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Register a new userThermodynamic electric quadrupole moments of nematic phases from first-principles calculation
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The electronic nematic phase emerging with spontaneous rotation symmetry breaking is a central issue of modern condensed matter physics. In particular, various nematic phases in iron-based superconductors and high-$T_{rm c}$ cuprate superconductors are extensively studied recently. Electric quadrupole moments (EQMs) are one of the order parameters characterizing these nematic phases in a unified way, and elucidating EQMs is a key to understanding these nematic phases. However, the quantum-mechanical formulation of the EQMs in crystals is a nontrivial issue because the position operators are non-periodic and unbound. Recently, the EQMs have been formulated by local thermodynamics, and such {it thermodynamic EQMs} may be used to characterize the fourfold rotation symmetry breaking in materials. In this paper, we calculate the thermodynamic EQMs in iron-based superconductors LaFeAsO and FeSe as well as a cuprate superconductor La$_2$CuO$_4$ by a first-principles calculation. We show that owing to the orbital degeneracy the EQMs in iron-based superconductors are mainly determined by the geometric properties of wave functions. This result is in sharp contrast to the cuprate superconductor, in which the EQMs are dominated by distortion of the Fermi surface.
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Higher-rank electric/magnetic multipole moments are attracting attention these days as candidate order parameters for exotic material phases. However, quantum-mechanical formulation of those multipole moments is still an ongoing issue. In this paper, we propose a thermodynamic definition of electric quadrupole moments as a measure of symmetry breaking, following previous studies of orbital magnetic dipole moments and magnetic quadrupole moments. The obtained formulas are illustrated with a model of orbital-ordered nematic phases of iron-based superconductors.
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Electronic nematicity is an important order in most iron-based superconductors, and FeSe represents a unique example, in which nematicity disentangles from spin ordering. It is commonly perceived that this property arises from strong electronic correlation, which can not be properly captured by density functional theory (DFT). Here, we show that by properly considering the paramagnetic condition and carefully searching the energy landscape with symmetry-preconditioned wavefunctions, two nematic solutions stand out at either the DFT+$U$ or hybrid functional level, both of which are lower in energy than the symmetric solution. The ground-state band structure and Fermi surface can be well compared with the recent experimental results. Symmetry analysis assigns these two new solutions to the $B_{1g}$ and $E_u$ irreducible representations of the D$_{4h}$ point group. While the $B_{1g}$ Ising nematicity has been widely discussed in the context of vestigial stripe antiferromagnetic order, the two-component $E_u$ vector nematicity is beyond previous theoretical discussion. Distinct from the $B_{1g}$ order, the $E_u$ order features mixing of the Fe $d$-orbitals and inversion symmetry breaking, which lead to striking experimental consequences, e.g. missing of an electron pocket.
Since its discovery, iron-based superconductivity has been known to develop near an antiferromagnetic order, but this paradigm fails in the iron chalcogenide FeSe, whose single-layer version holds the record for the highest superconducting transition temperature in the iron-based superconductors. The striking puzzle that FeSe displays nematic order (spontaneously broken lattice rotational symmetry) while being non-magnetic, has led to several competing proposals for its origin in terms of either the $3d$-electrons orbital degrees of freedom or spin physics in the form of frustrated magnetism. Here we argue that the phase diagram of FeSe under pressure could be qualitatively described by a quantum spin model with highly frustrated interactions. We implement both the site-factorized wave-function analysis and the large-scale density matrix renormalization group (DMRG) in cylinders to study the spin-$1$ bilinear-biquadratic model on the square lattice, and identify quantum transitions from the well-known $(pi,0)$ antiferromagnetic state to an exotic $(pi,0)$ antiferroquadrupolar order, either directly or through a $(pi/2,pi)$ antiferromagnetic state. These many phases, while distinct, are all nematic. We also discuss our theoretical ground-state phase diagram for the understanding of the experimental low-temperature phase diagram obtained by the NMR [P. S. Wang {it et al.}, Phys. Rev. Lett. 117, 237001 (2016)] and X-ray scattering [K. Kothapalli {it et al.}, Nature Communications 7, 12728 (2016)] measurements in pressurized FeSe. Our results suggest that superconductivity in a wide range of iron-based materials has a common origin in the antiferromagnetic correlations of strongly correlated electrons.
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