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Register a new userElectronic nematicity in FeSe: a first-principles perspective
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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.
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The mechanism behind the nematicity of FeSe is not known. Through elastoresitivity measurements it has been shown to be an electronic instability. However, so far measurements have extended only to small strains, where the response is linear. Here, we apply large elastic strains to FeSe, and perform two types of measurements. (1) Using applied strain to control twinning, the nematic resistive anisotropy at temperatures below the nematic transition temperature Ts is determined. (2) Resistive anisotropy is measured as nematicity is induced through applied strain at fixed temperature above Ts. In both cases, as nematicity strengthens the resistive anisotropy peaks about about 7%, then decreases. Below ~40 K, the nematic resistive anisotropy changes sign. We discuss possible implications of this behaviour for theories of nematicity. We report in addition: (1) Under experimentally accessible conditions with bulk crystals, stress, rather than strain, is the conjugate field to the nematicity of FeSe. (2) At low temperatures the twin boundary resistance is ~10% of the sample resistance, and must be properly subtracted to extract intrinsic resistivities. (3) Biaxial inplane compression increases both in-plane resistivity and the superconducting critical temperature Tc, consistent with a strong role of the yz orbital in the electronic correlations.
The large anisotropy in the electronic properties across a structural transition in several correlated systems has been identified as the key manifestation of electronic nematic order, breaking rotational symmetry. In this context, FeSe is attracting tremendous interest, since electronic nematicity develops over a wide range of temperatures, allowing accurate experimental investigation. Here we combine angle-resolved photoemission spectroscopy and theoretical calculations based on a realistic multi-orbital model to unveil the microscopic mechanism responsible for the evolution of the electronic structure of FeSe across the nematic transition. We show that the self-energy corrections due to the exchange of spin fluctuations between hole and electron pockets are responsible for an orbital-dependent shrinking of the Fermi Surface that affects mainly the $xz/yz$ parts of the Fermi surface. This result is consistent with our experimental observation of the Fermi Surface in the high-temperature tetragonal phase, that includes the $xy$ electron sheet that was not clearly resolved before. In the low-temperature nematic phase, we experimentally confirm the appearance of a large ($sim$ 50meV) $xz/yz$ splittings. It can be well reproduced in our model by assuming a moderate splitting between spin fluctuations along the $x$ and $y$ crystallographic directions. Our mechanism shows how the full entanglement between orbital and spin degrees of freedom can make a spin-driven nematic transition equivalent to an effective orbital order.
Bulk FeSe superconducts inside a nematic phase, that sets in through an orthorhombic distortion of the high temperature tetragonal phase. Bulk non-alloy tetragonal superconducting FeSe does not exist as yet. This raises the question whether nematicity is fundamental to superconductivity. We employ an advanced ab-initio ability and show that bulk tetragonal FeSe can, in principle, superconduct at almost the same Tc as the orthorhombic phase had that been the ground state. Further, we perform rigorous benchmarking of our theoretical spin susceptibilities against experimentally observed data over all energies and relevant momentum direction. We show that susceptibilities computed in both the tetragonal and orthorhombic phases already have the correct momentum structure at all energies, but not the desired intensity. The enhanced nematicity that simulates the correct spin fluctuation intensity can only lead to a maximum 10-15% increment in the superconducting Tc . Our results suggest while nematicity may be intrinsic property of the bulk FeSe, is not the primary force driving the superconducting pairing.
Electronic nematic phases have been proposed to occur in various correlated electron systems and were recently claimed to have been detected in scanning tunneling microscopy (STM) conductance maps of the pseudogap states of the cuprate high-temperature superconductor Bi2Sr2CaCu2O8+x (Bi-2212). We investigate the influence of anisotropic STM tip structures on such measurements and establish, with a model calculation, the presence of a tunneling interference effect within an STM junction that induces energy-dependent symmetry-breaking features in the conductance maps. We experimentally confirm this phenomenon on different correlated electron systems, including measurements in the pseudogap state of Bi-2212, showing that the apparent nematic behavior of the imaged crystal lattice is likely not due to nematic order but is related to how a realistic STM tip probes the band structure of a material. We further establish that this interference effect can be used as a sensitive probe of changes in the momentum structure of the samples quasiparticles as a function of energy.
The NMR spectrum of FeSe shows a dramatic broadening on cooling towards the bulk nematic phase at $T_s=90$ K, due to the formation of a quasi-static, short-range-ordered nematic domain structure. However, a quantitative understanding of the NMR broadening and its relationship to the nematic susceptibility is still lacking. Here, we show that the temperature and pressure dependence of the broadening is in quantitative agreement with the mean-field Edwards-Anderson parameter of an Ising-nematic model in the presence of random-field disorder introduced by non-magnetic impurities. Furthermore, these results reconcile the interpretation of NMR and Raman spectroscopy data in FeSe under pressure.
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