Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields - crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional
electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fermi surface exhibits the same spin texture as for weak ISB, but the orbital texture is completely different, raising questions about the effect on quasiparticle scattering. We demonstrate that the spin-orbital selection rules relevant for conventional Rashba system are obeyed as true spin selection rules in this correlated electron liquid and determine its spin coherence length from quasiparticle interference imaging.
The origin of spontaneous electronic nematic ordering provides important information for understanding iron-based superconductors. Here, we analyze a scenario where the $d_{xy}$ orbital strongly contributes to nematic ordering in FeSe. We show that t
he addition of $d_{xy}$ nematicity to a pure $d_{xz}/d_{yz}$ order provides a natural explanation for the unusual Fermi surface and correctly reproduces the strongly anisotropic momentum dependence of the superconducting gap. We predict a Lifshitz transition of an electron pocket mediated by temperature and sulphur doping, whose signatures we discuss by analysing available experimental data. We present the variation of momentum dependence of the superconducting gap upon suppression of nematicity. Our quantitatively accurate model yields the transition from tetragonal to nematic FeSe and the FeSe$_{1-x}$S$_{x}$ series, and puts strong constraints on possible nematic mechanisms.
Many of the exciting properties of strongly correlated materials are intricately linked to quantum critical points in their phase diagram. This includes phenomena such as high temperature superconductivity, unconventional superconductivity in heavy f
ermion materials, as well as exotic nematic states in Sr$_3$Ru$_2$O$_7$. One of the experimentally most successful pathways to reaching a quantum critical point is tuning by magnetic field allowing studies under well-controlled conditions on ultra-clean samples. Yet, spectroscopic evidence of how the electronic states change across a field-tuned quantum phase transition, and what the importance of quantum fluctuations is, is not available so far. Here we show that the surface layer of Sr$_2$RuO$_4$ is an ideal two-dimensional model system for a field-tuned quantum phase transition. We establish the existence of four van Hove singularities in close proximity to the Fermi energy, linked intricately to checkerboard charge order and nematicity of the electronic states. Through magnetic field, we can tune the energy of one of the van Hove singularities, with the Lifshitz transition extrapolated at ~32T. Our experiments open up the ability to directly study spectroscopically the role of quantum fluctuations at a field-tuned quantum phase transition in an effectively 2D strongly correlated electron material. Our results further have implications for what the leading instability in Sr$_2$RuO$_4$ is, and hence for understanding the enigmatic superconductivity in this material.
We measure the electronic structure of FeSe from within individual orthorhombic domains. Enabled by an angle-resolved photoemission spectroscopy beamline with a highly focused beamspot (nano-ARPES), we identify clear stripe-like orthorhombic domains
in FeSe with a length scale of approximately 1-5~$mu$m. Our photoemission measurements of the Fermi surface and band structure within individual domains reveal a single electron pocket at the Brillouin zone corner. This result provides clear evidence for a one-electron pocket electronic structure of FeSe, observed without the application of uniaxial strain, and calls for further theoretical insight into this unusual Fermi surface topology. Our results also showcase the potential of nano-ARPES for the study of correlated materials with local domain structures.
Quasiparticle interference (QPI) provides a wealth of information relating to the electronic structure of a material. However, it is often assumed that this information is constrained to two-dimensional electronic states. Here, we show that this is n
ot necessarily the case. For FeSe, a system dominated by surface defects, we show that it is actually all electronic states with negligible group velocity in the $z$ axis that are contained within the experimental data. By using a three-dimensional tight binding model of FeSe, fit to photoemission measurements, we directly reproduce the experimental QPI scattering dispersion, within a T-matrix formalism, by including both $k_z = 0$ and $k_z = pi$ electronic states. This result unifies both tunnelling and photoemission based experiments on FeSe and highlights the importance of $k_z$ within surface sensitive measurements of QPI.
We revisit the electronic structure of BaFe$_2$As$_2$, the archetypal parent compound of the Fe-based superconductors, using angle-resolved photoemission spectroscopy (ARPES). Our high-resolution measurements of samples detwinned by the application o
f a mechanical strain reveal a highly anisotropic 3D Fermi surface in the low temperature magnetic phase. By comparison of the observed dispersions with ab-initio calculations, we argue that overall it is magnetism, rather than orbital ordering, which is the dominant effect, reconstructing the electronic structure across the Fe 3d bandwidth. Finally, we measure band dispersions directly from within one domain without applying strain to the sample, by using the sub-micron focused beam spot of a nano-ARPES instrument.
We use high-resolution angle-resolved photoemission spectroscopy to map the three-dimensional momentum dependence of the superconducting gap in FeSe. We find that on both the hole and electron Fermi surfaces, the magnitude of the gap follows the dist
ribution of $d_{yz}$ orbital weight. Furthermore, we theoretically determine the momentum dependence of the superconducting gap by solving the linearized gap equation using a tight binding model which quantitatively describes both the experimental band dispersions and orbital characters. By considering a Fermi surface only including one electron pocket, as observed spectroscopically, we obtain excellent agreement with the experimental gap structure. Our finding of a scaling between the superconducting gap and the $d_{yz}$ orbital weight supports the interpretation of superconductivity mediated by spin-fluctuations in FeSe.
We report high resolution ARPES measurements of detwinned FeSe single crystals. The application of a mechanical strain is used to promote the volume fraction of one of the orthorhombic domains in the sample, which we estimate to be 80$%$ detwinned. W
hile the full structure of the electron pockets consisting of two crossed ellipses may be observed in the tetragonal phase at temperatures above 90~K, we find that remarkably, only one peanut-shaped electron pocket oriented along the longer $a$ axis contributes to the ARPES measurement at low temperatures in the nematic phase, with the expected pocket along $b$ being not observed. Thus the low temperature Fermi surface of FeSe as experimentally determined by ARPES consists of one elliptical hole pocket and one orthogonally-oriented peanut-shaped electron pocket. Our measurements clarify the long-standing controversies over the interpretation of ARPES measurements of FeSe.
