Bosonic IST’s in Nano-HoneyComb (NHC) Films

1. Bosonic IST’s in Nano-HoneyComb (NHC) Films M. D. Stewart, Jr. (Stew) J. M. Xu, Aijun Yin, and Jim Valles Brown University, Providence, RI USA

2. amorphous-Bi films Haviland, Liu and Goldman Insulators in 2D Insulator to Superconductor Transition (IST) thickness or H-tuned What’s the insulating phase? localized Cooper pairs (bosons) or localized electrons (fermions) or novel mixture

3. H amorphous-Indium Oxide (Hebard and Paalanen) Insulators in 2D Insulator to Superconductor Transition (IST) H-tuned What’s the insulating phase? Scaling Superinsulator behavior Magnetoresistance peak …probably localized bosons

4. Boson to Boson IST’s in NHC Films • Amorphous Nano-HoneyComb films • Patterning allows Cooper Pair detection • Thickness tuned IST • Patterning transforms IST • Direct observation of localized Cooper pairs • Vanishing energy scale at critical point • Magnetic Field tuned IST • Vanishing energy scale at critical point • Comparison to Indium Oxide films

5. Nano-honeycomb Films o  1 mm

6. Cooper Pair Detection Cooper pair phase obeys: S H  flux periodic properties period Only need, Lφ > S1/2 frustration

7. Nano-honeycomb Sheet Resistance (Ω/□) Temperature (K) Features: Reentrance, stronger insulator, broad superconducting transition Thickness Tuned IST’s Unpatterned Sheet Resistance (Ω/□) Temperature (K)

8. Insulator is exponentially localized NHC films R=R0 exp(-To/T)

9. R□ (kΩ) ∆G (1/kΩ) -1 0 1 Log [T(K)] Insulating Unpatterned Films IST of a-Bi/Sb films PRB 59, 11209 (1999) Insulator’s conductance:  weakly localized fermions

10. Insulator exhibits flux oscillations! 1)Period: HM = h/2eS  2e charge carriers 2) Activation energy oscillates

11. 1e vs. 2e oscillations • Patterned PbTe Films (1e) • Oscillation period  h/2eS • Negative magnetoresistance • 1e hopping • Poyarkov et al., JETP Lett. 44, 373 (1987) • NHC Films (2e) • Oscillation period  h/2eS • Positive Magnetoresistance •  2e transport

12. Energy scales in the insulator Oscillations Unpatterned film To (f=1/2) To (f=0) IST where To 0

13. Charge 2e Carriers • Cooper pairs in the insulator • Oscillations appear where unpatterned films can support pairing • Cooper pair transport in the insulator • Differs from quasi-particle transport in structurally granular films

14. grain JJ What governs the NHC film IST? ? = Josephson Junction Array physics? localizing charging energies vs. delocalizing Josephson energies Ec > Ej gives an insulator Ej oscillates in magnetic field

15. L JJA picture Estimate : For L = 50 nm, Ec = 104K/ Too large to be relevant! Effective islands encompass many holes? --- Need 1000’s of holes

16. Thickness tuned IST in NHC Films • Direct observation of strongly localized Cooper pairs • Patterning enhances boson localization • Vanishing energy scale at the critical point • JJA model requires large islands

17. H a-Indium Oxide Films Hebard and Paalanen (1990) Field tuned SIT • Reentrance • Metal at H = Hc • Dirty Boson scaling

18. Field tuned SIT – NHC films • Reentrant • Exponential insulator - R=Roexp(To(H)/T) • Metallic at the critical point?

19. To vs. H/HM H controls a single energy scale

20. Magneto-Oscillations ContinueMultiple field tuned IST’s oscillations  bosons Weak superconductors at matching fields

21. Superconducting Film for H>>HM

22. Effects of Nano-Honeycomb Geometry AAO Substrate • Multiply connected • Surface undulations Exp(To/T) R(H) peak

23. Magnetoresistance Peaks Indium Oxide Film PRL 107005 (2004) NHC Bi/Sb Film

24. R(T)’s of Indium Oxide Films Reentrance Hebard and Paalanen, PRL 65, 927 (1990) Activated Sambandamurthy et al., PRL 107005 (2004)

25. Boson to Boson IST’s in NHC Films • Method to “see” Cooper pairs in non-superconducting system • Created boson dominated SIT’s • How holes tend to localize Cooper pairs is unclear • Similarities to Indium Oxide films

26. High Magnetic Fields

27. Experimenters