Orbital transmutation and the electronic spectrum of FeSe in the nematic phase

Abstract

We consider the electronic spectrum near M = (π, π) in the nematic phase of FeSe (T < Tnem) and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the M point. These have been identified as having xz and yz orbital character well below Tnem, but remain split at T > Tnem, in apparent contradiction to the fact that in the tetragonal phase the xz and yz orbitals are degenerate. We argue that the data can be understood if we include spin-orbit coupling at the M point. We show that a finite spin-orbit coupling gives rise to the phenomenon of orbital transmutation, by which the dominant orbital character of some bands changes between T > Tnem and T Tnem. Due to this effect, one of the modes, identified as xz (yz) at T Tnem, becomes predominantly xy at T > Tnem and hence does not merge with the predominantly yz (xz) mode. Since both ARPES and STM are surface probes, we also discuss a complimentary, surface-specific scenario, which explores the hybridization between the xz and yz orbitals. This is not allowed in the bulk, but can exist at the surface. In this case, the orbital character of the modes changes from xz and yz at T Tnem to xz ± yz at T > Tnem. The two modes again do not merge at Tnem as they are split by the hybridization.

Revealing the single electron pocket of FeSe in a single orthorhombic domain

“…Overall, the dispersions closely resemble previous photoemission measurements on detwinned crystals of FeSe [17][18][19][20], though it should be noted that the geometry here is not fully equivalent to that in some reports [37]. We do not comment on the orbital characters of the bands, which have been strongly disputed [11,20,25], but only note that the connectivity of bands from the Z to the A point (or to M) is not obvious in such measurements due to the weak and broad features in between.…”

“…However, they also revealed the presence of only a single electronlike pocket around the M and A points at the Brillouin zone corner, despite the expectation of two electron pockets in most theoretical models [11,13,21,22]. The theoretical understanding of this discrepancy remains controversial and unresolved [18,[23][24][25][26][27].…”

On the Remarkable Superconductivity of FeSe and Its Close Cousins

“…Here ∆ b and ∆ s are the values of a bond order and site order term [20,94,95]. In addition, an orbital ordering term in the d xy orbital is allowed by symmetry and has been included in some more recent works [96,97]. From a LDA+U perspective an off-diagonal orbital order term that lowers the overall symmetry has been found to be the ground state, a result that would allow a band hybridization such that the Y-pocket is lifted [98].…”

“…A combination of decoherence of d xy states (without significant d xz,yz decoherence), nematic order, spin-orbit coupling and/or surface hybridization has been proposed to account for the observed configuration of the bands at the X point [97]. The second pocket (in the one Fe zone appearing at the Y point) is in this scenario of dominant d xy character everywhere in the nematic state (instead of d xz ) and difficult to observe spectroscopically due to its decoherence.…”

“…Recently, alternative explanations of the latter two experimental results were brought forward in terms of effects of the three dimensional electronic structure giving rise to some averaging in the sum over k on the r.h.s of Equation (18) [212] or possible lifting of the Y pocket due to band hybridizations [113,114]. However, the latter explanation has been questioned by a theoretical model of the expected spectral functions accounting for an electronic structure that has a nematic order parameter in the d xz /d yz channel and the d xy channel, and additionally hybridizations due to spin-orbit coupling are taken into account [97]. In the quest to find the microscopic origin of the strongly anisotropic order parameter, there have also been other theoretical proposals: Kang et al examined the effects of a modified orbital content on the Fermi surface which, together with strongly correlated states in the d xy orbital channel and an induced anisotropy in the pairing interaction from small nematic splitting of the electronic structure, can also account qualitatively for the observed structure of the order parameter [164]; see Figure 12d-e. As mentioned in the previous section, a phenomenological model of strongly anisotropic spin fluctuations, i.e., orbitally selective spin fluctuations can explain the modifications of the electronic structure in FeSe at low temperatures, thereby giving rise to the Fermi surface shrinkage and nematic distortion [36,161]; see Figure 12a.…”