Classification of engineered topological superconductors

I perform a complete classification of 2d, quasi-1d and 1d topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin-orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1d systems with Rashba spin-orbit coupling and time-reversal violating superconductivity, as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional "hidden" symmetries emerge, with a significant impact on the topological properties of the system. The latter, generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries.Comment: To appear in New Journal of Physics for the Focus on Majorana Fermions in Condensed Matter; Final version 19 pages, 6 figures: a new section was added concerning the appearance of MFs in two coupled Rasba semiconducting wires with proximity induced superconductivity and a finite supercurrent flow, without the application of a magnetic field. Generally improved discussion and references adde

Chirality Induced Tilted-Hill Giant Nernst Signal

We reveal a novel source of giant Nernst response exhibiting strong non-linear temperature and magnetic field dependence including the mysterious tilted-hill temperature profile observed in a pleiad of materials. The phenomenon results directly from the formation of a chiral ground state, e.g. a chiral d-density wave, which is compatible with the eventual observation of diamagnetism and is distinctly different from the usual quasiparticle and vortex Nernst mechanisms. Our picture provides a unified understanding of the anomalous thermoelectricity observed in materials as diverse as hole doped cuprates and heavy-fermion compounds like URu2Si2.Comment: 5 pages and 4 figures, Final version accepted by Phys. Rev. Let

Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface

We investigate the topological properties and the accessible Majorana fermion (MF) phases arising in a hybrid device consisting of a chain of magnetic adatoms placed on the surface of a conventional superconductor with Rashba spin-orbit coupling (SOC). By identifying the favored classical magnetic ground state of the adatom chain, we extract the corresponding phase diagram which exhibits an interplay of ferromagnetic (FM), antiferromagnetic (AFM) and spiral orders. We determine the parameter regime for which the FM or AFM phases dominate over the spiral and additionally become stable against thermal and quantum fluctuations. For the topological analysis we focus on the FM and AFM cases and employ a low-energy effective model relying on Shiba bound states. We find that for both magnetic patterns the hybrid system behaves as a topological superconductor which can harbor one or even two MFs per edge, due to chiral symmetry. As we show, the two magnetic orderings lead to qualitatively and quantitatively distinct topological features that are reflected in the spatial profile of the MF wavefunctions. Finally, we propose directions on how to experimentally access the diverse MF phases by varying the adatom spacing, the SOC strength, or the magnetic moment of the adatoms in consideration.Comment: 18 pages, 14 figure

Magnetic-Field-Induced Topological Reorganization of a P-wave Superconductor

In this work we illustrate the detrimental impact of the Cooper pair's spin-structure on the thermodynamic and topological properties of a spin-triplet superconductor in an applied Zeeman field. We particularly focus on the paradigmatic one-dimensional case (Kitaev chain) for which we self-consistently retrieve the energetically preferred Cooper pair spin-state in terms of the corresponding spin d-vector. The latter undergoes a substantial angular and amplitude reorganization upon the variation of the strength and the orientation of the field and results to a modification of the bulk topological phase diagram. Markedly, when addressing the open chain we find that the orientation of the d-vector varies spatially near the boundary, affecting in this manner the appearance of Majorana fermions at the edge or even altering the properties of the bulk region. Our analysis reveals the limitations and breakdown of the bulk-boundary correspondence in interacting topological systems.Comment: 5 pages, 3 panels of figures; Minor corrections in the new version, which will appear in Phys. Rev. B as a Rapid Communicatio

New mechanisms to engineer magnetic skyrmions and topological superconductors

We propose an alternative route to stabilize magnetic skyrmions which does not require Dzyaloshinkii-Moriya interactions, magnetic anisotropy, or an external Zeeman field. Our so-called magnetic skyrmion catalysis (MSC) solely relies on the emergence of flux in the system's ground state. We review scenarios that allow for a nonzero flux and summarize the magnetic skyrmion phases that it induces. Among these, we focus on the so-called skyrmionic spin-whirl crystal (Sk-SWC$_4$) phase. We discuss aspects of MSC using a concrete model for topological superconductivity, which describes the surface states of a topological crystalline insulator in the presence of proximity induced pairing. By assuming that the surface states can exhibit the Sk-SWC$_4$ phase, we detail how the addition of a pairing gap generates a chiral superconductor. For this purpose, we construct a low-energy model which renders the mechanism for topological superconductivity transparent. Moreover, by employing this model, we perform a self-consistent investigation of the appearance of the Sk-SWC$_4$ phase for different values of the pairing gap and the ground state's flux. Our analysis verifies the catalytic nature of our mechanism in stabilizing the Sk-SWC$_4$ phase, since the magnetization modulus becomes enhanced upon ramping up the flux. The involvement of MSC further shields magnetism against the suppression induced by the pairing gap. Remarkably, even if the pairing gap fully suppresses the Sk-SWC$_4$ phase for a given value of flux, this skyrmion phase can be restored by further increasing the flux. Our findings demonstrate that MSC enables topological superconductivity in a minimal and robust fashion.Comment: 20 pages, 2 figures, Proceedings SPIE 12656, Spintronics XVI (San Diego USA

Hybridization at superconductor-semiconductor interfaces

Hybrid superconductor-semiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of the two materials, as well as the electrostatic environment, which are currently not well understood. Here, we pursue to fill in this gap and address the role of band bending and superconductor-semiconductor hybridization in such devices by analyzing a gated single Al-InAs interface using a self-consistent Schrodinger-Poisson approach. Our numerical analysis shows that the band bending leads to an interface quantum well, which localizes the charge in the system near the superconductor-semiconductor interface. We investigate the hybrid band structure and analyze its response to varying the gate voltage and thickness of the Al layer. This is done by studying the hybridization degrees of the individual subbands, which determine the induced pairing and effective $g$-factors. The numerical results are backed by approximate analytical expressions which further clarify key aspects of the band structure. We find that one can obtain states with strong superconductor-semiconductor hybridization at the Fermi energy, but this requires a fine balance of parameters, with the most important constraint being on the width of the Al layer. In fact, in the regime of interest, we find an almost periodic dependence of the hybridization degree on the Al width, with a period roughly equal to the thickness of an Al monolayer. This implies that disorder and shape irregularities, present in realistic devices, may play an important role for averaging out this sensitivity and, thus, may be necessary for stabilizing the topological phase.Comment: 10 Figures. 16 pages. Published versio

Superfluid Stiffness and Josephson Quantum Capacitance: Adiabatic Approach and Topological Effects

We bring forward a unified framework for the study of the superfluid stiffness and the quantum capacitance of superconducting platforms exhibiting conventional spin-singlet pairing. We focus on systems which in their normal phase contain topological band touching points or crossings, while in their superconducting regime feature a fully gapped energy spectrum. Our unified description relies on viewing these two types of physical quantities as the charge current and density response coefficients obtained for ``slow" spatiotemporal variations of the superconducting phase. Within our adiabatic formalism, the two coefficients are given in terms of Berry curvatures defined in synthetic spaces. Our work lays the foundations for the systematic description of topological diagonal superfluid responses induced by singularities dictating the synthetic Berry curvatures. We exemplify our approach for concrete one- and two-dimensional models of superconducting topological (semi)metals. We discuss topological phenomena which arise in the superfluid stiffness of bulk systems and the quantum capacitance of Josephson junctions. We show that both coefficients become proportional to a topological invariant which counts the number of topological touchings/crossings of the normal phase band structure. These topological effects can be equivalently viewed as manifestations of chiral anomaly. Our predictions are experimentally testable in graphene-superconductor hybrids.Comment: 21 pages, 4 figures, and 4 appendices. This work accompanies preprint arXiv:2211.07676v3 which appears on the same day. Some parts of this work have been transferred from arXiv:2211.07676v