Interactions and transport in Majorana wires. Alfredo Levy Yeyati

Transcription

1 Interactions and transport in Majorana wires Alfredo Levy Yeyati SPICE Workshop: Spin dynamics in the Dirac systems, Mainz 6-9 June 2017

2 Content Low energy transport theory in Majorana wire junctions, PRB 94, (2016) Alex Zazunov, Reinhold Egger and ALY Josephson effect in multiterminal topological junctions (in preparation) With R. Egger and A. Zazunov (Dusseldorf) and Miguel Alvarado (UAM) Zero-energy pinning from interactions in Majorana nanowires, NPJ Quantum Materials 2, 13 (2017) Fernando Dominguez, Jorge Cayao, Pablo San José, Ramón Aguado, ALY & Elsa Prada

3 Hybrid nanowire devices (exp) Delft Saclay Copenhagen Stanford/Copenhagen Delft Weizmann

4 Theoretical modeling Minimal: lowest energy states Role of interactions Analytical results Extended: large discrete basis Role of disorder Numerical g L S g R Intermediate: effective low energy theory Transport, Subgap+continuum possible analytical results

5 Hamiltonian Approach T 0 Left lead Right lead ) ( 2 )/ ( 2 )/ ( 0 t i L R t i R L R L contact e c c e c c T H H H H T ) (1 4 W T transmission coefficient normal case: k k k R L k k k R L k R L c h c c c c H..,,, BCS superconductors: i i i c c ˆ Keldysh + Nambu formalism ) ( ˆ 0 0 ) ( ˆ * 2 )/ ( 2 )/ ( 0 t T e e T t T RL t i t i LR evt t 2 ) ( 0 e.g. Cuevas, Martín-Rodero & ALY, PRB (1996) bandwidth R L R RL LR L R L C R L eff g T T g dt S ˆ ˆ ˆ ˆ ˆ ˆ ˆ, ˆ ] ˆ, ˆ [ 1 1 Keldysh contour

6 Basic ingredient: Boundary Green functions ei/g Cuevas, Martín-Rodero & ALY, PRB (1996) TRANSMISSION BCS case S/(4e 2 /h) gˆ 0.95 R, A BCS 0.9 ( i0 ) ˆ ˆ 0 x 2 2 W ( i0 ) Cuevas, Martín-Rodero & ALY, PRL (1999) 0.8 Zero frequency noise (dc component) ,0 0,5 1,0 1,5 2,0 2,5 3,0 ev/ ,0 0,5 1,0 1,5 2,0 2,5 3,0 ev/ E. Scheer et al, PRL (1997) R. Cron et al, PRL (2001)

7 TS case: Boundary GF for the Kitaev model L/R chains in real space infinte chain (k space, Nambu) infinite chain GF in real space 0 1 Dyson equation for chain breaking 0 1 ε

8 Boundary GF for the Kitaev model Zazunov, Egger & ALY, PRB (2016) Boundary GFs in t limit 0 + ω

9 N-TS case: conductance and noise Zazunov, Egger & ALY, PRB (2016) resonant Andreev reflection zero-temperature conductance transmission coefficient Subgap shot-noise

10 Nagging issue: 2e 2 /h or not? Al/InGaAs/InAs Nichele et al. (CPH), preprint 2017 Courtesy by K. Flensberg

11 Courtesy by K. Flensberg

12 Courtesy by K. Flensberg

13 Equilibrium TS-TS case: frequency dependent noise Zazunov, Egger & ALY, PRB (2016) Andreev bound states (ABS): 4p periodicity zero-temperature Josephson current Martín-Rodero, ALY & García-Vidal, PRB (1996) BCS case

14 Non-equilibrium TS-TS case: MAR regime Zazunov, Egger & ALY, PRB (2016) /2 /3 Subgap features at /n instead of 2 /n Badiane et al., PRL (2011) San José et al., NJP (2013)

15 V = V = /2 V = /3

16 S-TS case: differential conductance Zazunov, Egger & ALY, PRB (2016) V = Peng et al., PRL (2015)

17 Multiterminal S-TS junctions Previous work: topological states from multiterminal Heck et al., PRB (2014) Riwar et al., Nature Comm. (2016) TS S Two-terminal S-TS: Josephson blockade Zazunov & Egger, PRB (2012) Zazunov, Egger & ALY, PRB (2016) Three-terminal S-TS: lifting of Josephson blockade? L R

18 Multiterminal S-TS junctions: role of MBS spin structure MBS spin-structure in single wire: Sticlet, Bena & Simon, PRL (2012) Prada, Aguado & San-José, arxiv MBS spin-structure in multiterminal junction: Spin canting angle g L g R q L q R

19 Multiterminal S-TS junctions: modeling L, L ˆ L q L S ˆLR ˆ R q R R, R

20 Multiterminal S-TS junctions: CPR results parallel case L R L R LR 0 s limit q q L q R L R ~ / 2 serial case s 0 limit L R / 2

21 Boundary GF for the spinful wire model infinte wire (k space, Nambu) Infinite wire: Real space GF as contour integral Im z z 1 Re z Dyson equation for chain breaking 0 1 ε

22 Boundary GF: LDOS and spin canting angle 5meV V c 2 2 5meV Parameters suitable for InAs/Al t 20meV; 4meV; 0.2 mev

23 Multiterminal S-TS junctions: CPR across topo transition 5meV parallel case L R ~ / 2 Kitaev limit S-TS

24 Zero-energy pinning from interactions Dominguez, Cayao, San-José, Aguado, ALY & Prada, NPJ QM (2017) Apparent absence of MBS hibridization in finite wires Theory (non-interacting) Exp: InSb/NbTiN L 1m; 20 mevnm; 0.5 mev; m * m e Zhang et al. arxiv

25 Zero-energy pinning from interactions Dominguez, Cayao, San-José, Aguado, ALY & Prada, NPJ QM (2017) electrostatic potential Poisson equation

26 Zero-energy pinning from interactions Self-consistent potential Energy levels R=50 nm; L=1 μm parameters for a InSb/Nb wire Dominguez et al., NPJ QM (2017)

27 Conclusions Transport in hybrid TS junctions: Zazunov, Egger and ALY, PRB 2016 General GF formalism Unified description of MBS+continuum Analytical results (N-TS,TS-TS,S-TS,etc) Josephson in multiterminal TS junctions: (in preparation) Kitaev limit: role of MBS spin angle Boundary GF spinful model: CPR across topological transition Interactions: Mechanism of Zero-energy pinning Dominguez, Cayao, San-Jose, Aguado, ALY & Prada, NPJ QM 2017

28 Thank you!