Majoranas in semiconductor nanowires Leo Kouwenhoven

Transcription

1 Majoranas in semiconductor nanowires Leo Kouwenhoven Önder Gül, Hao Zhang, Michiel de Moor, Fokko de Vries, Jasper van Veen David van Woerkom, Kun Zuo, Vincent Mourik, Srijit Goswami, Maja Cassidy, AHla Geresdi wires: Diana Car, SebasKen Plissard & Erik Bakkers materials: S. Conesa Boj, M. Quintero-Perez, K. Watanabe, T. Taniguchi theory: Michal Nowak, Michael Wimmer, Anton Akhmerov

2 INTRO

3 Majorana Fermion a particle that is equal to its own anti-particle γ = γ creating a Majorana is the same operation as annihilating it: meaning zero energy, zero spin and zero charge. okay for Bosons but not for Fermions (electron positron) How to detect a particle with everything zero? 1938 (Wilczek, Majorana Returns, Nature Physics, 2009 Wilczek, Majorana modes materialize, Nature, News&Views, 2012)

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5 ParKcle superposikons equal superposition of an electron and a hole c = c = c = γ 1 + iγ 2 creates an electron c = γ 1 - iγ 2 creates a hole γ 1 = ½ (c + c) is Majorana-1 γ 2 = ½i (c - c) is Majorana-2 satisfying γ 1 = γ 1 and γ 2 = γ 2 One Majorana is half a Fermion

6 c = γ 1 +iγ 2 γ 1 γ 2 non-local separation provides topological protection,kitaev, Read, Fu, Kane, Das Sarma, Beenakker, Alicea,... (see review Nick Read, Physics Today July 2012.)

7 Collective state & quasi-particles

8 from spakal to parkcle superposikon

9 from spakal to parkcle superposikon Superconductor in magnetic field Majorana = ½ x (electron + hole) = ½ x ( + ) Kitaev 2001

10 INTRO-2

11 Majorana recipe Lutchyn, Sau, Das Sarma, PRL 2010 Oreg, Refael, von Oppen, PRL 2010 one-dimensional quantum wire spin-orbit interacdon superconducdvity tune µ & apply magnedc field.zero bias anomalies Kouwenhoven, Del& (2012) Xu, Lund Heiblum, Weizmann Harlingen, Urbana-Champaign Marcus, Copenhagen

12 SOI + MagneKsm B < B crikcal B = B crikcal B > B crikcal E F TOPOLOGICALLY DISTINCT Number of crossing different in parity

13 SOI + MagneKc field + superconduckvity B < B crikcal B = B crikcal B > B crikcal Energy Momentum Y. Oreg et al. PRL(2010); R. M. Lutchyn et al PRL (2010);

14 Topology & bandstructure in 1D Non-Inverted band structure Inverted band structure Non-Inverted band structure TRIVIAL TOPOLOGICAL TRIVIAL Energy γ 1 = γ 1 γ 2 = γ 2 Position

15 Thesis 2016, TUDeli repository Kun Zuo & Vincent Mourik Trivial Topological

16 effeckve SOI from magnekc texture Kjaergaard, Wӧlms, Flensberg (PRB 2012) Klinovaja, Stano, Loss (PRL 2012) Nakosai, Tanaka, Nagaosa (PRB 2013) MarKn and Morpurgo (PRB 2012) Glazman (PRB 2013), and others.. Nadj-Perge, Yazdani, et al. (2014)

17 ZBP

18 E F superconductor superconductor B B so

19 Au V gate NbTiN 500 nm B

20 B E z = ½ µ B g InSb B (mev)

21 2.5 B (T) V bias (mv)

22 normal (Au) pinch-off increase V G super (NbTiN) normal (Au) B // wire

23 normal (Au) pinches off V G super (NbTiN) normal (Au) B // wire

24 ZBP exceeds normal state conductance di/dv (2e 2 /h) B = 0.6 T

25 A typical Majorana Device: 0T 0.24T 1um Majorana condi7on (single sub-band regime) B (T) 0.32T E Z > Δ 2 + μ 2 B ZBP 0.44T B Super gate NO ZBP 0.5T Super Gate Super gate

26 A typical Majorana Device: Where does the ZBP live? 1um The ZBP lives underneath the superconductor

27 Numerics Stanescu, Tewari, Sau & Das Sarma

28 Numerics Rainis, Triffunovic, Klinovaja & Loss

29 Angle

30 x Y x y

31 rotadon of magnedc field spin-orbit along y XZ plane T XZ plane spin-orbit XY plane // spin-orbit XY plane pinches off tunnel barrier spin- orbit B = 0.42 T

32 ZBP SPLITTING

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34 N1 S peak splihng is NOT an effect from the tunnel barrier!

35 if Kondo-1/2, then gµ B B < 60 µev and thus g < 1 << g InSb /50

36 PHASE DIAGRAM

37 superconductor B B so super-vg E Z E Z >

38 super-gate = -10 V -9 V -8 V -7 V B (T) -6 V -5 V -4 V -3 V B (T) B (T) 0 0

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40 Level-crossing & KONDO

41 Lee etal. ST-Kondo, Sasaki etal.

42 if Kondo-1/2, then gµ B B < 60 µev and thus g < 1 << g InSb /50

43 V (µv) How would Kondo effect look? how would spin ½ Kondo look? g = 50 g = 2

44 DISORDER

45 challenge: disorder Mourik et al (2012) Takei et al. (2013), Chang et al (2015) soe gap linked to disorder Liu et al (2012) Pikulin et al (2012) Lee et al (2014) Majorana signatures mimicked by disorder

46 Conclusions

47 Majorana recipe 1. One-dimensional quantum wire 2. Spin-orbit interaction 3. Superconductivity 4. Apply magnetic field (Lutchyn, Sau, Das Sarma, PRL 2010, Oreg, Refael, von Oppen, PRL 2010) Unique recipe for Majoranas. Take one ingredient out and Majoranas are gone. ZBP rigid over large ranges in B and Vg.

48 Theories are excluded that are based on: - an efffect from the tunnel barrier - T ~ 1 => no Coulomb blockade - ballistic wires => no localization effects - Kondo only possible if g < 0.5 = g InSb /100

49 BARRIER

50 Fermi level Sharp barrier 1. With a sharp tunnel barrier, only the top populated subband will be topological (holds Majorana s) and the other two bands as shown in the plot are all trivial. 2. As the tunnel barrier is sharp, the three bands have the same transmmision coefficient, therefore Majorana s as ZBP in the tunneling measurement will be clear. Dashed lines indicate the spin orbit gap

51 Fermi level Sharp barrier If we have a smooth barrier, the situakon would be different 1. For smooth barrier, what is the relevant length scale? 2. What are the coherence length of Majorana s, could we have mulkple Majorana s, like indicated in the figure. Dashed lines indicate the spin orbit gap

52 Fermi level An more exaggerated case, tunnel barrier is very smooth, could be relevant for T. Stanescu s soi gap paper, the two more possible Majorana s pairs are well separated (skll depend on the coherent length of Majorana s in the system): 1. Could we discriminate them? 2. What is the visibility difference in tunneling measurements of the Majorana s at the top subband vs. lower subbands? 3. How about the stability in B and chemical potenkal of these Majorana s at lower subbands compared to top subband Majorana s? Dashed lines indicate the spin orbit gap

53 rest

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55 Majorana island device S M Albrecht et al. Nature 531, (2016) doi: /nature17162

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