0.7 zν 0.73 in film (± 0.1); zν = 0.59±0.08 in single crystal Assuming z=1 due to long-range Coulomb interaction between charges, ν ~ 0.7 is consistent with (2+1)D XY model (ν=2/3): 2D SIT in the clean limit zν ~ 0.7 for H-driven SITs also in conventional 2D superconductors (e.g. a-bi and a-nbsi) and 2D superconducting LaTiO 3 /SrTiO 3 interfaces

15 Scaling analysis in the low-t (T < T max ) regime µ 0 H 2 *=13.45 T ρ(t) = ρ 0 (H)T α(h), α (H=H 2 *) 0 ρ(t,h)=ρ 2 * f 2 (T/T 2 *) ρ 2 *=6.404 mω cm (R /layer 97 kω)

16 Scaling analysis in the low-t (T < T max ) regime Scaling parameter T 2 * T 2 * ~ δ zν zν 1.15 Assuming z=1 due to long-range Coulomb interaction, ν 1: 2D SIT in the dirty limit Effects of disorder become manifest at low T, preventing the transition to an insulating state at H 1 * and causing the freezing of the vortex liquid into a vortex glass (SC at T=0). Transition from SC VG to an insulator occurs at H 2 * > H 1 *.

17 Contribution from SCFs Δσ SCF (T,H)= ρ -1 (T,H) ρ n -1 (T,H) Single crystal H c H c (T) field above which SCFs are suppressed and normal state is restored Dashed lines: [ρ n (T,0)-ρ(0)]/ρ(0)+αH 2 LSCO: Harris et al., PRL 75, 1391 (1995), Rourke et al., Nature Phys. 7, 455 (2011) YBCO: Rullier-Albenque et al., PRL 99, (2007); PRB 84, (2011)

18 Phase diagram Film True SIT in the dirty limit at H 2 * Hidden critical point at H 1 * (SIT in the clean limit) Pink lines: high-t (T>T max ) scaling region; green lines: low-t scaling region

19 Phase diagram

20 Sketch of the (T, H) phase diagram in underdoped La 2-x Sr x CuO 4 : Interplay of vortex physics and quantum critical behavior [Shi et al., Nature Phys. 10, 437 (2014)]

21 H-field-driven SIT in LSCO: Conclusions Three distinct phases at T=0 in underdoped La 2-x Sr x CuO 4 : o superconductor with T c (H) 0 (pinned vortex solid/bragg glass) o superconductor with T c = 0 (vortex glass) o high-field insulator with localized Cooper pairs (Mott hopping) H-field-driven SIT is not direct: two quantum phase transitions (beyond the conventional scenario) Scaling: - consistent with a model where superconductivity is destroyed by quantum phase fluctuations in a 2D superconductor - extends over a surprisingly wide range of T and H - independent of the nature of the insulator Interplay of vortex line physics and quantum criticality