Quasiparticle Interference in the Spin-Density Wave Phase of Iron-Based Superconductors

We propose an explanation for the electronic nematic state observed recently in parent iron-based superconductors [T.-M. Chuang et al., Science 327, 181 (2010)]. We argue that the quasi-one-dimensional nanostructure identified in the quasiparticle interference (QPI) is a consequence of the interplay of the magnetic ($\pi$, 0) spin-density wave (SDW) order with the underlying electronic structure. We show that the evolution of the QPI peaks largely reflects quasiparticle scattering between bands involved in the SDW formation. Because of the ellipticity of the electron pocket and the fact that only one of the electron pockets is involved in the SDW, the resulting QPI has a pronounced one-dimensional structure. We further predict that the QPI crosses over to two dimensionality on an energy scale, set by the SDW gap.

Figure 1

Constant energy intensity maps of the spectral density, $\sum _{\sigma }\mathrm{Im}\mathrm{Tr}{G}_{0\sigma }(\mathbf{k},\omega )$ (left panel), and absolute value of the QPI, $\sum _{\mathbf{k}\sigma }\mathrm{Im}\mathrm{Tr}[G_{0\sigma }(\mathbf{k},\omega )t_{\sigma }(\mathbf{k},\mathbf{k}+\mathbf{q},\omega )G_{0\sigma }(\mathbf{k}+\mathbf{q},\omega )]$, for nonmagnetic (middle panel) and magnetic (right panel) impurities obtained as described in the text. The arrows denote the characteristic scattering wave vectors which appear in the SDW state. The color bars refer to the intensity in units of states/eV.

Figure 2

Plots of QPI along AF, $q_x$ (a), and FM, $q_y$ (b), directions. The bottom curve is at $-50\mathrm{meV}$ and the top curve is at $+50\mathrm{meV}$. Consecutive curves are separated by 10 meV. Red, green, and black curves are guides to the eye.

Figure 3

Real space image of the QPI at $-7\mathrm{meV}$ away from the impurity site. The inset shows the corresponding QPI image. The QPI interference originating from the structure in the spectral density is reflected in the strong $\sim 10–15a$ modulation along the FM ($y$) direction and a weak $\sim 5–7a$ modulation along the AF ($x$) direction. We adopt the impurity potential as a mixture of the magnetic (20%) and nonmagnetic (80%) parts. Intensity refers to states/eV.

Figure 4

Constant energy intensity maps of the spectral density, $\sum _{\sigma }\mathrm{Im}\mathrm{Tr}{G}_{0\sigma }(\mathbf{k},\omega )$ (left panel), and QPI, $\sum _{\mathbf{k}\sigma }\mathrm{Im}\mathrm{Tr}[G_{0\sigma }(\mathbf{k},\omega )t_{\sigma }(\mathbf{k},\mathbf{k}+\mathbf{q},\omega )G_{0\sigma }(\mathbf{k}+\mathbf{q},\omega )]$, for nonmagnetic (middle panel) and magnetic (right panel) impurities and negative energies. The arrows denote the characteristic scattering wave vectors which appear in the SDW state. The color bars refer to the intensity in units of states/eV.