Quasiparticle interference in iron-based superconductors

We systematically calculate quasiparticle interference (QPI) signatures for the whole phase diagram of iron-based superconductors. Impurities inherent in the sample together with ordered phases lead to distinct features in the QPI images that are believed to be measured in spectroscopic imaging-scanning tunneling microscopy. In the spin-density wave phase the rotational symmetry of the electronic structure is broken, signatures of which are also seen in the coexistence regime with both superconducting and magnetic order. In the superconducting regime we show how the different scattering behavior for magnetic and nonmagnetic impurities allows to verify the $s^{+-}$ symmetry of the order parameter. The effect of possible gap minima or nodes is discussed.

Figure 1

(Color online) Schematic phase diagram for the iron-based superconductors [$\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{SmFeAs}\left({\text{O}}_{1-x}{\text{F}}_x\right)$] exhibiting a regime of coexistence of SDW and SC orders (Refs. 2, 3). Regimes (I)–(IV) refer to the various parts of the phase diagram.

Figure 2

(Color online) Constant energy intensity maps at $\omega =20\text{meV}$ (first row) and $w=-20\text{meV}$ (second row) of the spectral density, ${\sum }_{\sigma }\text{Im}{G}_{0\sigma }\left(\mathbf{k},\omega \right)$, (first panel from the left) and QPI, ${\sum }_{\mathbf{k}\sigma }\text{Im}\left[G_{0\sigma }\left(\mathbf{k},\omega \right)t_{\sigma }\left(\mathbf{k},\mathbf{k}+q,\omega \right)G_{0\sigma }\left(\mathbf{k}+q,\omega \right)\right]$ for nonmagnetic (second panel) and magnetic (third panel) impurities obtained as described in the text. The difference between QPI for nonmagnetic and magnetic impurities is displayed in the right panel. The color bars refer to the intensity in units of states/eV. The SDW order parameter is fixed at $W=40\text{meV}$ for zero doping.

Figure 3

(Color online) Constant energy intensity maps at $\omega =20\text{meV}$ (first row) and $w=-20\text{meV}$ (second row) of the spectral density and QPI, for nonmagnetic (second panel) and magnetic (third panel) impurities obtained as described in the text. The difference between QPI for nonmagnetic and magnetic impurities is displayed in the right panel. For SDW (region I in Fig. 1) with $W=40\text{meV}$ and with 7% electron doping (e-doping), for $\omega =20\text{meV}$ (first row) and $w=-20\text{meV}$ (second row). The color bars refer to the intensity in units of states/eV. The SDW order parameter is fixed at $W=40\text{meV}$ for 7% electron doping.

Figure 4

(Color online) The spectral density and the QPI maps for nonmagnetic and magnetic impurity scattering (from left to right) at 20 meV in SC state with nodeless $s^{+-}$ wave (upper panel) and isotropic $s^{++}$-wave (lower panel) symmetries of the superconducting gap. We set $\Delta =20\text{meV}$, 13% e-doping. The difference between QPI for nonmagnetic and magnetic impurities is displayed on the right panel. The arrows show scattering between electron and hole bands at ${\mathbf{q}}_0=\left(\pi ,0\right)$, $\left(0,\pi \right)$. The inset in the upper panel shows the experimental data taken from Ref. 28.

Figure 5

(Color online) Calculated spectral density in the superconducting state with nodal $s^{+-}$-wave symmetry for ${\Delta }^{\prime }=3\Delta$. The arrows refer to some intraelectron and interelectron pocket scattering wave vectors (i.e., wavevectors joining regions with large DOS). Observe that ${\mathbf{q}}_1^{\prime }$, and ${\mathbf{q}}_2^{\prime }$, ${\mathbf{q}}_3^{\prime }$, ${\mathbf{q}}_4^{\prime }$ are the scattering wave vectors for the same and the opposite signs of the superconducting order parameter, respectively. The evolution of the banana-shape structures is shown for $+5$ (black curve), $+10$ (brown curve), $+15$ (green curve), $+20$ (red curve), and $+30$ (blue curve) meV.

Figure 6

(Color online) The spectral density and the QPI maps for nonmagnetic and magnetic impurity scattering (from left to right) at $+20\text{meV}$ (upper panel) and $+10\text{meV}$ (lower panel) in SC state with nodal $s^{+-}$-wave order parameter of the superconducting gap $\left({\Delta }^{\prime }=3\Delta \right)$ and 13% of the electron doping. The difference between QPI for nonmagnetic and magnetic impurities is displayed on the right panel.

Figure 7

(Color online) Calculated spectral density and the QPI maps at $\omega =+20\text{meV}$ in the coexistence regime of $\text{SDW}+\text{SC}$. The upper panel refers to the regime II of the phase diagram (Fig. 1) with $W=40\text{meV}$, $\Delta =20\text{meV}$ and 10% e-doping. The lower panel describes the regime III with $W=10\text{meV}$, $\Delta =20\text{meV}$, and 12% e-doping.