majorana/fermi (1937) : “real version” of dirac...
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• Majorana/Fermi (1937) : “Real version” of Dirac Theory • Majorana disappears (1938) • Neutrino as Majorana (??): Double beta decay (lepton number!) • Neutralino of SUSY is a Majorana fermion • Read and Green (2000): 5/2 FQHE = Chiral p+ip SC • Kitaev (2001): Majorana 1D chain • Das Sarma, Freedman, Nayak (2005): 5/2 FQH ‘Majorana’ Qubit • Das Sarma, Nayak, Tewari (2006):SrRuO4 Majorana (half-vortex) • Fu, Kane (2008): Topological Insulator + SC • Sau, Lutchyn, Tewari, Das Sarma (2010): SO/SM + SC + FMI • Alicea (2010): SO/SM + SC • Lutchyn, Sau, Das Sarma (2010): Majorana Nanowire • Freedman, Kitaev: Topological Quantum Computation (~1995---)
Sankar Das Sarma, Univ. of Maryland April 15, 2011
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Order parameter amplitude suppressed at the core
Order parameter phase rotates by around the core
Low energy normal bound states in the core
CHIRAL, p-WAVE, SPINLESS; ZERO ENERGY MODE AT THE CORE
ZERO-ENERGY CORE STATE IS MAJORANA PROTECTED BY INDEX THEOREM (e-h symmetry)
Majorana is an anyon Not a regular fermion because it is zero-energy!
Bound states in vortex cores are e-h symmetric
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Missing operations in TQC using Majorana (Ising anyons)
Ising anyons are almost universal: need ϑ = π/4 phase gate and CNOT gate. " CNOT gate can be implemented by measuring the total parity of two topological qubits " One idea for ϑ = π/4 phase gate is Dynamical Topology Change (DTC) (Bravyi, Kitaev 2000; Bonderson, Das Sarma, Freedman, Nayak 2010)
Hard to implement in FQHE systems, but perhaps feasible in other systems such as Superconductor/Semiconductor/Magnetic Insulator heterostructures
Nayak, Simon, Stern, Freedman, Das Sarma, Rev. Mod. Phys. (2008)
ISH (Ising Semiconductor Heterostructure)
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arXiv 2010
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The proposal for FQH topological qubit, quantum memory, and NOT gate using non-Abelian Ising (SU2) 2 TQFT: Fabry-Perot interferometery using the quasiparticle current paths along edges encircling anti-dots
Interference is the only definitive way of establishing non-Abelian-ness
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Look for a many-body quantum state sensitive only to the topology
Quasiparticles in ( ) FQH system
Quasiparticles in vortex state of 2D p-wave superconductor
Das Sarma, Freedman, Nayak: Physics Today (2006)
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Qubit decoherence due to anyon tunneling: The limit to topological protection
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Experimental status: NOT observed
Majorana fermion - electrically neutral particle which is its own antiparticle
Simple clever modification of the Dirac equation that involves ONLY REAL
numbers
Question: Are equations for spin-1/2 particles necessarily complex ?
Relevance: particle physics (neutrinos)
(neutralinos) EMERGENT MAJORANA?
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Nature Physics 2009 September
Nature 2010 March
Barbara Goss Levi Search and Discovery The expanding search for Majorana particles
Robert F. Service Science 2011 April
Physics Today 2011 March
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Chiral p-wave superconductors
Topological insulator/ S-wave superconductor
Spin-orbit coupled Semiconductor/
S-wave superconductor
Fractional Quantum Hall
Majorana Fermions
Majorana for the Elite (5/2 FQHE)
Bringing Majorana to the Masses (ISH)
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Non-Abelian statistics
Majorana fermions
Topological degeneracy
Topological superconductors
Spin-orbit coupled
semiconductor
Topological Quantum
Computation
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Band structure of spin-split spin-orbit coupled semiconductor
Rashba induced chiral spin-texture allows singlet pairing
E
k
Sau, Lutchyn, Tewari, Das Sarma PRL(2010)
Need single non-degenerate Fermi-surface HSm= k2 + Vzσz
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Chiral p-wave superconductor SrRuO_4: Das Sarma, Nayak, Tewari (2006)
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Ordinary S-wave SC + 2D (or 1D) Semiconductor with Strong SO Coupling
Sau et al. PRB (2010) Sau, Tewari, Das Sarma Ann Phys’10
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1D wires with spin-orbit: helical state
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Majorana quantum wires
Lutchyn, Sau, Das Sarma PRL 2010
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Density of states across phase transition
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Fractional ac Josephson effect
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Josephson current through heterostructure
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Experimental proposal: nanowire embedded into SQUID
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Experimental considerations
Nature 442, 667 (2006)
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Multi-band semiconductor nanowires The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
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arXiv: 1103.2770
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Jay Sau and Sankar Das Sarma, unpublished
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The search for the Majorana ‘fermion’ may finally be coming to an end The Majorana mode may soon be observed in table-top experiments as an emergent zero-energy mode in solid state semiconductor-superconductor sandwich structures ‘Majorana’ may return after a 75-year hiatus – thanks to Michael Freedman
Happy Birthday Michael