Uniformly Frustrated XY Model: Strengthening of the Vortex Lattice by Intrinsic Disorder

In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice form, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature Tc increases with the applied field H, for strong enough pinning, the experimental decreasing dependence between Tc and H is recovered with a resulting more robust vortex lattice.

Mass of Abrikosov vortex in high-temperature superconductor YBa$$_2$$Cu$$_3$$O$$_{7-\delta }$$

For more than four decades, mass of Abrikosov vortices defied experimental observations. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBa$$_2$$ 2 Cu$$_3$$ 3 O$$_{7-\delta }$$ 7 - δ film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of $$2.2 \times 10^8$$ 2.2 × 10 8 electron masses per centimeter at 45 K and zero-frequency limit, and even larger off-diagonal mass of $$4.9 \times 10^8 m_e$$ 4.9 × 10 8 m e /cm.

The Abrikosov vortex in curved space

We study the self-gravitating Abrikosov vortex in curved space with and with-out a (negative) cosmological constant, considering both singular and non-singular solutions with an eye to hairy black holes. In the asymptotically flat case, we find that non-singular vortices round off the singularity of the point particle’s metric in 3 dimensions, whereas singular solutions consist of vortices holding a conical singularity at their core. There are no black hole vortex solutions. In the asymptotically AdS case, in addition to these solutions there exist singular solutions containing a BTZ black hole, but they are always hairless. So we find that in contrast with 4-dimensional ’t Hooft-Polyakov monopoles, which can be regarded as their higher-dimensional analogues, Abrikosov vortices cannot hold a black hole at their core. We also describe the implications of these results in the context of AdS/CFT and propose an interpretation for their CFT dual along the lines of the holographic superconductor.

Transmission coefficients of superconducting particles

Objectives. There is no general theory of superconductivity capable of fully describing this phenomenon, which imposes its own difficulties in the search for new superconducting materials, as well as in the study of their properties. In particular, the electrodynamics of a superconducting system is unexplored. With the aim of a possible further description of the electrodynamics of superconductors, the temperature dependences of the energy parameters of a Cooper pair in the potential field of Abrikosov vortex were analyzed.Methods. The basis for the obtained results of the work was the consideration of the transmission coefficient for a superconducting particle in the approximation of the Wentzel– Kramers–Brillouin method, as well as the relationship between the critical temperature and the London penetration depth and the coherence length based on the model of plasmon destruction of the superconducting state.Results. The dependences of the lifetime of a particle in a potential well, penetration depth, frequency of impacts of a particle against a potential barrier, blurring of the energy level, transmission coefficient, and potential and kinetic energy of a particle on temperature were obtained. The characteristic values of these parameters were obtained at absolute zero for various cuprate, organic, and other superconducting materials. The dependences of the critical electric potential on temperature, as well as the London penetration depth, coherence length, and electric potential on the transmission coefficient at different temperatures were obtained. The form of the dependences qualitatively corresponds to the experimental data.Conclusions. The results obtained can be used to construct a general theory of superconductivity, describe the electrodynamics of a superconducting state, and develop new superconductors with higher critical currents.

Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

Observation of magnetic adatom-induced Majorana vortex and its fusion with field-induced Majorana vortex in an iron-based superconductor

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the fusion of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and Majorana zero mode induced by magnetic Fe adatoms deposited on the surface and the realization of its fusion with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.