Electrostatic control of spin polarization in a quantum Hall - PowerPoint PPT Presentation

Electrostatic control of spin polarization in a quantum Hall ferromagnet: a platform to realize high order non- Abelian excitations Aleksander Kazakov & Leonid Rokhinson Department of Physics, Purdue University V. Kolkovsky, Z. Adamus, & Tomasz Wojtowicz Institute of Physics, Polish Academy of Science, Warsaw, Poland George Simion & Yuli Lyanda-Geller Department of Physics, Purdue University Luchon, France May 24 - 29, 2015

Engineering Majorana fermions requirements: 1D topological superconductor spinless (one mode) superconductor SC SC E Z E Z E F k k k pairing 2  D possible B so  B B so || B B = 0 Sau , et al ’10, Alicea , et al ‘10 2 6/11/2015 Leonid Rokhinson, Purdue University

parameter space 𝛦 2 + 𝐹 𝐺 2 single-spin condition: 𝐹 𝑎 > to protect superconductivity: 𝐹 𝑎 ~𝐹 𝑇𝑃 B so  B      2 2 2 2 ( / ) E k k d k SO D z D w>200nm k y    d=20nm 6 1 2.6 [meV], [10 cm ] E k k SO [ 110 ]    d=100nm 6 1 0.1 [meV], [10 cm ] E k k k x [110] SO smallest dimension defines E so : small d ⇒ large E so ⇒ large E F ⇒ less localization 3 6/11/2015 Leonid Rokhinson, Purdue Univesity

Characteristic 4  energy-flux relation modification of the Josephson phase 2  I  sin( f ) trivial superconductor Cooper pairs, topological superconductor 4  Majorana particles, I  sin( f/2) 𝑐 † = (𝛿 𝑚 − 𝑗𝛿 𝑛 ) Kitaev ‘01 Lutchyn ‘10 Kwon ’04 4 6/11/2015 Leonid Rokhinson, Purdue Univesity

ac Josephson effect direct inverse 𝜚 1 𝜚 1 𝜚 2 𝜚 2 V I 𝑒(Δ𝜚) = 2𝑓𝑊 𝐽 = 𝐽 0 + 𝐽 𝜕 sin(𝜕𝑢) ℏ 𝑒𝑢 𝐽 𝑡 = 𝐽𝑑 sin 𝜕 𝐾 𝑢 = 𝐽 𝑑 sin 2𝑓𝑊 ℎ𝜕 ℏ 𝑢 𝑊 = 2𝑓 Current oscillates with frequency  V Constant voltage steps  w 5 6/11/2015 Leonid Rokhinson, Purdue Univesity

Disappearance of the first Shapiro step V ~ dc rf 24 B=0 B=1.0 T B=1.6 T B=2.1 T B=2.5 T 12 V (  V) 0 -12 -24 -200 0 200 -200 0 200 -200 0 200 -200 0 200 -200 0 200 I (nA) I (nA) I (nA) I (nA) I (nA) f = 3 GHz LR, X. Liu, J. Furdyna, Nature Physics 8 , 795 (2012) 6 6/11/2015 Leonid Rokhinson, Purdue Univesity

Shapiro steps 2𝑓𝑤 𝑠𝑔 Δ𝐽 𝑜 = A|𝐾 𝑜 | ℏ𝜕 𝑠𝑔 12 dV/dI B=0, f = 3 GHz 10 40 5 32 f = 4 GHz 10 V rf = 14.25 mV 24 0 16 8 V (  V) 0 8 -8 -16 -24 -32 V rf (mV) -40 6 40 4 dV/dI 20 0 2 -300 -200 -100 0 100 200 300 I (nA) 0 -200 0 200 0 300 0 1000 1000 1000 100  I 0 (nA)  I 1  I 2  I 3  I 4 I (nA) 7 6/11/2015 Leonid Rokhinson, Purdue Univesity

dV/dI vs B step @ 6  V step @ 12  V 8 6/11/2015 Leonid Rokhinson, Purdue Univesity

4-periodic Josephson supercurrent in HgTe-based 3D TI Wiedenmann, …M . Klapwijk, …, Seigo Tarucha, L. W. Molenkamp arXiv:1503.05591 9 6/11/2015 Leonid Rokhinson, Purdue Univesity

Advantage of 1D wires: Majorana modes are localized easy to perform spectroscopy Disadvantage of 1D wires: Majorana modes are localized almost impossible to perform exchange magnetic quantum Hall superconductivity semiconductors effect new materials to support exotic non-Abelian excitations reconfigurable 1D topological superconductors in 2D systems 10 6/11/2015 Leonid Rokhinson, Purdue Univesity

Motivation and inspiration Topological Quantum Computation - From Basic Concepts to First Experiments Ady Stern & Netanel Lindner Science, 2013 , 339 , 1179 Exotic non-Abelian anyons from conventional fractional quantum Hall states David J. Clarke, Jason Alicea, and Kirill Shtengel Nature Commun., 2012 , 4, , 1348 11 6/11/2015 Leonid Rokhinson, Purdue Univesity

Development of a new system CdTe:Mn QW Ga [Ar]3d 10 4s 2 4p 1 As [Ar]3d 10 4s 2 4p 3 GaAs:Mn S=5/2 p-doping large s-d exchange (ferromagnetic) Mn [Ar]3d 5 4s 2 exchange split ~3 eV (Hunds rule), ½ filled Cd [Kr]4d 10 5s 2 CdTe:Mn Te [Kr]4d 10 5s 2 5p 4 neutral impurity, large s-d exchange 12 6/11/2015 Leonid Rokhinson, Purdue University

Development of a new system High mobility 2D gas in CdTe/CdMgTe QW m *=0.11, E g =1.44 eV add Mn into CdTe (neutral impurity with 5/2 spin) no Mn ~1% Mn 13 6/11/2015 Leonid Rokhinson, Purdue University

FQHE in CdTe:Mn T. Wojtowicz Betthausen, et al, Phys. Rev. B 90 , 115302 (2014) 14 6/11/2015 Leonid Rokhinson, Purdue Univesity

Anomalous Zeeman splitting in CdTe:Mn 𝑕𝜈 𝐶 𝑇𝐶 𝑕 ∗ 𝜈 𝐶 𝐶 + 𝑦 𝑁𝑜 𝐹 𝑡𝑒 𝔆 𝑇 𝐹 𝑜,↑↓ = (𝑜 + 1 2 )ℏ𝜕 𝑑 ± 1 2 𝑙 𝐶 𝑈 cyclotron Zeeman s-d exchange (>0) g * 1.6 1.3% Mn 0.13% Mn for n=1 8 6 4 E n (meV) E n (meV) E n (meV) 2 0 -2 -4 -6 -8 0 2 4 6 8 10 B (Tesla) B (Tesla) B (Tesla) 15 6/11/2015 Leonid Rokhinson, Purdue University

Magnetoreflectivity studies − (trion) to singlet 𝑌 negatively charged exciton complex 𝑌 transition under polarized 𝜏 + /𝜏 − light Wojtowicz, et al, PRB 59, R10437 (1999) 16 6/11/2015 Leonid Rokhinson, Purdue Univesity

new platform for non-Abelian excitations Ohmic SC contact 8  = 1/m 6 spin energy splitting (Kelvin) 4 2 0 -2 -4 B * -6 -8 0 2 4 6 8 10 magnetic field (Tesla) 17 6/11/2015 Leonid Rokhinson, Purdue University

new platform for non-Abelian excitations Ohmic SC contact 8 SC  = 1/m 1 ↑ > 0 1 ↑ < 0 𝜉 = 𝑛 , 𝐹 𝑎 6 𝜉 = 𝑛 , 𝐹 𝑎 spin energy splitting (Kelvin) 4 parafermions 2 0 𝐹 𝑎 -2 -4 𝐹 𝐺 B * B * 𝑦 -6 -8 0 2 4 6 8 10 SC magnetic field (Tesla) braiding sequence 18 6/11/2015 Leonid Rokhinson, Purdue University

Crossing of neighboring LLs |𝑜, 𝑡 1.0 80 |3, ↑ ↑↓ (meV) |3, ↓ 𝜉 60 𝜉 = 2 |2, ↑ 0.5 ↑↓ (K) |2, ↓ 2 ℏ𝜕 𝑑 + 𝐹 𝑡 40 |1, ↑ 𝐹 𝑡 0.0 |1, ↓ 20 |0, ↑ 𝐶 𝜉 𝑜 + 1 -0.5 |0, ↓ 0 -1.0 -20 0 3 6 9 12 0 5 10 magnetic field (T) (c) magnetic field (T) (a) |𝑞, 𝑡 ↑↓ (meV) 0.4 𝜉 = 2 3 , 4 3 , 2 5 , 8 𝜉 = 1 𝜉 = 1 𝑛 |↓ 𝑛 |↑ |4, ↓ 5 |3, ↓ parafermions |2, ↓ 0.2 ↑↓ 𝐷𝐺 + 𝐹 𝑡 𝐹 𝑡 |1, ↓ |4, ↑ 𝐹 𝐺 𝐹 𝑞 |3, ↑ 𝑦 0.0 |2, ↑ 1 3 , 5 3 |1, ↑ -0.2 7 8 9 10 (b) (d) magnetic field (T)

Quantum Hall ferromagnet & level crossing uniformly Mn-doped quantum well Jaroszynski, et al, PRL 89 , 266802 (2002) Jaroszynski, et al, AIP conference proceedings (2005) 20 6/11/2015 Leonid Rokhinson, Purdue Univesity

Gate control of exchange 𝐹 𝑡𝑒 ∝ 𝜔 𝑓 𝑦 𝜓 𝑁𝑜 (𝑦) 𝑒𝑦 0.4 V FG 0.3 band edge (meV) 0.2 0.1 V BG 0.4 0.0  bandedge [meV] 0.3 wave function 0 20 40 60 80 100 120 140 160 180 200 exchange dencity 0.2 0.2 distance (nm) 0.1 0.0 0.4 bandedge [meV] 0.0 100 120 140 front gate depth from surface [nm] 0.2 overlap ( x ) V G1 0.4  bandedge [meV] 0.3 V G2 exchange wave function dencity 0.2 0.2 0.0 0.1 0.0 100 120 140 0.0 100 120 140 back gate depth from surface [nm] depth from surface [nm] 21 6/11/2015 Leonid Rokhinson, Purdue Univesity

Structures with asymmetric doping 0.06 011414A 0.3 7x(5x1) 0.03 wafer #011414A 0.0 0.00 0 10 20 30 40 50 60 70 80 90 Layer number 0.06 011514A  bandedge [eV] 0.3 0.03 7x(2x1) wafer #011514A 0.0  0.00 0 10 20 30 40 50 60 70 80 90 Layer number 0.06 011614A 0.3 0.03 8x(3x1) 0.0 wafer #011614A 0.00 0 10 20 30 40 50 60 70 80 90 0.06 Layer number 011714A 0.3 0.03 6x(1x1) 0.0 wafer #011714A 0.00 0 10 20 30 40 50 60 70 80 90 75 100 125 150 175 Layer number x [nm] 22 6/11/2015 Leonid Rokhinson, Purdue Univesity

Gate control of s-d exchange crossing 1   and    1.3% Mn B @ 18° T=400 mK #011414 (1 ↓) 10 1.0 2 ) V BG = 0 B @ 18° T=400 mK #011414 d023 R xy (h/e R xx (k  ) 18 (0 ↑) 5 0.5 16 14 0 0.0   1 (0 ↓) 12   2 10 150 R xx (k  )   8 6.0 100 2 6 R xx (k  )   3 4 4.8 50 V BG (Volts) 2 0 0 3.6 -2 V BG -50 -4 2.4 change of the overlap with density -6 2 -100 1 -8 1.8 1.2 -10 1.6 2 -150 E xc   1.4 4 5 6 7 8 9 log noralised overlap 0.0 1.2 -200 B (T) 5 6 7 8 9 1 E xc = const B (Tesla) 0.8 simulation: 5-12 simulation: 21-23 data: wafer #011414 E  1/ 0.6 x c * (V g )/B * (-200) vs  (V g )/  (-200) data: B 0.6 0.8 1 1.2 1.4 1.6 1.8 2 log normalized dencity 23 6/11/2015 Leonid Rokhinson, Purdue Univesity

Gate control of the crossing 𝜉 = 2 V FG 0,3   2     > V BG 0,2 V top gate [V] 0.4  bandedge [meV] 0.3 wave function exchange 0,1 dencity 0.2 0.2   1 | 1 > 0.1 0.0  = 2 0,0 0.0 100 120 140 4 6 8 front gate depth from surface [nm] B [T] overlap 150 0,4      2  bandedge [meV] 0,3 exchange wave function  > dencity 0,2 0,2 V back gate [V] 100 0,1 0,0 0,0 100 120 140 back gate 50 depth from surface [nm]  = 2   1 |1,  > 0 4 6 8 B [T] 24 6/11/2015 Leonid Rokhinson, Purdue Univesity