Quasi-one-dimensional nanoscale modulation as sign of nematicity in iron pnictides and chalcogenides

Impurity scattering is found to lead to quasi-one-dimensional nanoscale modulation of the local density of states in iron pnictides and chalcogenides. This “quasiparticle interference” feature is remarkably similar across a wide variety of pnictide and chalcogenide phases, suggesting a common origin. We show that a unified understanding of the experiments can be obtained by simply invoking a fourfold symmetry breaking $d_{xz}\text{−}{d}_{yz}$ orbital splitting, of a magnitude already suggested by the experiments. This can explain the one-dimensional characteristics in the local density of states observed in the orthorhombic nematic, tetragonal paramagnetic, as well as the spin-density-wave and superconducting states in these materials.

Figure 1

Results in the nematic state for orbital splitting $\delta =60$ meV: (a)–(c) show the behavior of contours of constant energies (CCEs) for the quasiparticle energy $\omega =-100,-50,0\mathrm{meV}$ in the $(k_x,k_y)$ plane. ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$ are intrapocket scattering vectors associated with the electron pockets around $(0,\pm \pi )$ and $(\pm \pi ,0)$, respectively. Intrapocket scattering vectors for the hole pockets around (0,0) are not shown. ${\mathbf{q}}_3$ and ${\mathbf{q}}_4$ are the interpocket scattering vectors. (d)–(f) For most $\omega$, three parallel rodlike structures exist in the momentum space QPI, where the outer peaks are positive and the inner peak is negative. Since the orientation of these rodlike structures also changes near $\omega \sim -60$ meV, the orientation of 1D LDOS modulation (g)–(i) also changes from $x$ to $y$. Note: Here and hereafter the momentum space plots are in the units of $\pi /a$ with a range $[-1,1]$; and the real-space ($xy$-plane) plots are in the units of $a$ with a range $[-40,40]$. LDOS modulation shown for $80\times 80$ size with the impurity atom located at the center, with the calculation done for a $300\times 300$ lattice size.

Figure 2

QPI along the high-symmetry directions in the nematic state, for different energies, from $\omega =0.0\mathrm{meV}$ (bottom curve) to $\omega =-120\mathrm{meV}$ (top curve) with an energy step of $10\mathrm{meV}$. The brown and red curves are a guide to the eye for scattering vectors ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$.

Figure 3

Results in the $s^{+-}$ superconducting state for ${\mathrm{\Delta }}_0=20\mathrm{meV}$, and quasiparticle energy $\omega =-88\mathrm{meV}$ in the presence of orbital splitting $\delta =60\mathrm{meV}$: (a) Quasiparticle spectral function in the $(k_x,k_y)$ plane, (b) momentum-space QPI in the $(q_x,q_y)$ plane, and (c) real-space QPI. The pockets in (a) at $(\pm \pi ,0)$ are very small with a highly anisotropic spectral density distribution along them. The intrapocket scattering vector ${\mathbf{q}}_2$ is mainly responsible for the features observed near $(0,0)$ in the momentum-space QPI pattern. These consist of three parallel rodlike structures, the outer ones with a positive peak and the inner one with a negative peak. Real-space QPI consists of two bright spots separated by a distance of $\sim 11a_{\mathrm{Fe}\text{−}\mathrm{Fe}}$ as observed in the experiments [39]. The ranges for all the quantities are as in Fig. 1.

Figure 4

(a)–(c) show the quasiparticle spectral function for $-100\mathrm{meV}$ in the $(\pi ,0)$ SDW state for various temperatures. Total magnetization is $m_{\mathrm{tot}}=0.3$. The resulting momentum-space pattern with three parallel rodlike structures is along a direction reciprocal to the ferromagnetic chain and LDOS modulation with wavelength $\sim 8a\text{–}10a$ with a small change in temperature. The range for all the quantities are as in Fig. 1.

Figure 5

QPI along the high-symmetry directions in the SDW state for different temperatures, starting from $T=0.014t$ (bottom curve) to $T=0.036t$ (top curve) with steps of $0.04t$ ($T_N\approx 0.034t$). The brown curve is a guide to the eye for scattering vector ${\mathbf{q}}_2$.