A large part of condensed matter physics concerns itself with understanding the behaviour of electrons in solids and finding ways to control them. However, in mesoscopic systems (i.e., systems with nanometer to micrometre scale), the behaviour of electrons is difficult to predict through the Schrödinger equation. Instead, it is often more fruitful to use an approximate semiclassical theory that re-introduces the concept of particle trajectories into the quantumworld. These trajectories not only depend on the applied external fields but also on the Fermi surface of the material itself. The control over the Fermi surface allows to engineer electron trajectories not present in classical physics and therefore leads to new novel phenomena. For example, in highly anisotropic materials with open Fermi surfaces, the semiclassical trajectories of electrons in a magnetic field are no longer closed but instead move in an oscillating open trajectory that travels from one sample edge to the next. These open trajectories result in magnetoresistance oscillations with a period proportional to the flux passing through the sample—similar to the Aharonov–Bohm effect. However, unlike the Aharonov–Bohm effect, the magnetoresistance oscillations here are not due to interference effects....@en

We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device consists of quantum dots tunnel-coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions implements the universal set of quantum gates defined by Bravyi and Kitaev [1]. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweet spot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.

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Recent measurements of the out-of-plane magnetoresistance of delafossites (PdCoO₂ and PtCoO₂) observed oscillations closely resembling the Aharonov-Bohm effect. Here, we show that the magnetoresistance oscillations are explained by the Bloch-like oscillations of the out-of-plane electron trajectories. We develop a semiclassical theory of these Bloch-Lorentz oscillations and show that they are a consequence of the ballistic motion and quasi-2D dispersion of delafossites. Our model identifies the sample wall scattering to be the most likely factor limiting the visibility of these Bloch-Lorentz oscillations in existing experiments.

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We study the electronic properties of InAs/EuS/Al heterostructures as explored in a recent experiment, combining both spectroscopic results and microscopic device simulations. In particular, we use angle-resolved photoemission spectroscopy to investigate the band bending at the InAs/EuS interface. The resulting band offset value serves as an essential input to subsequent microscopic device simulations, allowing us to map the electronic wave function distribution. We conclude that the magnetic proximity effects at the Al/EuS as well as the InAs/EuS interfaces are both essential to achieve topological superconductivity at zero applied magnetic field. Mapping the topological phase diagram as a function of gate voltages and proximity-induced exchange couplings, we show that the ferromagnetic hybrid nanowire with overlapping Al and EuS layers can become a topological superconductor within realistic parameter regimes. Our work highlights the need for a combined experimental and theoretical effort for faithful device simulations.

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