A superconductor with $p_x+ip_y$ order has long fascinated the physics community because vortex defects in such a system host Majorana zero modes. Here we propose a simple construction of a chiral superconductor using proximitized quantum wires and twist angle engineering as basic ingredients. We show that a weakly coupled parallel array of such wires forms a gapless $p$-wave superconductor. Two such arrays, stacked on top of one another with a twist angle close to $90^\circ$, spontaneously break time reversal symmetry and form a robust, fully gapped $p_x+ip_y$ superconductor. We map out topological phases of the proposed system, demonstrate existence of Majorana zero modes in vortices, and discuss prospects for experimental realization.
Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
We analyze theoretically two different setups for s-wave superconductivity (SC) proximitized $j=3/2$ particles in Luttinger materials that are able to host Majorana bound states (MBSs). First, we consider a one-dimensional SC wire with intrinsic bulk inversion asymmetry (BIA). In contrast to wires, modeled by a quadratic dispersion with Rashba spin-orbit coupling, there are two topological phase transitions in our systems at finite magnetic fields. Second, we analyze a two-dimensional Josephson junction on the Luttinger model finding a topological region even in the absence of BIA and Rashba s…
We explore in detail the electronic phases of a system consisting of three non-colinear arrays of coupled quantum wires, each rotated 120 degrees with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a $s$-wave or $d \pm id$ superconductor, a charge density wave insulator, a two-dimensional Fermi liquid, and a 2D Luttinger liquid (also known as smectic metal or sliding Luttinger liquid). The model provides an effective description of electronic interactions in small-angle twisted bilayer graphene and we discuss its im…
We study the formation of Majorana states in superconductors using the Majorana polarization, which can locally evaluate the Majorana character of a given state. We introduce the definition of the Majorana polarization vector and the corresponding criterion to identify a Majorana state, and we apply it to some simple cases such as a one-dimensional wire with spin-orbit coupling, subject to a Zeeman magnetic field, and proximitized by a superconductor, as well as to an NS junction made with such a wire. We also apply this criterion to two-dimensional finite-size strips and squares subject to th…
Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as $(i)$ a tool for revealing the nature of correlated insulators and $(ii)$ a platform for Majorana-based topological qubits. In particular, we show that the band structure of a gate-defined wire immersed in an `inter-valley coherent' correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the …
Among the different platforms to engineer Majorana fermions in one-dimensional topological superconductors, topological insulator nanowires remain a promising option. Threading an odd number of flux quanta through these wires induces an odd number of surface channels, which can then be gapped with proximity induced pairing. Because of the flux and depending on energetics, the phase of this surface pairing may or may not wind around the wire in the form of a vortex. Here we show that for wires with discrete rotational symmetry, this vortex is necessary to produce a fully gapped topological supe…
Realizing Majorana modes in topological superconductors, i.e., the condensed-matter counterpart of Majorana fermions in particle physics, may lead to a major advance in the field of topologically-protected quantum computation. Here, we introduce one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized nanowires via periodically-modulated fields. This system realizes centrally-extended quantum-mechanical supersymmetry with spontaneous partial supersymmetry breaking. The ma…
Topological quantum computation using non-Abelian Majorana zero modes localized in proximitized semiconductor nanowires requires careful electrostatic control of wire-junctions so as to manipulate and braid the zero modes enabling anyonic fault-tolerant gate operations. We theoretically investigate the topological superconducting properties of such elementary wire-junctions, the so-called T junctions, finding that the existence of the junction may nonperturbatively affect the Majorana behavior by introducing spurious non-topological subgap states mimicking zero-modes. We propose a possible sol…
We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires …
We study a realistic Floquet topological superconductor, a periodically driven nanowire proximitized to an equilibrium s-wave superconductor. Due to both strong energy and density fluctuations caused from the superconducting proximity effect, the Floquet Majorana wire becomes dissipative. We show that the Floquet band structure is still preserved in this dissipative system. In particular, we find that both the Floquet Majorana zero and pi modes can no longer be simply described by the Floquet topological band theory. We also propose an effective model to simplify the calculation of the lifetim…
The growing interest in the modeling of superconductors has led to the development of effective numerical methods and software. One of the most utilized approaches for magnetoquasistatic simulations in applied superconductivity is the $H$ formulation. However, due to the large number of degrees of freedom (DOFs) present when modeling large and complex systems (e.g. large coils for fusion applications, electrical machines, and medical applications) using the standard $H$ formulation on a desktop machine becomes infeasible. The $H$ formulation solves the Faraday's law formulated in terms of the …
A semiconducting nanowire proximitized by an $s$-wave superconductor can be tuned into a topological state by an applied magnetic field. This quantum phase transition is marked by the emergence of Majorana zero modes at the ends of the wire. The fusion of Majorana modes at a junction between two nanowires results in a $4π$-periodic Josephson effect. We elucidate how the $4π$-periodicity arises across the topological phase transition in a highly-transparent short nanowire junction. Owing to a high transmission coefficient, Majorana zero modes coming from different wires are strongly coupled, wi…
The engineering of non-trivial topology in superconducting heterostructures is a very challenging task. Reducing the number of components in the system would facilitate the creation of the long-sought Majorana bound states. Here, we explore a route toward emergent topology in a trivial superconductor without a need for other proximitized materials. Specifically, we show that a vortex hosting an even number of flux quanta is capable of forming a quasi-one-dimensional topological sub-system that can be mapped to the Kitaev wire, if the vortex is trapped at a screw dislocation. This crystallograp…
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers [1]. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposa…
A one-dimensional semiconductor nanowire proximitized by a nearby superconductor may become a topological superconductor hosting localized Majorana zero modes at the two wire ends in the presence of spin-orbit coupling and Zeeman spin splitting (arising from an external magnetic field). The hallmark of the presence of such Majorana zero modes is the appearance of a zero-temperature quantized zero-bias conductance peak in the tunneling spectroscopy of the Majorana nanowire. We theoretically study the temperature and the tunnel coupling dependence of the tunneling conductance in such nanowires t…
We propose a targeted attack on making the Fe-based superconductor (FBS) AEFe2As2 (122) (AE = alkaline earth, here Ba or Sr) into a much cheaper, higher stability margin, round, twisted and effectively isotropic multifilament conductor suitable for 16-20 T dipole magnet construction. This white paper urges to greatly accelerate progress by providing a fundamental understanding of what controls the transport critical current density, Jc, of 122 polycrystals and then in the wire forms. High grain-to-grain Jc is the one key property not yet fully demonstrated in this new superconductor and this i…
