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Register a new userVortex-Core Charging Due to the Lorentz Force in a $d$-Wave Superconductor
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We derive augmented quasiclassical equations of superconductivity with the Lorentz force in the Matsubara formalism so that the charge redistribution due to supercurrent can be calculated quantitatively. Using it, we obtain an analytic expression for the vortex-core charge of an isolated vortex in extreme type-II materials given in terms of the London penetration depth and the equilibrium Hall coefficient. It depends strongly on the Fermi surface curvature and gap anisotropy, and may change sign even as a function of temperature due to the variation in the excitation curvature under the growing energy gap. This is also confirmed in our numerical study of high-$T_{rm c}$ superconductors.
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Quasiparticle states around a single vortex in a $p_xpm i p_y$-wave superconductor are studied on the basis of the Bogoliubov-de Gennes (BdG) theory, where both charge and current screenings are taken into account. Due to the violation of time reversal symmetry, there are two types of vortices which are distinguished by their winding orientations relative to the angular momentum of the chiral Cooper pair. The BdG solution shows that the charges of the two types of vortices are quite different, reflecting the rotating Cooper pair of the $p_xpm i p_y$-wave paring state.
As a model for the vortex core in MgB2 we study a two band model with a clean sigma band and a dirty pi band. We present calculations of the vortex core size in both bands as a function of temperature and show that there exists a Kramer-Pesch effect in both bands even though only one of the bands is in the clean limit. We present calculations for different pi band diffusivities and coherence lengths.
The Majorana fermion, which is its own anti-particle and obeys non-abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor, due to contamination from impurity states or other closely-packed Caroli-de Gennes-Matricon (CdGM) states, which hampers further manipulations of Majorana fermions. Here using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect free regions of (Li0.84Fe0.16)OHFeSe, which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can be naturally attributed to a MZM arising from this chiral topological surface states of a bulk superconductor. (Li0.84Fe0.16)OHFeSe thus provides an ideal platform for studying MZMs and topological quantum computing.
We study the effects of non-magnetic impurity scattering on the Andreev bound states (ABS) in an isolated vortex in a two-dimensional chiral p-wave superconductor numerically. We incorporate the impurity scattering effects into the quasiclassical Eilenberger formulation through the self-consistent $t$-matrix approximation. Within this scheme, we calculate the local density of states (LDOS) around two types of vortices: parallel (anti-parallel) vortex where the phase winding of the pair-potential coming from vorticity and that coming from chirality have the same (opposite) sign. When the scattering phase-shift $delta_0$ of each impurity is small, we find that impurities affect differently low energy quasiparticle spectrum around the two types of vortex in a way similar to that in the Born limit ($delta_0rightarrow 0$). For a larger $delta_0(leq pi/2)$ however we find that ABS in the vortex is strongly suppressed by impurities for both types of vortex. We found that there are some correlations between the suppression of ABS near vortex cores and the low energy density of states due to impurity bands in the bulk.
We probe the short-range pinning properties with the application of microwave currents at very high driving frequencies (47.7 GHz) on YBa$_2$Cu$_3$O$_{7-delta}$ films with and without sub-micrometer BaZrO$_3$ inclusions. We explore the temperature and field ranges 60 K$<T<T_c$ and 0$<mu_0H<$0.8 T, with the field applied along the c-axis. The magnetic field induces a much smaller increase of the microwave resistivity, $Delta rho_1(H)+mathrm{i}Delta rho_2(H)$, in YBa$_2$Cu$_3$O$_{7-delta}$/BaZrO$_3$ with respect to pure YBa$_2$Cu$_3$O$_{7-delta}$. $Delta rho_1(H)$ is slightly superlinear in pure YBa$_2$Cu$_3$O$_{7-delta}$ (suggesting a possible contribution of thermal activation), but linear or sublinear in YBa$_2$Cu$_3$O$_{7-delta}$/BaZrO$_3$ (suggesting a possible suppression of thermal activation as a consequence of BaZrO$_3$ inclusions). These features persist up to close to $T_c$. We discuss our data in terms of the ratio $r=Delta X_s(H)/Delta R_s(H)$ in the framework of the models for the microwave surface impedance in the mixed state. Large $r$ are found in YBa$_2$Cu$_3$O$_{7-delta}$/BaZrO$_3$, with little field dependence. By contrast, smaller values and stronger field dependences are found in pure YBa$_2$Cu$_3$O$_{7-delta}$. We discuss the different field dependence of the pinning constant.
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