Periodic Reporting for period 3 - ProMotion (Probing Majorana quasi-particles and ballistic spin-momentum locking in topolocical insulatornanostructures)
Período documentado: 2021-07-01 hasta 2022-12-31
In this project, we explore alternative ways – based on merging topological insulators (TIs) and conventional superconductors – to realize topological superconductivity and thus structures, which host Majorana bound states (MBS). The central goal is to conduct experiments that can detect these MBS. With two pairs of MBS, quantum-bits (qubits) can be constructed, which are less prone to disturbances of the environment. Thus, besides being objects of intense physical interest, MBS might also serve as a platform for fault-tolerant quantum computing.
The reporting period extends from 1.7.2018 to 31.12.2020. As material bases for our experiments, we use thin, strained films of HgTe, a strong topological insulator (TI), which features Dirac surface states with unrivaled charge carrier mobility giving rise to pronounced quantum effects like quantum Hall effect and Shubnikov-de Haas oscillations. Utilizing a top gate, the Fermi level can be tuned from the valence band via the Dirac surface states into the conduction band and allows studying Landau quantization in situations where different species of charge carriers contribute to magnetotransport. Recent work gives an overview of the various quantum effects that result from the interaction of the different types of charge carriers and forms the basis for the characterization of the material we use for nanofabrication. In addition to these studies, we have also investigated - via quantum capacitance measurements - the density of states of BiSbTeSe_2 (BSTS), an alternative to our HgTe material basis.
For probing MBS, we pursue four main thrusts: For two, we need one-dimensional wire structures that contain only a few modes and show resistance quantization. For that, we must engrave narrow constrictions into the HgTe films with a small cross-sectional area through which the electrical current is flowing. Such constriction we made for different thicknesses of the HgTe films ranging from 30 nm to (our standard) thickness of 80 nm and varied the width of the constrictions. Here we are still in the phase of optimizing the thickness of the layers and the etching parameters. The aim here is to reduce the effect of conductance fluctuations to be able to see the quantized conductance through the narrow constrictions.
In a third approach, we explore the presence of MBS in HgTe wires using the fractional ac Josephson effect. This experiment relies on the band structure of the wires, which features a gap at zero magnetic fields (flux). In this situation the energy spectrum of the system is trivial. This changes if a magnetic flux ϕ corresponding to half a magnetic flux quantum (ϕ=h/2e, with h = Planck’s constant and e = elementary charge) threads the wires’ cross-section. For half a flux quantum the gap closes and so-called perfectly transmitted modes appear, which render the energy spectrum into a topologically non-trivial one. If combined with a conventional superconductor this means that one can switch in the proximitized region of the wire between trivial and non-trivial topological superconductivity by simply adding half a flux quantum. When such wires are used as the normal unit of a planar Josephson junction, MBS are expected to occur at the boundaries between the superconducting contacts and the normal region. Theory predicts that in this situation, besides a 2π-periodic supercurrent, a 4π-periodic current also flows. The periodicity of the involved supercurrents is probed via the Shapiro steps, which occur in the I-V characteristics under microwave irradiation. Presently we have established samples and all the experimental setups to conduct these experiments. At zero magnetic field, we observe, surprisingly, that a small fraction of the supercurrent is 4π-periodic. This might indicate ballistic transport and/or Landau Zener transitions between upper and lower branches of the Andreev bound states. Our preliminary experiments also show that the fraction of the 4π-periodic can be tuned by the magnetic flux.
In our fourth experiment, we use a completely different approach, which relies on pinning magnetic flux in a hybrid structure consisting of HgTe covered with a superconducting film with periodically arranged holes (antidots). MBS bind to these magnetic vortices and should give rise to measurable changes in the electronic density of states. Here, we so far managed to fabricate corresponding devices and to show that magnetic vortices are pinned by the array. Measurements of the density of states in this system are still in their infancy.
For probing MBS, we pursue four main thrusts: For two, we need one-dimensional wire structures that contain only a few modes and show resistance quantization. For that, we must engrave narrow constrictions into the HgTe films with a small cross-sectional area through which the electrical current is flowing. Such constriction we made for different thicknesses of the HgTe films ranging from 30 nm to (our standard) thickness of 80 nm and varied the width of the constrictions. Here we are still in the phase of optimizing the thickness of the layers and the etching parameters. The aim here is to reduce the effect of conductance fluctuations to be able to see the quantized conductance through the narrow constrictions.
In a third approach, we explore the presence of MBS in HgTe wires using the fractional ac Josephson effect. This experiment relies on the band structure of the wires, which features a gap at zero magnetic fields (flux). In this situation the energy spectrum of the system is trivial. This changes if a magnetic flux ϕ corresponding to half a magnetic flux quantum (ϕ=h/2e, with h = Planck’s constant and e = elementary charge) threads the wires’ cross-section. For half a flux quantum the gap closes and so-called perfectly transmitted modes appear, which render the energy spectrum into a topologically non-trivial one. If combined with a conventional superconductor this means that one can switch in the proximitized region of the wire between trivial and non-trivial topological superconductivity by simply adding half a flux quantum. When such wires are used as the normal unit of a planar Josephson junction, MBS are expected to occur at the boundaries between the superconducting contacts and the normal region. Theory predicts that in this situation, besides a 2π-periodic supercurrent, a 4π-periodic current also flows. The periodicity of the involved supercurrents is probed via the Shapiro steps, which occur in the I-V characteristics under microwave irradiation. Presently we have established samples and all the experimental setups to conduct these experiments. At zero magnetic field, we observe, surprisingly, that a small fraction of the supercurrent is 4π-periodic. This might indicate ballistic transport and/or Landau Zener transitions between upper and lower branches of the Andreev bound states. Our preliminary experiments also show that the fraction of the 4π-periodic can be tuned by the magnetic flux.
In our fourth experiment, we use a completely different approach, which relies on pinning magnetic flux in a hybrid structure consisting of HgTe covered with a superconducting film with periodically arranged holes (antidots). MBS bind to these magnetic vortices and should give rise to measurable changes in the electronic density of states. Here, we so far managed to fabricate corresponding devices and to show that magnetic vortices are pinned by the array. Measurements of the density of states in this system are still in their infancy.
Already our experiment on the transport properties of extended strained HgTe films clarified some misconceptions, which can be found in the literature regarding the electrostatics of the system. On the nanostructured samples, the experiments on the fractional Josephson effect on HgTe wires have progressed the furthest so far. The suppression of Shapiro steps can be observed, and we expect to systematically probe the evolution of the 4π-periodic supercurrent – an indicator of topological superconductivity – as a function of the axial magnetic flux soon. If successful, this would constitute an important step towards using topological insulator wires as an element for topological qubits. The other experiments which are not yet so far advanced, could support this scenario and provide additional information.