InAs/GaSb A New 2D Topological Insulator 1. Old Material for New Physics 2. Quantized Edge Modes 3. Adreev Reflection 4. Summary Rui-Rui Du Rice University Superconductor Hybrids Villard de Lans, France 7-10, 2011
Transport Ivan Knez R. R. Du Rice MBE Gerry Sullivan Teledyne Scientific and Imaging ArXiv:1105.0137 (2011), PRL in press ArXiv:1106.5819 (2011) Acknowledge Shou-Cheng Zhang Xiao-Liang Qi Chao-Xing Liu Stanford Hackerman Program
Quantum Spin Hall Effect in Hg/Te Quantum Spin Hall Effect *Bulk charge energy gap Day, Physics Today, January 2008 *Gapless edge states odd number of Kramers pairs *Helical edge states four terminal conductance of 2e 2 /h *Observed in HgTe/CdTe QWs in mesoscopic samples Day, Physics Today, January 2008, p19-23 Bernevig et al, Science, 2006 Konig et al, Science, 2008
Coupled Electron-Hole Double Quantum Well 1. Band parameter DE = E1 H1 can be tuned by width, x, gates Al x Ga 1-x Sb 2. DE < 0 inverted -0.15 ev to 0 Tunneling mix e-h and opens a gap at finite k-vector Semicon. Gap Inverted 3. Used as infrared detector and night vision CCD 4. High mobility MBE wafers produced in best industrial labs (1~5 x 10 5 cm 2 /Vs)
Back Gate Front Gate InAs/GaSb as a QSH Insulator Liu et al, PRL 100, 236601 (2008) n-inv p-inv TI n- Metal p-metal NI
gate p n CMOS n p Oxide AuGe gate N+ Substrate Al - 1000Å SiN 2,500Å GaSb - 30Å AlSb - 500Å GaSb - 80Å InAs - 150Å AlSb - 500Å Buffer 15,000Å n+gaas Wafer and Device AuGe contacts Wafer A B C GaSb 8 nm 5nm 8nm InAs 15nm 12.5 nm 10nm DE = E1 H1-33 mev -18 mev ~ 0 E f, DE can be readily tuned by gates Simiconductor-TI transition QSHE InAs/GaSb/InAs/GaSb Superlattice - Helical surface states? Re-entrant Quantum Hall Effect Bound Excitons - BEC
1 Tuning Through Mini Gap in Meso Samples 12.9 kw x3? (Wafer A 1.5 by 0.5um Hall bar) 300 mk Holes Electrons G' Scattering Length ( / L)(2e 2 / h) Sample length
Naveh &Laikhtman, Euro. Phys. Lett. 55, 545 (2001) Intrinsic and extrinsic Origins of Bulk Conductivity E F E g0 1. Less inverted 2. Narrow QWs 3. Higher mobility 1. Wavefunctions do not 100% overlap -- residual e and h 2. Hybridized e-h not necessary charge neutral 3. Hybridized e-h can break due to impurities Wafer A E go ~ -33 mev, s (bulk) > 12 e 2 /h Wafer B E go ~ -18 mev, s (bulk) << 10 e 2 /h s (bulk) ~ 10 e 2 /h is a magic number Edge modes de-couple from bulk transport
Helical edge modes in four terminal geometry For phase coherent samples Landauer-Buttiker formula gives conductance value: G 14,23 4e h 2 1 2 3 4 Longer samples can be modeled by inserting phase breaking probes and applying LB-formula: 2 3 l G 14,23 2e h 2 l L l L 2 1 L 4
2 Wafer B Scaling Evidence for The Edge Modes Knez, Du, Sullivan L-Dependence, keep W =1mm W-Dependence, Keep L/W=2 Conclusion For geometry, the edge conductivity is ~ quantized to 4 e 2 /h
Robustness of Edge Quantization vs Bulk Conduct. Back gate To change Inversion Small inversion Slowly-Prop. Edge Modes 3 x 10 4 cm/s
Anomalous Magnetic Field Dependence All 300 mk B // = 1T B perp 1. Long samples show stronger positive MR bulk effect 2. mm samples weaker depend. 3. Edge states does not scatt. into and out of bulk lack of loop Decouple from bulk
Opens a Number of Exciting Experiments 1. Edge states extend all the way to the material edge (E f pinned above E c for InAs) 2. Good interface with superconductors due to low Schottky barrier --- SC Hybrids Examples Andreev Reflection Normal SC Majorana Bound State (MBS) Fu & Kane PRB 2008 Non-Equilibrium Josephson Effect Through Helical Edge State arxiv: 1108.3870 Cleavage STM/STS Front Gate B
1.Can we make Nb/InAs Junction - Test 2.Can we make Nb/InAs-GaSb Junction - New 1 Nb Nb V SGS 2D ne S, 2D ne N, 2 DS D ne N InAs InAs width 400 nm Multiple Adreev Reflection: 3 sets of peaks: Δ N, Δ S, Δ N +Δ S Δ N /Δ S ~ 0.67 Δ S =1.31meV ; Δ N =0.87 mev
3 Andreev Reflection in 3 Regimes electron side In the gap Width1 mm Nb Nb hole side Gate
3 Andreev Reflection in Nb/(InAs-GaSb)/Nb Knez, Du, Sullivan ArXiv:1106.5819 (2011)
Perfect Andreev Reflection V front =5V electron side V front =-2.1V hole side
3 Excess Current Suppressed by Magnetic Fields electron side
Temperature dependence