Majorana Zero Modes Protected by Hopf Invariant in Topologically Trivial Superconductors

Majorana zero modes are usually attributed to topological superconductors. We study a class of two-dimensional topologically trivial superconductors without chiral edge modes, which nevertheless host robust Majorana zero modes in topological defects. The construction of the specific single-band model is facilitated by the Hopf map and the Hopf invariant. This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.

Comments: 11 pages, 6 figures

Similar Publications

We show, that in contrast to the free electron model (standard BCS model), a particular gap in the spectrum of multiband superconductors opens at some distance from the Fermi energy, if conduction band is composed of hybridized atomic orbitals of different symmetries. This gap has composite superconducting-hybridization origin, because it exists only if both the superconductivity and the hybridization between different kinds of orbitals are present. So for many classes of superconductors with multiorbital structure such spectrum changes should take place. Read More

We propose potential geometry for fabrication of the graphite sheets with atomically smooth edges. For such sheets with Bernal stacking, the electron-electron interaction and topology should cause sufficiently high density of states resulting in the high temperature of either spin ordering or superconducting pairing. Read More

We study noncentrosymmetric superconductors with the tetrahedral $T_d$, tetragonal $C_{4v}$, and cubic point group $O$. The order parameter is computed self-consistently in the bulk and near a surface for several different singlet to triplet order parameter ratios. It is shown that a second phase transition below $T_c$ is possible for certain parameter values. Read More

The Gutzwiller wave function solution of the $t$-$J$-$U$ model is considered for the bilayer high-T$_C$ superconductor by using the so-called diagrammatic expansion method. The focus is on the influence of the interlayer effects on the superconducting state. The chosen pairing symmetry is a mixture of $d_{x^2-y^2}$ symmetry within the layers and the so-called $s^{\pm}$ symmetry for the interlayer contribution. Read More

Following the idea that hydrogen-rich compounds might be high-T$_c$ superconductors at high pressures, and the very recent breakthrough in predicting and synthesizing hydrogen sulfide with record-high T$_c$ = 203 K, ab initio evolutionary algorithm for crystal structure prediction was employed to find stable germanium hydrides. In addition to the earlier structure of germane with space group Ama2, we propose a new C2/m structure, which is energetically more favorable at pressures above 278 GPa (with inclusion of zero point energy). Our calculations indicate metallicity of the new C2/m phase of germane with T$_c$ = 67 K at 280 GPa. Read More

We calculate the energy of threshold fluctuation $\delta F_{thr}$ which triggers the transition of superconducting current-carrying bridge to resistive state. We find that dependence of $\delta F_{thr}$ on current $I$ is sensitive to presence of defects in the bridge (such as the inhomogeneity of local critical temperature $T_c$, variation of thickness/width or mean path length) and changes from $\delta F_{thr}\propto(1-I/I_c)^{5/4}$, which is valid for defectless bridge with length $L \gg \xi$ ($\xi$ is a coherence length), to $\propto(1-I/I_c)^{3/2}$, typical for a Josephson junction or short bridge with $L \ll \xi$ (here $I_c$ is the critical current of the bridge or Josephson junction). We also show that the relation $\delta F_{thr}(I=0)\propto I_c\hbar/e$ remains valid in broad temperature range for long and short bridges and both in dirty and clean limits. Read More

We report on the electronic transport and the impact of spin-filtering in mesa-structures made of epitaxial thin films of cuprate superconductor YBa2Cu3Ox(YBCO) and the manganite LaMnO3 (LMO) interlayer with the Au/Nb counterelectrode. Ferromagnetic resonance measurements of heterostructure Au/LMO/YBCO shows ferromagnetic state at temperatures below 150 K as in the case of reference LMO film grown on the neodymium gallate substrate. The heights of the tunneling barrier evaluated from resistive characteristics of mesa-structures at different thickness of interlayer showed an exponential decrease from 30 mV down to 5 mV with the increase of manganite interlayer thickness. Read More

We discuss the stability of highly degenerate zero-energy states tha appear at the surface of a nodal superconductor preserving time-reversal symmetry. The existence of such surface states is a direct consequence of the nontrivial topological numbers defined in the restricted Brillouin zones in the clean limit. In experiments, however, potential disorder is inevitable near the surface of a real superconductor, which may lift the high degeneracy at zero energy. Read More

We describe an approach, based on direct numerical solution of the Usadel equation, to finding stationary points of the free energy of superconducting nanorings. We consider both uniform (equilibrium) solutions and the critical droplets that mediate activated transitions between them. For the uniform solutions, we compute the critical current as a function of the temperature, thus obtaining a correction factor to Bardeen's 1962 interpolation formula. Read More

Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves via a learning process. Here we propose the implementation of basic protocols in quantum reinforcement learning, with superconducting circuits employing feedback-loop control. Read More