Majorana qubits in a topological insulator nanoribbon architecture

J. Manousakis, A. Altland, D. Bagrets, R. Egger, and Yoichi Ando

Phys. Rev. B 95, 165424 – Published 17 April 2017

Abstract

We describe designs for the realization of topological Majorana qubits in terms of proximitized topological insulator nanoribbons pierced by a uniform axial magnetic field. This platform holds promise for particularly robust Majorana bound states, with easily manipulable interstate couplings. We propose proof-of-principle experiments for initializing, manipulating, and reading out Majorana box qubits defined in floating devices dominated by charging effects. We argue that the platform offers design advantages which make it particularly suitable for extension to qubit network structures realizing a Majorana surface code.

Received 9 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.165424

Physics Subject Headings (PhySH)

Surface states Topological insulators Topological quantum computing Topological superconductors

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

J. Manousakis¹, A. Altland¹, D. Bagrets¹, R. Egger², and Yoichi Ando³

¹Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany
²Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
³Physics Institute II, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany

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Vol. 95, Iss. 16 — 15 April 2017

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Images

Figure 1
Schematic device with four Majorana states built from a TI nanoribbon in a uniform axial magnetic field $B$ . We assume that $B$ results in the flux $Φ = Φ_{0} / 2$ through the (thick) outer parts which are proximitized by an $s$ -wave superconductor (SC) layer. The 1D surface states in the nonproximitized narrow central part of the device are gapped since here the magnetic flux $Φ$ is well below $Φ_{0} / 2$ . The transparency of this junction can be tuned by an electrostatic top gate. Majorana end states are indicated as red dots. Note that this device is grounded.
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Figure 2
Majorana hybridization energy $ɛ$ (in units of $μ eV)$ vs constriction length $W$ (in nm) for the device in Fig. 1. Taking parameters for ${Bi}_{2} {Se}_{3}$ with $Δ = 0.18$ meV, $M_{0} ≃ 7.14$ meV, and $ϕ = 0$ , results are shown for several values of $μ$ . The quoted values for $ξ$ follow from Eq. (12). For $W ≫ ξ$ , these semilogarithmic plots are consistent with $ɛ \sim e^{- W / ξ}$ [see Eq. (11)], while $ɛ \to Δ$ for $W \to 0$ .
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Figure 3
Hybridization energy $ɛ$ (in $μ eV)$ vs electrochemical potential $μ$ (in meV) for several values of the constriction length $W$ . Parameters are as in Fig. 2, i.e., for ${Bi}_{2} {Se}_{3}$ with $Δ = 0.18$ meV, $M_{0} ≃ 7.14$ meV, and $ϕ = 0$ .
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Figure 4
Grounded vs floating devices. (a) Switchable grounding of TI nanoribbon devices: By tuning the gate voltage applied to a local top gate at the narrowed section, the Josephson coupling energy $E_{J}$ between the TI nanoribbon and a grounded superconducting reservoir can be changed. As a consequence, one can switch between a grounded and a floating device. (b) Floating version of the device in Fig. 1. The two $s$ -wave superconductors are connected by a superconducting bridge, i.e., the Majorana box is characterized by a single charging energy. Normal leads (vertical black lines) are tunnel-coupled to individual MBSs and amongst themselves by interference links to allow for interferometric readout of Pauli operators. The external boxes are symbolic for quantum dots or single-electron transistors which can be used to pump single electrons through the device and manipulate or read out qubit states. For details, see main text.
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Figure 5
2D network of Majorana box qubits using proximitized TI nanoribbons for implementing a Majorana surface code. Stabilizers of type A or B correspond to products of eight Majorana operators around a minimal plaquette as indicated. Access elements for initialization, manipulation, and readout of stabilizers are not shown but described in the main text.
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