Pseudospin Soliton in the ν=1 Bilayer Quantum Hall State. A. Sawada. Research Center for Low Temperature and Materials Sciences Kyoto University

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1 YKIS2007, Sawada Pseudospin Soliton in the ν=1 Bilayer Quantum Hall State A. Sawada Research Center for Low Temperature and Materials Sciences Kyoto University

2 Collaborators Fukuda (Kyoto Univ.) K. Iwata (Kyoto Univ.) D. Terasawa (Tohoku Univ.) M. Morino (Tohoku Univ.) S. Kozumi (Tohoku Univ.) Z.F. Ezawa (Tohoku Univ.) Y. Hirayama (Tohoku Univ.) N. Kumada (NTT Basic Res. Lab.) In press A. Fukuda et al. Phys. Rev. Lett. Cond-mat/

3 Introduction Quantum Hall Effect 2-D Electron System Low Temperature High Magnetic Field R xy [kω] R xx [kω] B [T] Hall Resistance Magnetoresistance h/νe 2 Quantized ν:landau Level Filling Factor Integer or Fractional 0

4 Composite Boson Model Composite Boson=One Electron+Odd Number Flux Quanta Exchange Symmetry Phase Exp{iπ(1+m)} Aharonov-Bohm Effect Girvin and MacDonald Phys. Rev. Lett. 58, 1252(1987) Ezawa et al. Phys. Rev. 46, 7765(1992). Quantum Hall State is incompressible (100K) ΔnΔφ h Δn=0, Δφ=, no coherence, no superconductivity Bilayer System Δn d Δφ d h Density Difference Δn d 0 Phase Difference Δφ d Macro Coherence arise Wen and Zee Phys. Rev. Lett. 69, 1811(1992) Ezawa and Iwazaki, Phys. Rev. B 48, 15189(1993)

5 Experiments of ν=1 bilayer QHE Stable for Density Difference Phase Transition σ= n f - n b n f + n b Next Slide A. Sawada et al. Phys. Rev. Lett (1998) S.Q. Murphy et al. Phys. Rev. Lett (1994) DC-Josephson like Tunnel Conductance Disappearance of Hall Resistance I.B. Spielman et al. Phys. Rev. Lett (2000) M. Kellogg et al. Phys. Rev. Lett (2004)

6 Bilayer ν =1 Quantum Hall Effect - In-plane Field Effect - B = B cosθ tot B = B sinθ // tot Excitation Gap Δ R xx exp(-δ/2τ ) Commensurate Phase Incommensurate Phase Coherence C-IC Phase Transition K. Yang et al. Phys. Rev. Lett. 72, 732(1994) Pokrovsky-Talapov Form Phase Transition for In-plane Field S. Q. Murphy et al. Phys. Rev. Lett., (1994) Incommensurate θ=const. Commensurate θ=-qr

7 Theory Exact Diagonalization 8 Electron,d/l=2 More precise measurement Cusp K. Yang et al., Phys. Rev. B, (1996) ξ:string Size ρ ps is Hartree-Fock value

8 4. Experimental System Dilution Refrigerator Lowest Temperature 6 mk Cooling Power(@100 mk) 400 μw Highest Magnetic Field 15 T Electrical Transport Rotation of Sample

9 Sample Sample Parameter Layer Distance d = 23.1 nm Tunneling Energy Δ SAS = 11 K Mobility (@ n T = 1.0 x cm -2 ) 1.0 x 10 6 cm 2 /Vs B B = = B B tot // tot cosθ sinθ

10 Magneto and Hall Resistance Field Dependence N t = cm -2 Θ=50.3 Θ C =46.2 Offset by 2kΩ Soliton What is the peak?

11 Color-scale Plots of Magnetoresistance as a Function of Magnetic Field and Electron Density No QH Phase Commensurate Phase Incommensurate Phase IC Soliton Phase

12 Definition of Boundaries Phase Boundaries R xx [Ω] θ=38 o θ=45 o θ=53 o C No- QHE C IC No- QHE S C IC N tot [x10 cm ] Transition from C Phase Clear No Clear IC No-QHE,S IC Transition, Increase of Resistance Maximum of Gradient

13 Phase Diagram In-plane Field and Electron Density Space 11-2 Ntot [x10 cm ] Commensurate (b) (d) (f) No-QHE Soliton Incommensurate B// [T]

14 Related Theoretical Papers Coherent System Pokrovsky-Talapov Form +Capacitance energy Soliton State Charge Imbalance A) C.B. Hanna, et al., Phys. Rev. B 63, (2001). A) E. Papa and A.M. Tsvelik, Phys. Rev. 66, (2002). A) S. Park, et al., Phys. Rev. B 66, (2002). A) S. Park and K. Moon, Solid State. Comm. 132, 851(2004). A) Z.F. Ezawa, et al., Physica E in press. B) C.B. Hanna, Phys. Rev. B 66, (2002). B) L.R. Radzihovsky Phys. Rev. Lett. 87, (2001). B) M. Abolfath, et al. Phys. Rev. B 65, (2002).

15 Soliton Phase Image of Soliton Phase Soliton B // Soliton: Solution of sine-gordon EQ Part of 2π Phase Slip φ=ϕ Qx y x Pseudospin Direction x φ I 相 ξ Like Pseudospin Domain State 2π ξ Electron Pseudospin up : Front Layer down : Back Layer

16 Two-axis Goniometer In Mixer of Dilution Refrigerator α β Sample Hall Sensor Rotation of θ-axis Rotation of φ-axis

17 Anisotropic Conductance n t = cm -2,θ=53.5,T=0.32K R xx [Ω] B 6000 φ= ν=1 B I φ=90.0 φ=67.5 φ=45.0 φ=22.5 φ=0 Sample I 1000 B I Two Axis Goniometer φ=0 B tot [ T ]

18 Temperature Dependence of Anisotropy R xx 90 /R xx 0

19 In-plane Field Dependence of Anisotropy θ C Anisotropy appear Near C-IC Transition Point As temperature is low, Anisotropy at ν=1 is disappear.

20 Density Difference Dependence of σ= n f - n b n f + n b Anisotropy Φ= 0 70mK Φ=90

21 Activation Energy Total Density and In-plane Field Dependence Unit of N tot : cm -2 No-QHE Δ [K] d/l Commensurate Incommensurate X Soliton Δ [K] Ql Q=(2πd/φ 0 )B: In-plane Field Wave Number l=(h/2πeb ) 1/2 : Magnetic Length Δ [K] Cusp Continuous or Discontinuous Smooth

22 Magnetoresistance as a Function of Density Imbalance Parameter and Total Density Soliton State n T = Θ=57.9 T=100mK σ= n f - n b n f + n b

23 Phase Diagram Theory and Experiment Pokrovsky-Talapov Form No-QHE d/l Incommensurate Commensurate Soliton Ql CC: Commensurate Canted IC: Incommensurate Canted L. Radzihovsky, Phys. Rev. Lett., (2001) M. Abolfath et al., Phys. Rev. B, (2002)

24 Exact Diagonalization Calculation of Ground State Energy Exact Diagonalization 8 Electron,d/l= x10-3 Δ/Ec C I 11-2 N tot =1.2 x 10 cm d/l = 2.0 K. Yang et al., Phys. Rev. B, (1996) Qξ EX Similar experimental result, Transition point, different ρ ps is Hartree-Fock value

25 Summary Magnetoresistance Peak (Soliton Phase) in Bilayer ν=1 Quantum Hall State Phase diagram of Bilayer ν=1 Quantum Hall State in B // n t space Anisotropic Magnetotransport to angle between B and I Soliton Lattice Phase or Charge Imbalanced Phase Soliton Phase is unstable when the density imbalance is large Charge imbalance exist or not?