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Register a new userMulti-Atom Quasiparticle Scattering Interference for Superconductor Energy-Gap Symmetry Determination
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Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $Delta_mathbf{k}^alpha$, for all momenta $mathbf{k}$ on the Fermi surface of every band $alpha$. While there are a variety of techniques for determining $|Delta_mathbf{k}^alpha|$, no general method existed to measure the signed values of $Delta_mathbf{k}^alpha$. Recently, however, a new technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where $Delta_mathbf{k}^alpha$ has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the $Delta_mathbf{k}^alpha$ it generates to the $Delta_mathbf{k}^alpha$ determined from single-atom scattering in FeSe where $s_{pm}$ energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for $Delta_mathbf{k}^alpha$ of opposite sign.
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Phase-sensitive measurements of the superconducting gap in Fe-based superconductors have proven more difficult than originally anticipated. While quasiparticle interference (QPI) measurements based on scanning tunneling spectroscopy are often proposed as defnitive tests of gap structure, the analysis typically relies on details of the model employed. Here we point out that the temperature dependence of momentum-integrated QPI data can be used to identify gap sign changes in a qualitative way, and present an illustration for $s_{pm}$ and $s_{++}$ states in a system with typical Fe-pnictide Fermi surface.
The cuprate high-temperature superconductors are known to host a wide array of effects due to interactions and disorder. In this work, we look at some of the consequences of these effects which can be visualized by scanning tunneling spectroscopy. These interaction and disorder effects can be incorporated into a mean-field description by means of a self-energy appearing in the Greens function. We first examine the quasiparticle scattering interference spectra in the superconducting state at optimal doping as temperature is increased. Assuming agreement with angle-resolved photoemission experiments which suggest that the scattering rate depends on temperature, resulting in the filling of the $d$-wave gap, we find that the peaks predicted by the octet model become progressively smeared as temperature is increased. When the scattering rate is of the same order of magnitude as the superconducting gap, the spectral function shows Fermi-arc-like patterns, while the power spectrum of the local density of states shows the destruction of the octet-model peaks. We next consider the normal state properties of the optimally-doped cuprates. We model this by adding a marginal Fermi liquid self-energy to the normal-state propagator, and consider the dependence of the QPI spectra on frequency, temperature, and doping. We demonstrate that the MFL self-energy leads to a smearing of the caustics appearing in the normal-state QPI power spectrum as either temperature or frequency is increased at fixed doping. The smearing is found to be more prominent in the MFL case than in an ordinary Fermi liquid. We also consider the case of a marginal Fermi liquid with a strongly momentum-dependent self-energy which gives rise to a visible nodal-antinodal dichotomy at the normal state, and discuss how the spectra as seen in ARPES and STS differ from both an isotropic metal and a broadened $d$-wave superconductor.
Using both two orbital and five orbital models, we investigate the quasiparticle interference (QPI) patterns in the superconducting (SC) state of iron-based superconductors. We compare the results for nonmagnetic and magnetic impurities in sign-changed s-wave $cos(k_x)cdotcos(k_y)$ and sign-unchanged $|cos(k_x)cdotcos(k_y)|$ SC states. While the patterns strongly depend on the chosen band structures, the sensitivity of peaks around $(pmpi,0)$ and $(0,pmpi)$ wavevectors on magnetic or non-magnetic impurity, and sign change or sign unchanged SC orders is common in two models. Our results strongly suggest that QPI may provide direct information of band structures and evidence of the pairing symmetry in the SC states.
Using a realistic ten-orbital tight-binding model Hamiltonian fitted to the angle-resolved photoemission (ARPES) data on LiFeAs, we analyze the temperature, frequency, and momentum dependencies of quasiparticle interference (QPI) to identify gap sign changes in a qualitative way, following our original proposal [Phys. Rev. B 92, 184513 (2015)]. We show that all features present for the simple two-band model for the sign-changing $s_{+-}$-wave superconducting gap employed previously are still present in the realistic tight-binding approximation and gap values observed experimentally. We discuss various superconducting gap structures proposed for LiFeAs, and identify various features of these superconducting gaps functions in the quasiparticle interference patterns. On the other hand, we show that it will be difficult to identify the more complicated possible sign structures of the hole pocket gaps in LiFeAs, due to the smallness of the pockets and the near proximity of two of the gap energies.
Quasiparticle interference (QPI) provides a wealth of information relating to the electronic structure of a material. However, it is often assumed that this information is constrained to two-dimensional electronic states. Here, we show that this is not necessarily the case. For FeSe, a system dominated by surface defects, we show that it is actually all electronic states with negligible group velocity in the $z$ axis that are contained within the experimental data. By using a three-dimensional tight binding model of FeSe, fit to photoemission measurements, we directly reproduce the experimental QPI scattering dispersion, within a T-matrix formalism, by including both $k_z = 0$ and $k_z = pi$ electronic states. This result unifies both tunnelling and photoemission based experiments on FeSe and highlights the importance of $k_z$ within surface sensitive measurements of QPI.
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