Topological quantum computation, featuring qubits built out of anyonic excitations known as Majorana zero modes (MZMs), have long presented an exciting pathway towards scalable quantum computation. Recently, the advent of altermagnetic materials has presented a new pathway towards localized MZMs on the boundary of two-dimensional materials, consisting of an altermagnetic film, subject to a superconducting proximity effect from a superconducting substrate. In this work, we demonstrate the possibility for an altermagnet-superconductor heterostructure, to not only harbor MZMs, but also freely manipulate their position along the topological boundary of the material, via rotation of the Néel vector. Using this mechanism, on a square platform, we utilize a time-dependent method to simulate the Z-gate via braiding, and then extend this to a larger H-junction, where we implement the $\sqrt{\rm X}$ and $\sqrt{\rm Z}$ gate on a single-qubit system. Further, this structure is eminently scalable to many-qubit systems, thus providing the essential ingredients towards universal quantum computation.
We investigate a heterostructure system with a spin-orbit coupled semiconductor sandwiched by an s-wave superconductor and a ferromagnetic insulator, which supports Majorana fermions (MFs) at the superconducting vortex cores. We propose a scheme of transporting and braiding the MFs, which only requires application of point-like gate voltages in a system with nano-meter patterns. By solving the time-dependent Bogoliubov-de Gennes equation numerically, we monitor the time evolutions of MF wave-functions and show that the braiding of MFs with non-Abelian statistics can be achieved by adiabatic sw…
After a decade of intense theoretical and experimental efforts, demonstrating braiding of Majorana modes remains an unsolved problem in condensed matter physics due to platform specific challenges. In this work, we propose topological superconductor -- magnetic multilayer heterostructures with on-chip microwave cavity readout as a novel platform for initializing, braiding and reading out Majorana modes. Stray fields from a skyrmion in the magnetic layers can nucleate a vortex in the topological superconducting layer. Such a vortex is known to host Majorana bound states at its core. Through ana…
A versatile control of magnetic systems, widely used to store information, can also enable manipulating Majorana bounds states (MBS) and implementing fault-tolerant quantum information processing. The proposed platform relies on the proximity-induced superconductivity in a two-dimensional electron gas placed next to an array of magnetic tunnel junctions (MTJs). A change in the magnetization configuration in the MTJ array creates tunable magnetic textures thereby removing several typical requirements for MBS: strong spin-orbit coupling, applied magnetic field, and confinement by one-dimensional…
Recent experiments have provided evidence for chiral charge order in Kagome superconductors (SCs). This intriguing possibility motivates us to unveil the first pathway to engineer topological superconductivity by harnessing the interplay of charge Chern insulators (CIs) and conventional SCs. We here identify under which conditions a pyramidal SC/CI/SC heterostructure induces an effective 1D spinless p-wave SC that allows pinning Majorana zero modes (MZMs) at termination edges and domain walls. As we reveal, such a MZM track is controlled by the phase difference of the two SCs involved and addi…
Quantum information protected by the topology of the storage medium is expected to exhibit long coherence times. Another feature are topologically protected gates generated through braiding of Majorana bound states. However, braiding requires structures with branched topological segments which have inherent difficulties in the semiconductor-superconductor heterostructures now believed to host Majorana bound states. In this paper, we construct quantum bits taking advantage of the topological protection and non-local properties of Majorana bound states in a network of parallel wires, but without…
In this work, we demonstrate that making a cut (a narrow vacuum regime) in the bulk of a quantum anomalous Hall insulator (QAHI) creates a topologically protected single helical channel with counter-propagating electron modes, and inducing superconductivity on the helical channel through proximity effect will create Majorana zero energy modes (MZMs) at the ends of the cut. In this geometry, there is no need for the proximity gap to overcome the bulk insulating gap of the QAHI to create MZMs as in the two-dimensional QAHI/superconductor (QAHI/SC) heterostructures. Therefore, the topological reg…
The quantum Hall states at filling factors $ν=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. The non-Abelian statistics of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-Pérot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $ν=7/2$. At both $ν=5/2$ and $7/2$ we also examine, for the first time,…
We propose a platform for braiding Majorana non-Abelian anyons based on a heterostructure between a $d$-wave high-$T_c$ superconductor and a quantum spin-Hall insulator. It has been recently shown that such a setup for a quantum spin-Hall insulator leads to a pair of Majorana zero modes at each corner of the sample, and thus can be regarded as a higher-order topological superconductor. We show that upon applying a Zeeman field in the region, these Majorana modes split in space and can be manipulated for braiding processes by tuning the field and pairing phase. We show that such a setup can ach…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from …
We demonstrate operation of a small Fabry-Perot interferometer in which highly coherent Aharonov-Bohm oscillations are observed in the integer and fractional quantum Hall regimes. Using a novel heterostructure design, Coulomb effects are drastically suppressed. Coherency of edge mode interference is characterized by the energy scale for thermal damping, ${T_0=206}mK$ at $ν=1$. Selective backscattering of edge modes originating in the ${N=0,1,2}$ Landau levels allows for independent determination of inner and outer edge mode velocities. Clear Aharonov-Bohm oscillations are observed at fractiona…
We investigate the Josephson effect in TNT and NTN junctions, consisting of topological (T) and normal (N) phases of semiconductor-superconductor 1D heterostructures in the presence of a Zeeman field. A key feature of our setup is that, in addition to the variation of the phase of the superconducting order parameter, we allow the orientation of the magnetic field to change along the junction. We find a novel magnetic contribution to the Majorana Josephson coupling that permits the Josephson current to be tuned by changing the orientation of the magnetic field along the junction. We also predic…
Chiral Majorana edge modes are theoretically proposed to perform braiding operations for the potential quantum computation. Here, we suggest a scheme to regulate trajectories of the chiral Majorana fermion based on a quantum anomalous Hall insulator (QAHI)-topological superconductor heterostructure. An applied external gate voltage to the QAHI region introduces a dynamical phase so that the outgoing Majorana fermions can be prominently tuned to different leads. The trajectory is mechanically analyzed and the electrical manipulation is represented by the oscillating transmission coefficients ve…
Exotic states of topological materials are challenging or impossible to create under ambient conditions.1-4 Moreover, it is unclear whether topological superconductivity, as a critical element for topological quantum computing, exists in any naturally occurring materials.5-7 Although these problems can be overcome through the combination of materials in heterostructures, there are still many requisites, such as low temperatures and specific magnetic fields.8,9 Herein, an intrinsic topological superconductor that does not depend on particular external conditions is demonstrated. It is accomplis…
This is a colloquium-style introduction to the midgap excitations in superconductors known as Majorana fermions. These elusive particles, equal to their own antiparticle, may or may not exist in Nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole excitations. What is needed is a superconductor to hide the charge difference, and a topological (Berry) phase to eliminate the energy difference from zero-point motion. A pair of widely separated Majorana fermions, bound to magnetic or electrostatic defects, has non-Abelian exchange statistic…
Read and Rezayi $Z_k$ parafermion wavefunctions describe $ν=2+\frac{k}{kM+2}$ fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the $ν=2/k$ FQH-superconductor heterostructure and find the superconducting analogue of the $Z_k$ parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional (1D) chains each with a pair of counter-propagating modes. We show that by inducing intra-ch…
