Electronically driven nematic order is often considered as an essential ingredient of high-temperature superconductivity. Its elusive nature in iron-based supercon- ductors resulted in a controversy not only as regards its origin but also as to the degree of its influence on the electronic structure even in the simplest representative material FeSe. Here we utilized angle-resolved photoemission spectroscopy and density functional theory calculations to study the influence of the nematic order on the electronic structure of FeSe and determine its exact energy and momentum scales. Our results strongly suggest that the nematicity in FeSe is electronically driven, we resolve the recent controversy and provide the necessary quantitative experimental basis for a successful theory of superconductivity in iron-based materials which takes into account both, spin-orbit interaction and electronic nematicity.
The importance of antiferromagnetic fluctuations are widely acknowledged in most unconventional superconductors. In addition, cuprates and iron pnictides often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. However, these nematic correlations are intertwined with antiferromagnetic or charge orders, preventing us to identify the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systemati…
Understanding the interplay of structural and electronic symmetry breaking in Fe-based high temperature superconductors remains of high interest. In this work we grow strain-patterned multilayer FeSe thin films in a range of thicknesses using molecular beam epitaxy. We study the formation of electronic nematic domains and spatially-varying strain using scanning tunneling microscopy and spectroscopy. We directly visualize the formation of edge dislocations that give rise to a two-dimensional edge dislocation network in the films. Interestingly, we observe a 45 degree in-plane rotation of the di…
In a material prone to a nematic instability, anisotropic strain in principle provides a preferred symmetry-breaking direction for the electronic nematic state to follow. This is consistent with experimental observations, where electronic nematicity and structural anisotropy typically appear hand-in-hand. In this work, we discover that electronic nematicity can be locally decoupled from the underlying structural anisotropy in strain-engineered iron-selenide (FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe with a nanoscale network of modulations that give rise to sp…
We investigate nematic states in both bulk FeSe and FeSe thin films. It is found that their band structures and signature features that were observed in a variety of experiments can be perfectly explained by introducing the $d$-wave nematic orders that are required to have contributions from all $t_{2g}$ d-orbitals, which contradicts the conventional wisdom that the nematicity is simply driven by the orbital degeneracy between the $d_{xz}$ and $d_{yz}$ orbitals. These orders can be generated by the Coulomb interaction between the nearest neighbor Fe sites. In the presence of spin-orbital coupl…
The nature of the nematic state in FeSe remains one of the major unsolved mysteries in Fe- based superconductors. Both spin and orbital physics have been invoked to explain the origin of this phase. Here we present experimental evidence for frustrated, short-range magnetic order, as suggested by several recent theoretical works, in the nematic state of FeSe. We use a combination of magnetostriction, susceptibility and resistivity measurements to probe the in-plane anisotropies of the nematic state and its associated fluctuations. Despite the absence of long-range magnetic order in FeSe, we obs…
We report comprehensive angle-resolved photoemission investigations on the electronic structure of single crystal multiple-layer FeSe films grown on CaF2 substrate by pulsed laser deposition (PLD) method. Measurements on FeSe/CaF2 samples with different superconducting transition temperatures Tc of 4 K, 9 K and 14 K reveal electronic difference in their Fermi surface and band structure. Indication of the nematic phase transition is observed from temperature-dependent measurements of these samples; the nematic transition temperature is 140-160 K, much higher than 90 K for the bulk FeSe. Potassi…
The electronic structure of FeSe thin films grown on SrTiO3 substrate is studied by angle-resolved photoemission spectroscopy (ARPES). We reveal the existence of Dirac cone band dispersions in FeSe thin films thicker than 1 Unit Cell below the nematic transition temperature, whose apex are located -10 meV below Fermi energy. The evolution of Dirac cone electronic structure for FeSe thin films as function of temperature, thickness and cobalt doping is systematically studied. The Dirac cones are found to be coexisted with the nematicity in FeSe, disappear when nematicity is suppressed. Our resul…
Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review…
Superconductivity emerges in proximity to a nematic phase in most iron-based superconductors. It is therefore important to understand the impact of nematicity on the electronic structure. Orbital assignment and tracking across the nematic phase transition prove to be challenging due to the multiband nature of iron-based superconductors and twinning effects. Here, we report a detailed study of the electronic structure of fully detwinned FeSe across the nematic phase transition using angle-resolved photoemission spectroscopy. We clearly observe a nematicity-driven band reconstruction involving d…
The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the nematic/structural transition at $T_{s}\approx$90~K. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strain-free samples. The anisotropy peaks slightly below $T_{s}$ and decreases to nearly zero on cooling down t…
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 the 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 discu…
We present a comprehensive study of the evolution of the nematic electronic structure of FeSe using high resolution angle-resolved photoemission spectroscopy (ARPES), quantum oscillations in the normal state and elastoresistance measurements. Our high resolution ARPES allows us to track the Fermi surface deformation from four-fold to two-fold symmetry across the structural transition at ~87 K which is stabilized as a result of the dramatic splitting of bands associated with dxz and dyz character. The low temperature Fermi surface is that a compensated metal consisting of one hole and two elect…
To elucidate the origin of nematic order in FeSe, we performed field-dependent 77Se-NMR measurements on single crystals of FeSe. We observed orbital ordering from the splitting of the NMR spectra and Knight shift and a suppression of it with magnetic field B0 up to 16 T applied parallel to the Fe-planes. There is a significant change in the distribution and magnitude of the internal magnetic field across the orbital ordering temperature Torb while stripe-type antiferromagnetism is absent. Giant antiferromagnetic (AFM) spin fluctuations measured by the NMR spin-lattice relaxation are gradually …
A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature ($T_{\rm c}$). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving nonmagnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe overlap with each other, the effects of two orders on superconductivity remain perplexing. Here we construct the three-dimensional electronic phase diagram, temperature ($T$) against pressure ($P$) and isovalent S-su…
Formation of electronic nematicity is a common thread of unconventional superconductors. In iron-based materials, the long-range nematic order is revealed by the orthorhombic lattice distortion, which importance is a highly controversial topic due the small magnitude of the distortion. Here, we study the local crystal structure of FeSe and its interaction with electronic degrees of freedom using ultrafast electron diffraction, x-ray pair distribution function analysis, and transmission electron microscopy and find a significant lattice response to local nematicity. The study demonstrates how l…
The importance of the spin-orbit coupling (SOC) effect in Fe-based superconductors (FeSCs) has recently been under hot debate. Considering the Hund's coupling-induced electronic correlation, the understanding of the role of SOC in FeSCs is not trivial and is still elusive. Here, through a comprehensive study of 77Se and 57Fe nuclear magnetic resonance, a nontrivial SOC effect is revealed in the nematic state of FeSe. First, the orbital-dependent spin susceptibility, determined by the anisotropy of the 57Fe Knight shift, indicates a predominant role from the 3dxy orbital, which suggests the coe…
Superconducting FeSe single crystals of (001) orientation are synthesized via a hydrothermal ion-release route. An Ising spin-nematic order is identified by our systematic measurements of in-plane angular-dependent magnetoresistance (AMR) and static magnetization. The turn-on temperature of anisotropic AMR signifies the Ising spin-nematic ordering temperature Tsn, below which a two-fold rotational symmetry is observed in the iron plane. A downward curvature appears below Tsn in the temperature dependence of static magnetization for the weak in-plane magnetic field as reported previously. Remar…
We investigate the electronic structures of FeSe in the presence of different possible orders. We find that only ferro-orbital order (FO) and collinear antiferro-magnetism (C-AFM) can simultaneously induce splittings at $Γ$ and M. Bicollinear antiferro-magnetism (B-AFM) and spin-orbit coupling (SOC) have very similar band structure on $Γ$-M near the Fermi level. The temperature insensitive splitting at $Γ$ and the temperature dependent splitting at M observed in recent experiments can be explained by the d-wave bond nematic (dBN) order together with SOC. The recent observed Dirac cones and the…
We analyze theoretically the magnetic anisotropy in the nematic phase of FeSe by computing the spin and the orbital susceptibilities from the microscopic multiorbital model. In particular, we take into account both the $xz/yz$ and the recently proposed non-local $xy$ nematic ordering and show that the latter one could play a crucial role in reproducing the experimentally-measured temperature dependence of the magnetic anisotropy. This provides a direct fingerprint of the different nematic scenarios on the magnetic properties of FeSe.
Isoelectronic substitution is an ideal tuning parameter to alter electronic states and correlations in iron-based superconductors. As this substitution takes place outside the conducting Fe planes, the electronic behaviour is less affected by the impurity scattering experimentally and relevant key electronic parameters can be accessed. In this short review, I present the experimental progress made in understanding the electronic behaviour of the nematic electronic superconductors, FeSe1-xSx. A direct signature of the nematic electronic state is in-plane anisotropic distortion of the Fermi surf…
The nature of the tetragonal-to-orthorhombic structural transition at $T_s\approx90$ K in single crystalline FeSe is studied using shear-modulus, heat-capacity, magnetization and NMR measurements. The transition is shown to be accompanied by a large shear-modulus softening, which is practically identical to that of underdoped Ba(Fe,Co)$_2$As$_2$, suggesting very similar strength of the electron-lattice coupling. On the other hand, a spin-fluctuation contribution to the spin-lattice relaxation rate is only observed below $T_s$. This indicates that the structural, or "nematic", phase transition …
High-resolution time- and angle-resolved photoemission measurements were made on FeSe superconductors. With ultrafast photoexcitation, two critical excitation fluences that correspond to two ultrafast electronic phase transitions were found only in the $d_{yz}$-orbit-derived band near the Brillouin-zone center within our time and energy resolution. Upon comparison to the detailed temperature dependent measurements, we conclude that there are two equilibrium electronic phase transitions (at approximately 90 and 120 K) above the superconducting transition temperature, and an anomalous contributi…
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, the…
Electronic nematicity in correlated metals often occurs alongside another instability such as magnetism. As a result, the question remains whether nematicity alone can drive unconventional superconductivity or anomalous (quantum critical) transport in such systems. In FeSe, nematicity emerges in isolation, providing a unique opportunity to address this question. Studies to date, however, have proved inconclusive; while signatures of nematic criticality are observed upon sulfur substitution, they appear to be quenched under the application of pressure due to the emergent magnetism. Here, we stu…
The exotic normal state of iron chalcogenide superconductor FeSe, which exhibits vanishing magnetic order and possesses an electronic nematic order, triggered extensive explorations of its magnetic ground state. To understand its novel properties, we study the ground state of a highly frustrated spin-$1$ system with bilinear-biquadratic interactions using unbiased large-scale density matrix renormalization group. Remarkably, with increasing biquadratic interactions, we find a paramagnetic phase between Néel and stripe magnetic ordered phases. We identify this phase as a candidate of nematic qu…
The interplay between the nematic order and magnetism in FeSe is not yet well understood. There is a controversy concerning the relationship between orbital and spin degrees of freedom in FeSe and their relevance for superconductivity. Here we investigate the effect of S substitution on the nematic transition temperature ($T_{\rm n}$) and the low-energy spin fluctuations (SF) in FeSe single crystals. We show that the low-energy SF emerge below the nematic transition. The difference between the onset temperature for the critical SF ($T_{\rm SF}$) and $T_{\rm n}$ is small for FeSe but significan…
Understanding superconductivity requires detailed knowledge of the normal electronic state from which it emerges. A nematic electronic state that breaks the rotational symmetry of the lattice can potentially promote unique scattering relevant for superconductivity. Here, we investigate the normal transport of superconducting FeSe$_{1-x}$S$_x$ across a nematic phase transition using high magnetic fields up to 69 T to establish the temperature and field-dependencies. We find that the nematic state is an anomalous non-Fermi liquid, dominated by a linear resistivity at low temperatures that can tr…
Motivated by the recent low-tempearture experiments on bulk FeSe, we study the electron correlation effects in a multiorbital model for this compound in the nematic phase using the U(1) slave-spin theory. We find that a finite nematic order helps to stabilize an orbital selective Mott phase. Moreover, we propose that when the d- and s-wave bond nematic orders are combined with the ferro-orbital order, there exists a surprisingly large orbital selectivity between the xz and yz orbitals even though the associated band splitting is relatively small. Our results explain the seemingly unusual obser…
We present $^{77}$Se-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\rm s}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperat…
An SDW antiferromagnetic (SDW-AF) low temperature phase transition is generally observe and the AF spin fluctuations are considered to play an important role for the superconductivity paring mechanism in FeAs superconductors. However, a similar magnetic phase transition is not observed in FeSe superconductors, which has caused considerable discussion. We report on the intrinsic electronic states of FeSe as elucidated by transport measurements under magnetic fields using a high quality single crystal. A mobility spectrum analysis, an ab initio method that does not make assumptions on the transp…
We report on the synthesis and physical properties of FeSe$_{1-x}$Te$_x$ single crystals with a low Te content (x = 0.17, 0.21, 0.25), where the replacement of Se with Te partially suppresses superconductivity. Resistivity and Hall effect measurements indicate weak anomalies at elevated temperatures ascribed to nematic transitions. A quasi-classical analysis of transport data, including in a pulsed magnetic field of up to 25 T, confirms the inversion of majority carriers type from holes in FeSe to electrons in FeSe$_{1-x}$Te$_x$ at x $>$ 0.17. The temperature-dependent term in the elastoresist…
The recent study of $^{77}$Se nuclear magnetic resonance (NMR) in a $β$-FeSe single crystal proposed that ferro-orbital order breaks the $90^\circ$ $C_4$ rotational symmetry, driving nematic ordering. Here, we report an NMR study of the impact of small strains generated by gluing on nematic state and spin fluctuations. We observe that the local strains strongly affect the nematic transition, considerably enhancing its onset temperature. On the contrary, no effect on low-energy spin fluctuations was found. Furthermore we investigate the interplay of the nematic phase and superconductivity. Our …
One dimensional hybrid systems play an important role in the search for topological superconductivity. Nevertheless, all one dimensional hybrid systems so far have been externally defined. Here we show that one-dimensional domain wall in a nematic superconductor can serve as an emergent hybrid system in the presence of spin-orbit coupling. As a concrete setting we study the domain wall between nematic domains in FeSe, which is well established to be a nematic superconductor. We first show on the symmetry grounds that spin-triplet pairing can be induced at the domain wall by constructing a Ginz…
FeSe is a unique member of the family of iron-based superconductors, not only because of the high values of $T_{c}$ in FeSe monolayer, but also because in bulk FeSe superconductivity emerges inside a nematic phase without competing with long-range magnetic order. Near $T_{c}$, superconducting order necessarily has $s+d$ symmetry, because nematic order couples linearly the $s$-wave and $d$-wave harmonics of the superconducting order parameter. Here we argue that the near-degeneracy between $s$-wave and $d$-wave pairing instabilities in FeSe, combined with the sign-change of the nematic order pa…
The nematic order (nematicity) is considered one of the essential ingredients to understand the mechanism of Fe-based superconductivity. In most Fe-based superconductors (pnictides), nematic order is reasonably close to the antiferromagnetic order. In FeSe, in contrast, a nematic order emerges below the structure phase transition at T_s = 90 K with no magnetic order. The case of FeSe is of paramount importance to a universal picture of Fe-based superconductors. The polarized ultrafast spectroscopy provides a tool to probe simultaneously the electronic structure and the magnetic interactions th…
Bulk FeSe is a special iron-based material in which superconductivity emerges inside a well-developed nematic phase. We present a microscopic model for this nematic superconducting state, which takes into account the mixing between $s-$wave and $d-$wave pairing channels and the changes in the orbital spectral weight promoted by the sign-changing nematic order parameter. We show that nematicity gives rise to a $\cos2θ$ variation of the pairing gap on the hole pocket that agrees with ARPES and STM data for experimentally-extracted Fermi surface parameters. We further argue that, in BCS theory, $…
FeSe is an intriguing iron-based superconductor. It presents an unusual nematic state without magnetism and can be tuned to increase the critical superconducting temperature. Recently it has been observed a noteworthy anisotropy of the superconducting gaps. Its explanation is intimately related to the understanding of the nematic transition itself. Here we show that the spin-nematic scenario driven by orbital-selective spin-fluctuations provides a simple scheme to understand both phenomena. The pairing mediated by anisotropic spin modes is not only orbital selective but also nematic, leading t…
A hallmark of the iron-based superconductors is the strong coupling between magnetic, structural and electronic degrees of freedom. However, a universal picture of the normal state properties of these compounds has been confounded by recent investigations of FeSe where the nematic (structural) and magnetic transitions appear to be decoupled. Here, using synchrotron-based high-energy x-ray diffraction and time-domain Moessbauer spectroscopy, we show that nematicity and magnetism in FeSe under applied pressure are indeed strongly coupled. Distinct structural and magnetic transitions are observed…
We study the crystal structure of the tetragonal iron selenide FeSe and its nematic phase transition to the low-temperature orthorhombic structure using synchrotron x-ray and neutron scattering analyzed in both real and reciprocal space. We show that in the local structure the orthorhombic distortion associated with the electronically driven nematic order is more pronounced at short length scales. It also survives up to temperatures above 90 K where reciprocal-space analysis suggests tetragonal symmetry. Additionally, the real-space pair distribution function analysis of the synchrotron x-ray …
We revisit bulk FeSe through the systematic first-principles electronic structure calculations. We find that there are a series of staggered $n$-mer antiferromagnetic (AFM) states with corresponding energies below that of the collinear AFM state which is the ground state for the parent compounds of most iron-based superconductors. Here the staggered $n$-mer ($n$ any integer $>1$) means that a set of $n$ adjacent spins parallel on a line along $b$-axis with spins in antiparallel between $n$-mers and along $a$-axis. Among them, the lowest energy states are quasi-degenerate staggered dimer and st…
The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing property of the iron based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains however a challenge, because their associated susceptibilities are not easily accessible by conventional probes. Here using FeSe as a model system, and symmetry resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural …
Strain is a powerful experimental tool to explore new electronic states and understand unconventional superconductivity. Here, we investigate the effect of uniaxial strain on the nematic and superconducting phase of single crystal FeSe using magnetotransport measurements. We find that the resistivity response to the strain is strongly temperature dependent and it correlates with the sign change in the Hall coefficient being driven by scattering, coupling with the lattice and multiband phenomena. Band structure calculations suggest that under strain the electron pockets develop a large in-plane…
In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, atomic layers of FeSe reverse the situation, having high temperature superconductivity appearing alongside a suppression of nematic order. To investigate this phenomenon, we study a minimal electronic model of FeSe, with interactions that enhance nematic fluctuations. This model is sign problem free, and is simulated using determinant quantum Monte Carlo (DQMC). We developed a DQMC algorithm with parallel tempering, which proves to be an efficient source of global updates and allows us to access the r…
Mechanism of unconventional superconductivity in FeSe has been intensely scrutinized recently because of a variety of exotic properties unprecedented for other iron-based superconductors. A central unanswered question concerns the origin of the interaction that causes the nematic transition at $T_s=90\,K$ without accompanying magnetic order. Elucidating the nature of spin excitations in the normal state is a key to addressing this issue. Here we report, from inelastic neutron-scattering measurements in FeSe single crystals, that high-energy spin excitation spectra of FeSe exhibit characteristi…
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…
Recent resonant inelastic x-ray scattering (RIXS) experiments have detected a significant high-energy spin-excitation anisotropy in the nematic phase of the enigmatic iron-based superconductor FeSe, whose origin remains controversial. We apply an itinerant model previously used to describe the spin-excitation anisotropy as measured by neutron scattering measurements, with magnetic fluctuations included within the RPA approximation. The calculated RIXS cross section exhibits overall agreement with the RIXS data, including the high energy spin-excitation anisotropy.
Unconventional superconductivity often competes or coexists with other electronic orders. In iron-based superconductors, relationship between superconductivity and the nematic state, where the lattice rotational symmetry is spontaneously broken in the electronic states, has been discussed but unclear. Using spectroscopic-imaging scanning tunneling microscopy, we investigate how the band structure and the superconducting gap evolve in FeSe$_{1-x}$S$_x$, as the sulfur substitution suppresses nematicity that eventually diminishes at the nematic end point (NEP) at $x=0.17$. Anisotropic quasipartic…
Superconductivity originates from pairing of electrons. Pairing channel on Fermi surface and pairing glue are thus two pivotal issues for understanding a superconductor. Recently, high-temperature superconductivity over 40 K was found in electron-doped FeSe superconductors including K$_x$Fe$_{2-y}$Se$_2$, Li$_{0.8}$Fe$_{0.2}$OHFeSe, and 1 monolayer FeSe thin film. However, their pairing mechanism remains controversial. Here, we studied the systematic evolution of electronic structure in potassium-coated FeSe single crystal. The doping level is controlled precisely by in situ evaporating potass…
The origin of the 90 K nematic transition in the chalcogenide FeSe, which displays no magnetic order down to T=0, remains a major puzzle for a unifying theory for the iron-based superconductors. We analyze this problem in light of recent experimental data which reveal very small Fermi pockets in this material. We show that the smallness of the Fermi energy leads to a near-degeneracy between magnetic fluctuations and fluctuations in the charge-current density-wave channel. While the two fluctuation modes cooperate to promote the same preemptive Ising-nematic order, they compete for primary orde…
We present a phenomenological theory of the interplay between nematic order and superconductivity in the vicinity of a vortex induced by an applied magnetic field. Nematic order can be strongly enhanced in the vortex core. As a result, the vortex cores become elliptical in shape. For the case where there is weak bulk nematic order at zero magnetic field, the field-induced eccentricity of the vortex core has a slow power-law decay away from the core. Conversely, if the nematic order is field-induced, then the eccentricity is confined to the vortex core. We discuss the relevance of our results t…
FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering at ambient pressure. Here, to study how the pairing interaction evolves with nematicity, we measured the thermal conductivity and specific heat of FeSe$_{1-x}$S$_x$, where the nematicity is suppressed by isoelectronic sulfur substitution. We find that in the whole nematic ($0\leq x \leq 0.17$) and tetragonal ($x=0.20$) regimes, the application of small magnetic field causes a steep increase of both quantities. This indicates the existence of deep minima or line nodes in …
Field-induced incipient spin-density phase stabilized inside the nematic phase of FeSe$_{1-x}$S$_x$
University of Oxford（牛津大学）；Laboratoire National des Champs Magnetiques Intenses, EMFL, CNRS, Univ. Grenoble Alpes, INSA-T, Univ. Toulouse 3（法国国家强磁场实验室）；National High Magnetic Field Laboratory and Department of Physics, Florida State University（佛罗里达州立大学）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
The lifting of $d_{xz}$-$d_{yz}$ orbital degeneracy is often considered a hallmark of the nematic phase of Fe-based superconductors, including FeSe, but its origin is not yet understood. Here we report a high resolution Angle-Resolved Photoemission Spectroscopy study of single crystals of FeSe, accounting for the photon-energy dependence and making a detailed analysis of the temperature dependence. We find that the hole pocket undergoes a fourfold-symmetry-breaking distortion in the nematic phase below 90~K, but in contrast the changes to the electron pockets do not require fourfold symmetry-b…
We report a high-resolution laser-based angle-resolved photoemission spectroscopy (laser-ARPES) study of single crystals of FeSe, focusing on the temperature-dependence of the hole-like bands around the ${\rm Γ}$ point. As the system cools through the tetragonal-orthorhombic "nematic" structural transition at 90~K, the splitting of the $d_{xz}$/$d_{yz}$ bands is observed to increase by a magnitude of 13 meV. Moreover, the onset of a $\sim$10 meV downward shift of the $d_{xy}$ band is also at 90~K. These measurements provide clarity on the nature, magnitude and temperature-dependence of the ban…
Quantum spin Hall (QSH) effect is an intriguing phenomenon arising from the helical edge states in two-dimensional topological insulators. We use molecular beam epitaxy (MBE) to prepare FeSe films with atomically sharp nematic domain boundaries, where tensile strains, nematicity suppression and topological band inversion are simultaneously achieved. Using scanning tunneling microscopy (STM), we observe edge states at the Fermi level that spatially distribute as two distinct strips in the vicinity of the domain boundaries. At the endpoint of the boundaries, a bound state at the Fermi level is f…
To understand the nematicity in Fe-based superconductors, nontrivial $k$-dependence of the orbital polarization ($ΔE_{xz}(k)$, $ΔE_{yz}(k)$) in the nematic phase, such as the sign reversal of the orbital splitting between $Γ$- and X,Y-points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole- and electron-pockets are elongated along the $k_y$- and $k_x$-axes respectively, consistently with experi…
