We measured the complex conductivity, $σ$, of FeSe$_{1-x}$Te$_x$ ($x=0-0.5$) films in the superconducting state which show a drastic increase of the superconducting transition temperature, $T_\textrm{c}$, when the nematic order disappears. Since the magnetic penetration depth, $λ$ $(>$ 400 nm), of Fe(Se,Te) is longer than the typical thickness of the film ($\sim$100 nm), we combined the coplanar waveguide resonator and cavity perturbation techniques to evaluate both the real and imaginary parts of $σ$. Films with a nematic order showed a qualitatively different temperature dependence in penetration depth and quasiparticle scattering time when compared with those without nematic order, suggesting that nematic order influences the superconducting gap structure. Conversely, the proportionality between superfluid density, $n_\textrm{s}$ ($\proptoλ^{-2}$), and $T_\textrm{c}$ was observed irrespective of the presence or absence of nematic order. This result indicates that the amount of superfluid has a stronger impact on the $T_\textrm{c}$ of Fe(Se,Te) than the presence or absence of nematic order. Combining these results with band dispersions calculated using density functional theory, we propose that the change of the Fermi surface associated with nematicity is the primary factor influencing the change of $T_\textrm{c}$ and the superconducting gap structure in Fe(Se,Te).
The angular-dependent magnetoresistance (AMR) of the ab plane is measured on the single crystals of FeSe1-xSx (x = 0, 0.07, 0.13 and 1) and FeSe1-yTey (y = 0.06, 0.61 and 1) at various temperatures under fields up to 9 T. A pronounced twofold-anisotropic carrier-scattering effect is identified by AMR, and attributed to a magnetic-field-induced spin nematicity that emerges from the tetragonal normal-state regime below a characteristic temperature Tsn. This magnetically polarized spin nematicity is found to be ubiquitous in the isoelectronic FeSe1-xSx and FeSe1-yTey systems, no matter whether th…
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…
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…
Robust short-range-ordered nematicity in FeSe evidenced by high-pressure NMR
我们报告了高压$^{77}$ Se NMR研究FeSe单晶，揭示了一个突出的不均匀的NMR谱线宽度加宽冷却后，与磁场施加沿tetraxide [110]方向。这些数据表明存在短程有序的，不均匀的电子向列性，它具有令人惊讶的长时间尺度超过毫秒。短程有序的生存温度高达$8$倍的结构转变温度，并保持对压力的鲁棒性，相反，强的压力依赖性的轨道排序，结构转变，和基态磁性。FeSe的（$P$，$T$）空间中的静态向列性的这种扩展区域表明了一个非常大的波动区域，并为理解铁基超导体中的电子向列性提供了新的见解和约束。
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…
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…
Pressure Induced Stripe-order Antiferromagnetism and First-order Phase Transition in FeSe
为了阐明FeSe的磁结构和向列性的起源，我们对FeSe单晶进行了高压$^{77}$ Se NMR研究。我们发现，抑制的结构转变温度与压力高达约2 GPa的各向异性的奈特位移。在2GPa以上，打破空间四重旋转对称性的条序反铁磁性由不同场取向下的NMR谱确定，温度低至50 mK。磁相变是一级相变，这意味着存在一个伴随的结构转变通过自旋-晶格耦合。条纹型自旋波动在高温下观察到，并保持强大的压力。这些结果为FeSe中向列性和磁性之间的强耦合提供了明确的证据，从而支持了铁基超导体中磁驱动向列性的普遍假设。
FeSe undergoes a transition from a tetragonal to a slightly orthorhombic phase at 90\,K, and becomes a superconductor below 8\,K. The orthorhombic phase is sometimes called a nematic phase because quantum oscillation, neutron, and other measurements detect a significant asymmetry in $x$ and $y$. How nematicity affects superconductivity has recently become a matter of intense speculation. Here we employ an advanced \emph{ab-initio} Green's function description of superconductivity and show that bulk tetragonal FeSe would, in principle, superconduct with almost the same T$_{c}$ as the nematic ph…
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.
We report pair distribution function measurements of the iron-based superconductor FeSe above and below the structural transition temperature. Structural analysis reveals a local orthorhombic distortion with a correlation length of about 4 nm at temperatures where an average tetragonal symmetry is observed. The analysis further demonstrates that the local distortion is larger than the distortion at temperatures where the average observed symmetry is orthorhombic. Our results suggest that the low-temperature macroscopic nematic state in FeSe forms from an imperfect ordering of orbital-degenerac…
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 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 ene…
The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-$T_c$ superconductors, regardless of cuprate or pnictide family. The nematic state in high-$T_c$ systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin film…
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…
Magnetism induced by external pressure ($p$) was studied in a FeSe crystal sample by means of muon-spin rotation. The magnetic transition changes from second-order to first-order for pressures exceeding the critical value $p_{\rm c}\simeq2.4-2.5$ GPa. The magnetic ordering temperature ($T_{\rm N}$) and the value of the magnetic moment per Fe site ($m_{\rm Fe}$) increase continuously with increasing pressure, reaching $T_{\rm N}\simeq50$~K and $m_{\rm Fe}\simeq0.25$ $μ_{\rm B}$ at $p\simeq2.6$ GPa, respectively. No pronounced features at both $T_{\rm N}(p)$ and $m_{\rm Fe}(p)$ are detected at $…
Two distinct superconducting pairing states divided by the nematic end point in FeSe$_{1-x}$S$_{x}$
非常规超导性经常与其他电子序竞争或共存。在铁基超导体中，超导电性与电子态中晶格旋转对称性自发破缺的超导态之间的关系已经讨论过，但不清楚。使用光谱成像扫描隧道显微镜，我们调查如何的能带结构和超导能隙的FeSe $_{1-x}$ S $_x$的演变，作为硫取代抑制向列性，最终在$x=0.17$的最后一个端点（NEP）减少。各向异性的准粒子干涉图案，这代表的能带结构，逐渐成为各向同性的增加$x$没有检测到异常的带参数在NEP。相比之下，超导能隙在超导相几乎是完整的，一旦$x$超过NEP，它就会突然收缩。我们的观察意味着，存在或不存在的向列性的结果在两个不同的配对状态，而配对相互作用是不敏感的向列性的强度。这为理解配对机制提供了线索。
The iron-based superconductors are characterized by multiple-orbital physics where all the five Fe 3$d$ orbitals get involved. The multiple-orbital nature gives rise to various novel phenomena like orbital-selective Mott transition, nematicity and orbital fluctuation that provide a new route for realizing superconductivity. The complexity of multiple-orbital also asks to disentangle the relationship between orbital, spin and nematicity, and to identify dominant orbital ingredients that dictate superconductivity. The bulk FeSe superconductor provides an ideal platform to address these issues be…
Electric Transport of a Single Crystal Iron Chalcogenide FeSe Superconductor: Evidence of Symmetry Breakdown Nematicity and Additional Ultrafast Dirac cone-Like Carriers
在FeAs超导体中普遍观察到SDW反铁磁（SDW-AF）低温相变，AF自旋涨落对超导配对机制起着重要作用.然而，在FeSe超导体中没有观察到类似的磁相变，这引起了相当多的讨论。我们报告的内在电子状态的铁硒阐明运输测量下磁场使用高品质的单晶。一个迁移率谱分析，从头算方法，不作假设的多载流子系统中的输运参数，提供了非常重要和明确的证据，另一个隐藏的顺序，最有可能的对称性破缺从四碳C4对称性的C2对称向列性与选择性d-轨道分裂，存在于超导FeSe的情况下以外的AF磁序自旋涨落。FeSe中的本征低温相处于几乎补偿的半金属态，但另外伴随有狄拉克锥状超快电子$\sim$ 10 $^4$ cm $^2$（VS）$^{-1}$作为少数载流子。
Interrelationships between nematicity, antiferromagnetic spin fluctuations and superconductivity: Role of hotspots in FeSe$_{1-x}$S$_{x}$ revealed by high pressure $^{77}$Se NMR study
FeSe is a unique high-$T_c$ iron-based superconductor in which nematicity, superconductivity, and magnetism are entangled with each other in the $P$-$T$ phase diagram. We performed $^{77}$Se-nuclear magnetic resonance measurements under pressures of up to 3.9 GPa on 12% S-substituted FeSe, in which the complex overlap between the nematicity and magnetism are resolved. A pressure-induced Lifshitz transition was observed at 1.0 GPa as an anomaly of the density of states and as double superconducting (SC) domes accompanied by different types of antiferromagnetic (AF) fluctuations. The low-$T_{\rm…
The interplay of orbital and spin degrees of freedom is the fundamental characteristic in numerous condensed matter phenomena, including high temperature superconductivity, quantum spin liquids, and topological semimetals. In iron-based superconductors (FeSCs), this causes superconductivity to emerge in the vicinity of two other instabilities: nematic and magnetic. Unveiling the mutual relationship among nematic order, spin fluctuations, and superconductivity has been a major challenge for research in FeSCs, but it is still controversial. Here, by carrying out 77Se nuclear magnetic resonance (…
Electronic nematic behavior has been identified and studied in iron-based superconductors for some time, particularly in the well-known BaFe$_2$As$_2$ system, where it is well-known to compete with superconductivity. On the other hand, it has been shown recently that FeSe displays a negligible effect of nematicity on superconductivity near the superconducting transition, and actual cooperation between the two orders when the system is doped with S. Recently it has also been proposed that LiFeAs undergoes a nematic transition in the superconducting state itself. Generally, we expect superconduc…
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 sulfur substituted FeSe system, FeSe$_{1-x}$S$_{x}$, provides a versatile platform for studying the relationship between nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on FeSe$_{0.91}$S$_{0.09}$, we established the pressure($p$)-temperature($T$) phase diagram in which the nematic state is suppressed with pressure showing a nematic quantum phase transition (QPT) around $p$ = 0.5 GPa, two SC regions, separated by the QPT, appear and antiferromagnetic (AFM) phase emerges above $\sim$3.3 GPa. From 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 electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe the expected electron pocket at the $Y$ point in the 1-Fe Brillouin zone. It has been speculated that this pocket, essential for an understanding of the superconducting state, is either absent or incoherent. Here, we perform a theoretical study of the preferred nematic order originating from nearest-neighbor Coulomb interactions in an electronic model relevant for FeSe. We find that at low temperatures the dominating nematic components are of inter-orbit…
Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO3, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists a…
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…
We present a systematic angle-resolved photoemission spectroscopy study of the superconducting gap in FeSe. The gap function is determined in a full Brillouin zone including all Fermi surfaces and kz-dependence. We find significant anisotropy of the superconducting gap in all momentum directions. While the in-plane anisotropy can be explained by both, nematicity-induced pairing anisotropy and orbital-selective pairing, the kz-anisotropy requires additional refinement of theoretical approaches.
Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here we introduce the "form factor" that generalizes the nonlocal order parameter into the …
We systematically studied in-plane optical conductivity of FeSe$_{1-x}$Te$_{x}$ thin films fabricated on CaF$_{2}$ substrates for $x$ = 0, 0.1, 0.2, and 0.4. This system shows a large enhancement of superconducting transition temperature $T_{\mathrm{c}}$ at $x \sim$ 0.2 and a gentle decrease in $T_{\mathrm{c}}$ with further increasing $x$. The low-energy optical conductivity spectrum is described by the sum of narrow and broad Drude components, associated with coherent and incoherent charge dynamics, respectively. With increasing Te content, the spectral weight of the narrow Drude component de…
A rich variety of nematic/smectic orders in Fe-based superconductors is an important unsolved problem in strongly correlated electron systems. A unified understanding of these orders has been investigated for the last decade. In this article, we explain the $B_{1g}$ symmetry nematic transition in FeSe$_{1-x}$Te$_x$, the $B_{2g}$ symmetry nematicity in AFe$_2$As$_2$ (A=Cs, Rb), and the smectic state in BaFe$_2$As$_2$ based on the same framework. We investigate the quantum interference mechanism between spin fluctuations by developing the density wave equation. The observed rich variety of nemat…
