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Zoltán Scherübl 24.10.2013 BME Nanophysics Seminar - Lecture

Superconductivity , Nanowires , Quantum Dots , Cooper-pairs , Majoranna-fermions alias 3 more JCs. Zoltán Scherübl 24.10.2013 BME Nanophysics Seminar - Lecture. The Hamiltonian:. Constant DOS assumed : ρ η Tunnel-couplings :. Δ →∞ limit: no quasiparticles.

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Zoltán Scherübl 24.10.2013 BME Nanophysics Seminar - Lecture

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  1. Superconductivity, Nanowires, QuantumDots, Cooper-pairs, Majoranna-fermionsalias 3 more JCs Zoltán Scherübl 24.10.2013 BME NanophysicsSeminar - Lecture

  2. The Hamiltonian: Constant DOS assumed: ρη Tunnel-couplings: Δ→∞ limit: no quasiparticles Uα→∞ limit: 0 or 1 e / dot, local Andreevprocess is forbidden 9 basisstates:

  3. Inthis limit only |0> and |S> arecoupled: Andreev-excitations: excitation of DQD w/o couplingtonormalleads: Calculation of current (master-equation): Normalleadsareintegrated out →reduceddensity-matrix → firstordertunnelingprocess→reduceddensitymatrix is diagonal Master-equation: Fermi’sgoldenruletransitionrate Occupationprobability Zerothorderspectralfunction: delta-peaksatAndreev-excitaionenergies BroadeningduetoΓN: secondorder→ notdiscussed Current:

  4. Results: Triplett-blockade: Asymmetriccurrentinbiasvoltage Cooper-pairscansplittothedots, and tunnelintothenormalleads Reverse: ifthedot is occupiedwithtriplettelectrons, thecurrentisblocked Differentialconductance:

  5. Andreevexcitationenergysplitting: Non degeneratedotlevels (Δε≠0) Althoughleft-rightsymmetry is broken, IL = IR Infirstorderonly CAR is allowed

  6. Couplingtwodots: Energyshiftsdueto SC in (1,1) regime: Secondordertermareequal → neglected Fourthorder: Twoprocesseslowersthe S energy: 1. Exchange: electrontunneltotheotherdot, and backwards ((0,2) intermediatestate) 2. CAR: 2 electrontunnelfromthedotsto SC, and backwards ((0,0) intermediatestate) Bi =0 → Analyiticsolution: At 3D, ballistic SC: At 3D: diffusive SC: slightybetterprefactor: butξ0 → Problem: summingfordifferentpathswithdifferentfactor Prefactor → ~Å interactionlength

  7. In 1D singlechannel, ballistic SC: Interactionlength: 1. Exchange: SinceU is large, exchangeisneglected Effect of SOI: w/o B only 1 of 4 (1,1) statecouplesto S Effect of B&SOI: 2 splitoffstateshavefinite CAR (T+,T-) 1 state has no CAR (T0) 1 state has CAR amplitude (S) Operation: Initialization: adiabaticsweepfrom (0,0) to (1,1) Tuningthedotlevelsortunnelcouplings Avoiddecoherenceduetochargenoise: far from Readout : sweepfrom (1,1) to (0,0) – triplettblockade Uptonow: Coupling 2 single-spinqubit (δESactsas a 2-qubit gate) Non-local S-T qubit Coupling S-T qubits (Fig. 2(b))

  8. Hamiltonian of 1 S-T qubit (coupledto SC): Cooper-pairbox: finitechargingenergy (EC), fix electronnumber (N) 2 S-T qubitcoulpedto a long ( >> ξ0 ) CPB: capacitivecoupling |00> is not part of S-T qubitbase, but: Numbers: → → VABsaturateswith ECfor fixed γ,δ Large VABwithsmallδrequireslargeγ (fewchannel NW highqualityinterface)

  9. Majoranaboundstatesuppress LAR infavor of CAR

  10. Majorana Hamiltonian: Excitationenergy: E Levelwidth: ΓM << EM neededforsuppression of LAR Unitaryscatteringmatrix: Basis: propagating electrones and holesinleads Assumptions: no cross-coupling, energydependenceneglected 2 MBSs Lowexcitationenergy, weakcoupling: Off-diag of S: onlyoff-diagelement: only CAR (ornormaltunneling) withprobability Probability of LAR:

  11. Probability of e1→ e2 and e1→ h2equal→ CAR cannot be detectedinthecurrent→noise: Assumption: equallybaisedleads, lowtemperature ( ), weakcoupling ( ) →Shot-noisedominates→transferedchargefromFano-factor ( ) Someniceformulas: Zero-frequencynoisepower: Lowenergyweakcoupling limit: Total noise: → Cooper-pairtransfer Separateleads: → suppression of LAR The positivecross-correlation is maximal, since (here =) Note: highvoltageregime: (time is notenoughforcorrelationstodevelop)

  12. Exactlysolvablemodel: 2D TI, with SC and 2 magnet Fermi levelwithinthegap: Decaylengthin SC: in magnet: Foronlyboundstateis MBS For and

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