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We study the momentum-integrated quasiparticle interference (QPI) in the FeSe-based superconductors. This method was recently proposed theoretically and has been applied to determine the pairing symmetry in these materials experimentally. Our findings suggest that, if the incipient bands and the superconducting (SC) pairing on them are taken into consideration, then the experimentally measured bound states and momentum-integrated QPI can be well fitted, even if the SC order parameter does not change sign on the Fermi surfaces. Therefore, we offer an alternative explanation to the experimental data, calling for more careful identification of the pairing symmetry that is important for the pairing mechanism.

We have investigated the in-gap bound states (IGBS) induced by a single nonmagnetic impurity in multiband superconductors with incipient bands. Contrary to the naive expectation, we found that even if the superconducting (SC) order parameter is sign-preserving s-wave on the Fermi surfaces, the incipient bands may still affect the appearance and locations of the IGBS, although the gap between the incipient bands and the Fermi level is much larger than the SC gap. Therefore in scanning tunneling microscopy experiments, the IGBS induced by a single nonmagnetic impurity are not the definitive evidences for the sign-changing order parameter on the Fermi surfaces. Our findings have special implications for the experimental determination of the pairing symmetry in the FeSe-based superconductors., Comment: To be published in Phys. Rev. B Rapid Commun

Based on recent high-resolution angle-resolved photoemission spectroscopy measurement in monolayer FeSe grown on SrTiO$_{3}$, we constructed a tight-binding model and proposed a superconducting (SC) pairing function which can well fit the observed band structure and SC gap anisotropy. Then we investigated the spin excitation spectra in order to determine the possible sign structure of the SC order parameter. We found that a resonance-like spin excitation may occur if the SC order parameter changes sign along the Fermi surfaces. However, this resonance is located at different locations in momentum space compared to other FeSe-based superconductors, suggesting that the Fermi surface shape and pairing symmetry in monolayer FeSe grown on SrTiO$_{3}$ may be different from other FeSe-based superconductors.

Combining the recent scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) measurements, we construct a tight-binding model suitable for describing the band structure of monolayer FeSe grown on SrTiO$_{3}$. Then we propose a possible pairing function, which can well describe the gap anisotropy observed by ARPES and has a hidden sign-changing characteristic. At last, as a test of this pairing function we further study the nonmagnetic impurity-induced bound states, to be verified by future STM experiments.

A pronounced local in-gap zero-energy bound state (ZBS) has been observed by recent scanning tunneling microscopy (STM) experiments on the interstitial Fe impurity (IFI) and its nearest-neighboring (nn) sites in $\mathrm{FeTe_{0.5}Se_{0.5}}$ superconducting (SC) compound. By introducing a new impurity mechanism, the so-called tunneling impurity, and based on the Bogoliubove-de Gennes (BDG) equations we investigated the low-lying energy states of the IFI and the underlying Fe-plane. We found the peak of ZBS does not shift or split in a magnetic field as long as the tunneling parameter between IFI and the Fe-plane is sufficiently small and the Fe-plane is deep in the SC state. Our results are in good agreement with the experiments. We also predicted that modulation of spin density wave (SDW), or charge density wave (CDW) will suppress the intensity of the ZBS., Comment: 5 pages, 4 figures

We investigate the one-dimensional $p$-wave superconducting model with periodically modulated hopping and show that under time-reversal symmetry, the number of the Majorana zero modes (MZMs) strongly depends on the modulation period. If the modulation period is odd, there can be at most one MZM. However if the period is even, the number of the MZMs can be zero, one and two. In addition, the MZMs will disappear as the chemical potential varies. We derive the condition for the existence of the MZMs and show that the topological properties in this model are dramatically different from the one with periodically modulated potential.

Effects of disorder on electron-doped iron pnictides are investigated systematically based on self-consistent Bogoliubov-de Gennes equations. Multiply impurities with same scattering potential (SP) are randomly distributed in a square lattice. Probability distribution functions of normalized order parameters for different impurity concentrations $\delta_{imp}$, different electron doping concentrations $\delta$ are investigated for given SPs. Samples are found to be very robust against weak SP, in which order parameters do not have qualitative change even at very large $\delta_{imp}$. While strong SP is able to easily break down the order parameters. For moderate SP, variations of order parameters on and around impurities strongly depend on $\delta$, however the distribution functions of normalized order parameters have similar behavior as $\delta_{imp}$ increases. Compared with superconducting (SC) order, the magnetic order is more sensitive to multi-impurity effect. The spatial spin density wave pattern has already been destroyed before the system loses its superconductivity. Dependence of SC order on temperature is similar to that of impurity-free case, with the critical temperature being remarkably suppressed for high $\delta_{imp}$., Comment: 7 pages, 8 figures

Based on the possible superconducting (SC) pairing symmetries recently proposed, the quasiparticle interference (QPI) patterns in electron- and hole-doped Sr$_{2}$IrO$_{4}$ are theoretically investigated. In the electron-doped case, the QPI spectra can be explained based on a model similar to the octet model of the cuprates while in the hole-doped case, both the Fermi surface topology and the sign of the SC order parameter resemble those of the iron pnictides and there exists a QPI vector resulting from the interpocket scattering between the electron and hole pockets. In both cases, the evolution of the QPI vectors with energy and their behaviors in the nonmagnetic and magnetic impurity scattering cases can well be explained based on the evolution of the constant-energy contours and the sign structure of the SC order parameter. The QPI spectra presented in this paper can be compared with future scanning tunneling microscopy experiments to test whether there are SC phases in electron- and hole-doped Sr$_{2}$IrO$_{4}$ and what the pairing symmetry is.

The quasiparticle interference (QPI) patterns in BiS$_{2}$-based superconductors are theoretically investigated by taking into account the spin-orbital coupling and assuming the recently proposed $d^{*}_{x^{2}-y^{2}}$-wave pairing symmetry. We found two distinct scattering wave vectors whose evolution can be explained based on the evolution of the constant-energy contours. The QPI spectra presented in this paper can thus be compared with future scanning tunneling microscopy experiments to test whether the pairing symmetry is $d^{*}_{x^{2}-y^{2}}$-wave in BiS$_{2}$-based superconductors., Comment: Due to the size limit, the original high-resolution figures can be asked for by emailling flygaoonly@gmail.com

The quasiparticle interference (QPI) in Sr$_{2}$RuO$_{4}$ is theoretically studied based on two different pairing models in order to propose an experimental method to test them. For a recently proposed two-dimensional model with pairing primarily from the $\gamma$ band, we found clear QPI peaks evolving with energy and their locations can be determined from the tips of the constant-energy contour (CEC). On the other hand, for a former quasi-one-dimensional model with pairing on the $\alpha$ and $\beta$ bands, the QPI spectra are almost dispersionless and may involve off-shell contributions to the scatterings beyond the CEC. The different behaviors of the QPI in these two models may help to resolve the controversy of active/passive bands and whether Sr$_{2}$RuO$_{4}$ is a topological superconductor., Comment: 6 pages, 4 figures. Due to the size limits, the original high-resolution figures can be asked for by emailling flygaoonly@gmail.com

Based on a phenomenological model with $s_{\pm}$ or s-wave pairing symmetry, the mixed-state effect on the low-energy spin dynamics in optimally-doped iron pnictide superconductors is studied by solving Bogoliubov-de Gennes equations. Our results of the spin susceptibility at $\mathbf{q}=\mathbf{Q}$ in the normal, superconducting and mixed states agree qualitatively with recent neutron scattering experiments. We also propose that the field-induced intensity change shows different behaviors between the $s_{\pm}$ and s-wave symmetries in both momentum and real space, thus it can be used to distinguish these two pairing symmetries.

Based on a phenomenological model and the Kubo formula, we investigate the superfluid density $\rho_s(T)$ and then the penetration depth $\lambda(T)$ of the iron-based superconductors in the coexistence region of the spin-density-wave(SDW) and superconductivity, and also in the over-doped region. Our calculations show a dramatic increase of $\lambda(0)$ with the decrease of the doping concentration $x$ below $x=0.1$. This result is consistent with the experimental observations. At low temperatures, $\rho(T)$ shows an exponential-law behavior, while at higher temperatures, the linear-in-$T$ behavior is dominant before it trends to vanish. The evolution of $\Delta\lambda(T)$ can be roughly fitted by a exponential function at overdoped levels while in other doping range it is a power-law function with the exponent depending on the doping concentration. We show that the Uemura relation holds for the iron-based superconductors only at very low doping levels., Comment: prl 109 187007 2012

Based on a phenomenological model with $s_{\pm}$ or s-wave pairing symmetry, the mixed-state effect on quasiparticle interference in iron-based superconductors is investigated by solving large-scale Bogoliubov-de Gennes equations based on the Chebyshev polynomial expansion. Taking into account the presence of magnetic field, our result for the $s_{\pm}$ pairing is in qualitative agreement with recent scanning tunneling microscopy experiment while for the s-wave pairing, the result is in apparent contradiction with experimental observations, thus excluding the s-wave pairing. Furthermore, we treat the effect of vortices rigorously instead of approximating the vortices as magnetic impurities, thus our results are robust and should be more capable of explaining the experimental data.

The impurity-induced quasiparticle interference(QPI) in the parent compounds of iron-pnictide superconductors is investigated based on a phenomenological two-orbital four-band model and T-matrix method. We find the QPI is sensitive to the value of the magnetic order which may vary from one compound to another. For small value of the magnetic order, the pattern of oscillation in the local density of states (LDOS) induced by the QPI exhibits two-dimensional characteristics, consistent with the standing wave state observed in the 1111 compound. For larger value of the magnetic order, the main feature of the spatial modulation of the LDOS is the existence of one-dimensional stripe structure which is in agreement with the nematic structure in the parent compound of the 122 system. In both cases the system shows $C_2$ symmetry and only in the larger magnetic order case, there exist in-gap bound states. The corresponding QPI in $q$-space is also presented. The patterns of modulation in the LDOS at nonzero energies are attributed to the interplay between the underlying band structure and Fermi surfaces., Comment: 9 pages,12 figures

The quasiparticle states around a nonmagnetic impurity in electron-doped iron-based superconductors with spin-density-wave (SDW) order are investigated as a function of doping and impurity scattering strength. In the undoped sample, where a pure SDW state exists, two impurity-induced resonance peaks are observed around the impurity site and they are shifted to higher (lower) energies as the strength of the positive (negative) scattering potential (SP) is increased. For the doped samples where the SDW order and the superconducting order coexist, the main feature is the existence of sharp in-gap resonance peaks whose positions and intensity depend on the strength of the SP and the doping concentration. In all cases, the local density of states exhibits clear $C_2$ symmetry. We also note that in the doped cases, the impurity will divide the system into two sublattices with distinct values of magnetic order. Here we use the band structure of a two-orbital model, which considers the asymmetry of the As atoms above and below the Fe-Fe plane. This model is suitable to study the properties of the surface layers in the iron-pnictides and should be more appropriate to describe the scanning tunneling microscopy experiments., Comment: 11 pages, 18 figures

The electronic and magnetic structures in the normal and superconducting states of iron pnictides are investigated by solving self-consistently the Bogoliubov-de Gennes equation. It is shown that strong electron correlations can induce domain walls, which separate regions with different spin density wave orders. At zero or low electron doping, $90^\circ$ domain walls are formed while anti-phase domain walls are produced at higher electron doping. On the domain walls, larger electron densities are always present. The results agree qualitatively with recent observations of scanning tunneling microscopy and superconducting quantum interference device microscopy., Comment: 5 pages,5 figures