1. Andreev Reflection in Quantum Hall Effect Regime H. Takayanagi 髙柳 英明 Tokyo University of Science,Tokyo International Center for Materials NanoArchitechtonics (MANA), National Institute for Materials Science, Tsukuba

2. Superconducting Junctions using AlGaAs/GaAs Heterostructures with High H c 2 NbN Electrodes Hideaki Takayanagi, Tatsushi Akazaki & Yuichi Harada, NTT Basic Research Laboratories Minoru Kawamura, Riken Junsaku Nitta, Tohoku University

3. Andreev Reflection An incident electron from the normal conductor is reflected as a hole and a Cooper pair is created in the superconductor. The differential resistance of the S/N interface decreases or increases within the superconducting energy gap depending on the Andreev reflection probability (A) and normal reflection probability (B).

4. Andreev Reflection in High Magnetic Field A 2DEG exhibits QHE in a strong perpendicular magnetic field. The QHE is represented in terms of edge states. Andreev reflection between superconductor and edge states was first proposed by Zyuzin[1] and have been investigated theoretically and experimentally by several authors. [1] A. Yu Zyuzin Phys. Rev. B 50(1994) 323. [2] H. Takayanagi and T. Akazaki, Physica B 249-251(1998)462. [3] T. D. Moore and D. A. Williams, Phys. Rev. B 59(1999)7308.

5. SNS junction with NbN sueprconducting electrodes & a 2DEG in a AlGaA/GaAs single heterostructure Advantages of these materials –NbN High H c2 > 18T –2DEG in AlGaAs/GaAs heterostructure High electron mobility Low carrier density Problem –High Schottky barrier between NbN and GaAs Sample

6. Sample Fabrication AuGeNi layer is inserted between NbN and GaAs. The samples are annealed at 450 ℃ in N 2 atmosphere.

7. Properties of 2DEG &NbN n=7.36x10 15 m -2  =18.3m 2 /Vs Magnetic field dependence of a Hall-bar shaped sample with normal conductor electrode (left). Temperature dependence of the resistance of NbN thin film (right).

8. V Dependence of dV/dI The differential resistance of a SNS junction. A decrease of a resistance (about 6%) is observed within V ~ 5mV, which corresponds to 2 .  is the superconducting energy gap of NbN.

9. Magnetic Field Dependence I dV/dI v.s. V curves at weak magnetic fields. As magnetic field is increased, the Hall voltage arises in the 2DEG. So the voltage drop mainly occurs in the 2DEG rather than S/N interface. This causes the energy gap structure moves to higher voltages.

10. Magnetic Field Dependence II Magnetic field dependence of zero-bias resistance. The inset shows the junction length L dependence of  R.

11. Remarkable Features –The SNS junctions with superconducting electrodes show deep resistance minima between =4 and =3. –The minima does not appear in the junction with normal electrode. –The resistance minima become smaller as the junction length L become longer. –Resistance of the SNS junctions are almost same as the usual value h/ e 2, when the filling factor is integer. These resistance minima can be explained by Andreev reflection.

12. A Simple Explanation Imported from a model of S/N junctions at zero magnetic field. (1)

13. L-dependence The transmission probability T is calculated using Eq.(1) for several samples with different junction length L. T is almost proportional to 1/L as same as diffusive case.

14. Summary The SNS junction using a 2DEG in an AlGaAs/GaAs single heterostructure and High H c2 superconductor NbN was fabricated. The transport properties of the SNS junctions have been investigated in the quantum Hall regime. Large resistance minima appear between the quantum Hall plateau, which are explained in terms of Andreev reflection between NbN and extended states at the center of the Landau level.

15. How we can use graphene for this experiment ?