| 1. |
- Aasen, David, et al.
(författare)
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Milestones toward Majorana-based quantum computing
- 2016
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Ingår i: Physical Review X. - 2160-3308. ; 6:3
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2) validation of a prototype topological qubit, and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well.
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| 2. |
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| 3. |
- Escribano, Samuel D., et al.
(författare)
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Semiconductor-ferromagnet-superconductor planar heterostructures for 1D topological superconductivity
- 2022
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Ingår i: npj Quantum Materials. - : Springer Science and Business Media LLC. - 2397-4648. ; 7:1
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Tidskriftsartikel (refereegranskat)abstract
- Hybrid structures of semiconducting (SM) nanowires, epitaxially grown superconductors (SC), and ferromagnetic-insulator (FI) layers have been explored experimentally and theoretically as alternative platforms for topological superconductivity at zero magnetic field. Here, we analyze a tripartite SM/FI/SC heterostructure but realized in a planar stacking geometry, where the thin FI layer acts as a spin-polarized barrier between the SM and the SC. We optimize the system’s geometrical parameters using microscopic simulations, finding the range of FI thicknesses for which the hybrid system can be tuned into the topological regime. Within this range, and thanks to the vertical confinement provided by the stacking geometry, trivial and topological phases alternate regularly as the external gate is varied, displaying a hard topological gap that can reach half of the SC one. This is a significant improvement compared to setups using hexagonal nanowires, which show erratic topological regions with typically smaller and softer gaps. Our proposal provides a magnetic field-free planar design for quasi-one-dimensional topological superconductivity with attractive properties for experimental control and scalability.
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| 4. |
- Geier, Max, et al.
(författare)
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Fermion-parity qubit in a proximitized double quantum dot
- 2024
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Ingår i: Physical Review Research. - 2643-1564. ; 6:2
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Tidskriftsartikel (refereegranskat)abstract
- Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same fermion parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to charge noise acting on the potential of each dot, as well as fluctuations of the (weak) interdot tunneling. At weak interdot tunneling, relaxation is suppressed because of disjoint qubit states. However, for strong interdot tunneling the system is protected against noise affecting each quantum dot separately (energy-level noise, dot-superconductor tunneling fluctuations, and hyperfine interactions). Finally, we describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages.
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| 5. |
- Hell, Michael, et al.
(författare)
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Coupling and braiding Majorana bound states in networks defined in proximate two-dimensional electron gases
- 2017
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Ingår i: Physical Review B. - 2469-9950. ; 96:3
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Tidskriftsartikel (refereegranskat)abstract
- Two-dimensional electron gases with strong spin-orbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (S stripes) or where a narrow stripe has been removed from a uniform layer (N stripes). The coupling of the MBSs can be tuned for both types in a wide range (<1neV to >10μeV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majorana-stripe ends as well as Majorana trijunctions formed in a tuning-fork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gate controlled in a range similar to the intrastripe coupling while maintaining a sizable gap to the excited states (tens of μeV). Altogether, this suggests that braiding can carried out on a time scale of 10-100 ns.
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| 6. |
- Hell, Michael, et al.
(författare)
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Distinguishing Majorana bound states from localized Andreev bound states by interferometry
- 2018
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Ingår i: Physical Review B. - 2469-9950. ; 97:16
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Tidskriftsartikel (refereegranskat)abstract
- Experimental evidence for Majorana bound states (MBSs) is so far mainly based on the robustness of a zero-bias conductance peak. However, similar features can also arise due to Andreev bound states (ABSs) localized at the end of an island. We show that these two scenarios can be distinguished by an interferometry experiment based on embedding a Coulomb-blockaded island into an Aharonov-Bohm ring. For two ABSs, when the ground state is nearly degenerate, cotunneling can change the state of the island, and interference is suppressed. By contrast, for two MBSs the ground state is nondegenerate, and cotunneling has to preserve the island state, which leads to h/e-periodic conductance oscillations with magnetic flux. Such interference setups can be realized with semiconducting nanowires or two-dimensional electron gases with proximity-induced superconductivity and may also be a useful spectroscopic tool for parity-flip mechanisms.
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| 7. |
- Hell, Michael, et al.
(författare)
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Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires
- 2016
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Ingår i: Physical Review B. - 1098-0121. ; 94:3
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Tidskriftsartikel (refereegranskat)abstract
- We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating interisland Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently (D. Aasen, arXiv:1511.05153). We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures.
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| 8. |
- Hell, Michael, et al.
(författare)
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Two-Dimensional Platform for Networks of Majorana Bound States
- 2017
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Ingår i: Physical Review Letters. - 0031-9007. ; 118:10
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Tidskriftsartikel (refereegranskat)abstract
- We model theoretically a two-dimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBSs) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved either by imposing a phase difference (by driving a supercurrent or using a magnetic-flux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBSs. Finally, we outline how a network of Majorana stripes can be designed.
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| 9. |
- Huang, Guangyao, et al.
(författare)
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Tunnel spectroscopy of Majorana bound states in topological superconductor/quantum dot Josephson junctions
- 2014
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Ingår i: Physical Review B (Condensed Matter and Materials Physics). - 1098-0121. ; 90:21
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Tidskriftsartikel (refereegranskat)abstract
- We theoretically investigate electronic transport through a junction where a quantum dot (QD) is tunnel coupled on both sides to semiconductor nanowires with strong spin-orbit interaction and proximity-induced superconductivity. The results are presented as stability diagrams, i.e., the differential conductance as a function of the bias voltage applied across the junction and the gate voltage used to control the electrostatic potential on the QD. A small applied magnetic field splits and modifies the resonances due to the Zeeman splitting of the QD level. Above a critical field strength, Majorana bound states (MBS) appear at the interfaces between the two superconducting nanowires and the QD, resulting in a qualitative change of the entire stability diagram, suggesting this setup as a promising platform to identify MBS. Our calculations are based on a nonequilibrium Green's function description and is exact when Coulomb interactions on the QD can be neglected. In addition, we develop a simple pictorial view of the involved transport processes, which is equivalent to a description in terms of multiple Andreev reflections, but provides an alternative way to understand the role of the QD level in enhancing transport for certain gate and bias voltages. We believe that this description will be useful in future studies of interacting QDs coupled to superconducting leads (with or without MBS), where it can be used to develop a perturbation expansion in the tunnel coupling.
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| 10. |
- Kirsanskas, Gediminas, et al.
(författare)
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Designing pi-stacked molecular structures to control heat transport through molecular junctions
- 2014
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Ingår i: Applied Physics Letters. - : AIP Publishing. - 0003-6951 .- 1077-3118. ; 105:23
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Tidskriftsartikel (refereegranskat)abstract
- We propose and analyze a way of using pi stacking to design molecular junctions that either enhance or suppress a phononic heat current, but at the same time remain conductors for an electric current. Such functionality is highly desirable in thermoelectric energy converters, as well as in other electronic components where heat dissipation should be minimized or maximized. We suggest a molecular design consisting of two masses coupled to each other with one mass coupled to each lead. By having a small coupling (spring constant) between the masses, it is possible to either reduce or perhaps more surprisingly enhance the phonon conductance. We investigate a simple model system to identify optimal parameter regimes and then use first principle calculations to extract model parameters for a number of specific molecular realizations, confirming that our proposal can indeed be realized using standard molecular building blocks. (C) 2014 AIP Publishing LLC.
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| 11. |
- Kirsanskas, Gediminas, et al.
(författare)
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Yu-Shiba-Rusinov states in phase-biased superconductor-quantum dot-superconductor junctions
- 2015
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Ingår i: Physical Review B (Condensed Matter and Materials Physics). - 1098-0121. ; 92:23
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Tidskriftsartikel (refereegranskat)abstract
- We study the effects of a phase difference on Yu-Shiba-Rusinov (YSR) states in a spinful Coulomb-blockaded quantum dot contacted by a superconducting loop. In the limit where charging energy is larger than the superconducting gap, we determine the subgap excitation spectrum, the corresponding supercurrent, and the differential conductance as measured by a normal-metal tunnel probe. In absence of a phase difference only one linear combination of the superconductor lead electrons couples to the spin, which gives a single YSR state. With finite phase difference, however, it is effectively a two-channel scattering problem and therefore an additional state emerges from the gap edge. The energy of the phase-dependent YSR states depend on the gate voltage and one state can cross zero energy twice inside the valley with odd occupancy. These crossings are shifted by the phase difference towards the charge degeneracy points, corresponding to larger exchange couplings. Moreover, the zero-energy crossings give rise to resonant peaks in the differential conductance with magnitude 4e(2)/h. Finally, we demonstrate that the quantum fluctuations of the dot spin do not alter qualitatively any of the results.
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| 12. |
- Li, Tommy, et al.
(författare)
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Four-Majorana qubit with charge readout : Dynamics and decoherence
- 2018
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Ingår i: Physical Review B. - 2469-9950. ; 98:20
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Tidskriftsartikel (refereegranskat)abstract
- We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.
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| 13. |
- Maiani, Andrea, et al.
(författare)
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Nonsinusoidal current-phase relations in semiconductor-superconductor- ferromagnetic insulator devices
- 2023
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Ingår i: Physical Review B. - 2469-9950. ; 107:24
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Tidskriftsartikel (refereegranskat)abstract
- Coherent tunneling processes of multiple Cooper pairs across a Josephson junction give rise to high harmonics in the current phase relation. In this work, we propose and study Josephson junctions based on semiconductor-superconductor-ferromagnetic insulator heterostructures to engineer nonsinusoidal current-phase relations. The gate-tunability of the charge carriers' density in the semiconductor, together with the adjustable magnetization of the ferromagnetic insulator, provides control over the content of the supercurrent harmonics. At finite exchange field, hybrid junctions can undergo a 0 - π phase transition, resulting in a supercurrent reversal. Close to the transition, single-pair tunneling is suppressed and the current-phase relation is dominated by the second-harmonic, indicating transport primarily by pairs of Cooper pairs. Finally, we demonstrate that noncollinear magnetization or spin-orbit coupling in the leads and the junction can lead to a gate-tunable Josephson diode effect with efficiencies of up to ∼30%.
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| 14. |
- Pedersen, Jonas, et al.
(författare)
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Interplay between interference and Coulomb interaction in the ferromagnetic Anderson model with applied magnetic field
- 2009
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Ingår i: Physical Review B. - 1550-235X. ; 79
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Tidskriftsartikel (refereegranskat)abstract
- We study the competition between interference due to multiple single-particle paths and Coulomb interaction in a simple model of an Anderson-type impurity with local-magnetic-field-induced level splitting coupled to ferromagnetic leads. The model along with its potential experimental relevance in the field of spintronics serves as a nontrivial benchmark system where various quantum-transport approaches can be tested and compared. We present results for the linear conductance obtained by a spin-dependent implementation of the density-matrix renormalization-group scheme which are compared with a mean-field solution as well as a seemingly more advanced Hubbard-I approximation. We explain why mean field yields nearly perfect results while the more sophisticated Hubbard-I approach fails even at a purely conceptual level since it breaks hermiticity of the related density matrix. Furthermore, we study finite bias transport through the impurity by the mean-field approach and recently developed higher-order density-matrix equations. We found that the mean-field solution fails to describe the plausible results of the higher-order density-matrix approach both quantitatively and qualitatively, as it does not capture some essential features of the current-voltage characteristics such as negative differential conductance.
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| 15. |
- Pedersen, Jonas, et al.
(författare)
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Noncollinear magnetoconductance of a quantum dot
- 2005
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. ; 72
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Tidskriftsartikel (refereegranskat)abstract
- We study theoretically the linear conductance of a quantum dot connected to ferromagnetic leads. The dot level is split due to a noncollinear magnetic field or intrinsic magnetization. The system is studied in the noninteracting approximation, where an exact solution is given, and, furthermore, with Coulomb correlations in the weak tunneling limit. For the noninteracting case, we find an antiresonance for a particular direction of the applied field, noncollinear to the parallel magnetization directions of the leads. The antiresonance is destroyed by the correlations, giving rise to an interaction induced enhancement of the conductance. The angular dependence of the conductance is thus distinctly different for the interacting and noninteracting cases when the magnetizations of the leads are parallel. However, for antiparallel lead magnetizations, the interactions do not alter the angle dependence significantly.
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| 16. |
- Schulenborg, Jens, et al.
(författare)
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Detecting Majorana modes by readout of poisoning-induced parity flips
- 2023
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Ingår i: Physical Review B. - 2469-9950. ; 107:12
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Tidskriftsartikel (refereegranskat)abstract
- Reading out the parity degree of freedom of Majorana bound states is key to demonstrating their non-Abelian exchange properties. Here, we present a low-energy model describing localized edge states in a two-arm device. We study parity-to-charge conversion based on coupling the superconductor bound states to a quantum dot whose charge is read out by a sensor. The dynamics of the system, including the readout device, is analyzed in full using a quantum-jump approach. We show how the resulting signal and signal-to-noise ratio differentiates between local Majorana and Andreev bound states.
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| 17. |
- Schulenborg, Jens, et al.
(författare)
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Multilevel effects in quantum dot based parity-to-charge conversion of Majorana box qubits
- 2021
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Ingår i: Physical Review B. - 2469-9950. ; 103:24
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Tidskriftsartikel (refereegranskat)abstract
- Quantum dot based parity-to-charge conversion is a promising method for reading out quantum information encoded nonlocally into pairs of Majorana zero modes. To obtain a sizable parity-to-charge visibility, it is crucial to tune the relative phase of the tunnel couplings between the dot and the Majorana modes appropriately. However, in the presence of multiple quasidegenerate dot orbitals, it is in general not experimentally feasible to tune all couplings individually. This paper shows that such configurations could make it difficult to avoid a destructive multiorbital interference effect that substantially reduces the readout visibility. We analyze this effect using a Lindblad quantum master equation. This exposes how the experimentally relevant system parameters enhance or suppress the visibility when strong charging energy, measurement dissipation, and, most importantly, multiorbital interference is accounted for. In particular, we find that an intermediate-time readout could mitigate some of the interference-related visibility reductions affecting the stationary limit.
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| 18. |
- Seoane Souto, Ruben, et al.
(författare)
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Timescales for charge transfer based operations on Majorana systems
- 2020
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Ingår i: Physical Review B - Condensed Matter and Materials Physics. - 1550-235X.
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Tidskriftsartikel (refereegranskat)abstract
- In this Rapid Communication we analyze the efficiency of operations based on transferring charge from a quantum dot (QD) to two coupled topological superconductors, which can be used for performing non-Abelian operations on Majorana bound states (MBSs). We develop a method which allows us to describe the full time evolution of the system as the QD energy is manipulated. Using a full counting statistics analysis, we set bounds to the operation timescales. The lower bound depends on the superconducting phase difference due to a partial decoupling of the different MBS parity sectors, while the upper bound is set by the tunneling of quasiparticles to the MBSs. Using realistic parameters, we find the existence of a regime where the operation can be carried out with a fidelity close to unity. Finally, we propose the use of a two-operation protocol to quantify the effect of the dephasing and accumulated dynamical phases, demonstrating their absence for certain superconducting phase differences.
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| 19. |
- Souto, Rubén Seoane, et al.
(författare)
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Multiterminal transport spectroscopy of subgap states in Coulomb-blockaded superconductors
- 2022
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Ingår i: Physical Review B. - 2469-9950. ; 106:23
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Tidskriftsartikel (refereegranskat)abstract
- Subgap states are responsible for the low-bias transport features of hybrid superconducting-semiconducting devices. Here we analyze the local and nonlocal differential conductance of Coulomb-blockaded multiterminal superconducting islands that host subgap states with different spatial structures. The emerging patterns of their transport spectroscopy are used to characterize the possible topological nature of these devices and offer the possibility of controlling their transport properties. We develop a next-to-leading order master equation to describe the multiterminal transport in superconductors with both strong Coulomb interactions and multiple subgap states, coupled with metallic leads. We show that the nonlocal differential conductance characterizes the spatial extension of the subgap states and signals the presence of degenerate bound states with a finite support on different parts of the device. Additionally, it displays sharp sign changes as a function of the induced charge of the superconductor, signaling energy crossings among its lowest excited states.
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| 20. |
- Spånslätt, Christian, 1987-
(författare)
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Topological states of matter in low dimensions
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A central theme in condensed matter physics is the classification and characterization of states of matter. In the recent decades, it has become evident that there exists a large class of quantum mechanical systems that must be classified according to properties deeply rooted in the mathematical field of topology, rather than in terms of which symmetries they break. Together with rapid technological developments, such topological states of matter pose a promising path for a fundamentally new generation of quantum devices and exotically engineered materials, with applications in quantum metrology, quantum sensing, and quantum computations.This doctoral thesis comprises a study of a general theoretical framework describing topological states of matter, followed by applications in systems of low dimension. Together, these two parts form the foundation for the following accompanying papers:PAPERS I-II concerns Majorana zero modes in various Josephson junction setups of one-dimensional topological superconductors. In addition to determining the mathematical conditions for the existence of such exotic states, the papers also provide experimental proposals for their detection. PAPER III deals with the nature of a widely used model of a synthetically engineered one-dimensional topological superconductor. It is shown that in a certain parameter limit, the superconducting order parameter obtains a geometric contribution, which originates from the directional nature of the Rashba spin-orbit coupling. This geometrical dependence is argued to manifest itself in various Josephson junction setups, and in particular as a direct connection between the charge current density and the local curvature.PAPER IV proposes a method of constructing non-local order parameters for two-dimensional Chern insulators, and describes how such operators can be used to distinguish between different topological sectors.
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| 21. |
- Tsintzis, Athanasios, et al.
(författare)
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Majorana Qubits and Non-Abelian Physics in Quantum Dot-Based Minimal Kitaev Chains
- 2024
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Ingår i: PRX Quantum. - 2691-3399. ; 5:1
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Tidskriftsartikel (refereegranskat)abstract
- The possibility of engineering artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of topological superconducting phases in other platforms. Although a true topological phase would require long chains, a two-site chain realized in a double quantum dot can already be tuned to points in parameter space where it hosts zero-energy states that seem identical to the Majorana bound states that characterize a topological phase. These states have been named "poor man's Majorana bound states"(PMMs) because they lack formal topological protection. In this work, we propose a pathway for next-generation experiments on PMMs. The pathway starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality and then moves on to initialization and readout of the parity of a PMM pair, which allows the measurement of quasiparticle poisoning times. The next step is to couple two PMM systems to form a qubit. We discuss measurements of the coherence time of such a qubit, as well as a test of Majorana fusion rules in the same setup. Finally, we propose and analyze three different types of braidinglike experiments that require more complex device geometries. Our conclusions are supported by calculations based on a realistic model with interacting and spinful quantum dots, as well as by simpler models to gain physical insight. Our calculations show that it is indeed possible to demonstrate non-Abelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. However, our findings also reveal that doing so requires some extra care, appropriately modified protocols, and awareness of the details of this particular platform.
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