Searching for Majorana quasiparticles at vortex cores in iron-based superconductors

The unambiguous detection of the Majorana zero mode (MZM), which is essential for future topological quantum computing, has been a challenge in recent condensed matter experiments. The MZM is expected to emerge at the vortex core of topological superconductors as a zero-energy vortex bound state (ZVBS), amenable to detection using scanning tunneling microscopy/spectroscopy (STM/STS). However, the typical energy resolution of STM/STS has made it challenging to distinguish the MZM from the low-lying trivial vortex bound states. Here, we review the recent high-energy-resolution STM/STS experiments on the vortex cores of Fe(Se,Te), where the MZM is expected to emerge, and the energy of the lowest trivial bound states is reasonably high. Tunneling spectra taken at the vortex cores exhibit a ZVBS well below any possible trivial state, suggesting its MZM origin. However, it should be noted that ZVBS is a necessary but not sufficient condition for the MZM; a qualitative feature unique to the MZM needs to be explored. We discuss the current status and issues in the pursuit of such Majorananess, namely the level sequence of the vortex bound states and the conductance plateau of the ZVBS. We also argue for future experiments to confirm the Majorananess, such as the detection of the doubling of the shot noise intensity and spin polarization of the MZM.Comment: 22 pages, 7 figure

Ultrasonic Studies of a Single Crystalline La_<1.85>Sr_<0.15>CuO_4 in High Magnetic Fields(Transport and Fermiology)

Temperature dependence of the sound velocity of a single crystalline La_Sr_CuO_4 has been measured in high magnetic fields. An increase of the sound velocity due to the flux line lattice (FLL) pinning is observed at a temperature below the superconducting transition temperature T_C. Anisotropic activation energies to depin flux lines are evaluated separately from measurements under various settings of the directions of wave vector k, polarization vector u and magnetic fields H using the analysis based oh the thermally assisted flux flow model. Besides the FLL elasticity, anomalous temperature dependence of elastic constants of c_ and (c_-c_)/2 (softening at low temperatures and hardening at lower temperatures below 10K) is observed in high magnetic fields

Reduction of the Superfluid Density in the Vortex-Liquid Phase of Bi2Sr2CaCu2Oy

In-plane complex surface impedance of a Bi2Sr2CaCu2Oy single crystal was measured in the mixed state at 40.8 GHz.The surface reactance, which is proportional to the real part of the effective penetration depth, increased rapidly just above the first-order vortex-lattice melting transition field and the second magnetization peak field.This increase is ascribed to the decrease in the superfluid density rather than the loss of pinning.This result indicates that the vortex melting transition changes the electronic structure as well as the vortex structure.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

The electronic state of vortices in YBa2Cu3Oy investigated by complex surface impedance measurement

The electromagnetic response to microwaves in the mixed state of YBa2Cu3Oy(YBCO) was measured in order to investigate the electronic state inside and outside the vortex core. The magnetic-field dependence of the complex surface impedance at low temperatures was in good agreement with a general vortex dynamics description assuming that the field-independent viscous damping force and the linear restoring force were acting on the vortices. In other words, both real and imaginary parts of the complex resistivity, \rho_1, and \rho_2, were linear in B. This is explained by theories for d-wave superconductors. Using analysis based on the Coffey-Clem description of the complex penetration depth, we estimated that the vortex viscosity \eta at 10 K was (4 \sim 5) \times 10^{-7} Ns/m^2. This value corresponds to \omega_0 \tau \sim 0.3 - 0.5, where \omega_0 and \tau are the minimal gap frequency and the quasiparticle lifetime in the vortex core, respectively. These results suggest that the vortex core in YBCO is in the moderately clean regime. Investigation of the moderately clean vortex core in high-temperature superconductors is significant because physically new effects may be expected due to d-wave characteristics and to the quantum nature of cuprate superconductors. The behavior of Z_s as a function of B across the first order transition (FOT) of the vortex lattice was also investigated. Unlike Bi2Sr2CaCu2Oy (BSCCO), no distinct anomaly was observed around the FOT in YBCO. Our results suggest that the rapid increase of X_s due to the change of superfluid density at the FOT would be observed only in highly anisotropic two-dimensional vortex systems like BSCCO. We discuss these results in terms of the difference of the interlayer coupling and the energy scale between the two materials.Comment: 10 pages, 6 figures, to be published in Phys. Rev. B, one reference adde