Jasmin Bedow

Two-dimensional magnet-superconductor hybrids (2D-MSH) are promising candidates to realize devices for topology-based quantum technologies and superconducting spintronics. So far, studies have focused on 2D-MSH systems with collinear ferro- or antiferromagnetic layers. Here, we present the discovery of topological superconductivity in a noncollinear MSH system where a magnetic spiral is realized in an Fe monolayer proximity coupled to a superconducting Ta(110) substrate. By combining low-temperature spin-polarized scanning tunneling spectroscopy with an in-depth theoretical study, we can conclude that the system is in a topological nodal-point superconducting phase with low-energy edge modes. Furthermore, we reveal that for this noncollinear spin texture, these edge modes exhibit a magnetization direction-dependent dispersion. This means that a spatial shift of the magnetic spiral could be used to reverse the chirality of an edge mode in future MSH-based devices.

Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wave functions as well as their expectation values, correlators, and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. We show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our Letter opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any noninteracting superconductor.

The creation of topological quantum gates using Majorana zero modes -- an outstanding problem in the field of topological quantum computing -- relies on our ability to control the braiding process of these particles in time and space. Here, we propose two-dimensional magnet-superconductor hybrid structures as a new platform for the successful implementation of topologically protected √σ_z-, σ_z- and σ_x-quantum gates using Majorana zero modes. We utilize a braiding protocol that makes use of recent advances in the ability to control the spin of individual atoms using electron-spin-resonance techniques. We visualize the braiding process in time and space by computing the non-equilibrium local density of states, which is proportional to the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments.

We demonstrate that checkerboard magnet-superconductor hybrid (MSH) systems possess a rich phase diagram exhibiting both strong topological superconducting (STSC) and topological nodal point superconducting (TNPSC) phases. We show that TNPSC phases exist both for ferromagnetic and antiferromagnetic systems, yielding a plethora of qualitatively different edge mode structures. Checkerboard MSH systems also facilitate the emergence of STSC phases, which can be induced even in the limit of vanishing magnetization. Our results provide a new path for the quantum engineering of topological superconducting phases using atomic manipulation techniques.

The experimental advances in the study of time-dependent phenomena has opened a new path to investigating the complex electronic structure of strongly correlated and topological materials. Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities in s-wave superconductors provide an ideal candidate system to study the response of a system to time-dependent manipulations of the magnetic environment. Here, we show that by imposing a time-dependent change in the magnetic exchange coupling, by changing the relative alignment of magnetic moments in an impurity dimer, or through a periodic drive of the impurity moment, one can tune the system through a time-dependent quantum phase transition, in which the system undergoes a transition from a singlet to a doublet ground state. We show that the electronic response of the system to external perturbations can be imaged through the time-dependent differential conductance, dI(t)/dV, which, in analogy to the equilibrium case, is proportional to a non-equilibrium local density of states. Our results open the path to visualizing the response of complex quantum systems to time-dependent external perturbations.