Pomeranchuk instability in the nematic phase of two monolayer FeSe/SrTiO3
C. Y. Tang, X. -L. Peng, Y. -H. Yuan, P. Zhang, G. -N. Phan, S. -Y. Gao, Y. -B. Huang, L. -Y. Kong, T. Qian, W. Li, Q. -K. Xue, Z. -Q. Wang, K. Jiang, Y. -J. Sun, H. Ding
Nematicity, where electrons break rotational symmetry while preserving translational symmetry, is ubiquitous in strongly correlated quantum matters, including high-Tc cuprates and iron-based superconductors. A central question in nematicity is whether it is driven by Pomeranchuk instability in momentum space or orbital order (polarization) in real space, especially as nematicity intertwines with superconductivity. FeSe/SrTiO3 (STO), where nematicity occurs without long-range magnetic order, is an ideal platform for studying the nature and origin of the electronic nematicity. Here we present direct evidence of Pomeranchuk nematic order in two monolayer FeSe/STO using angle-resolved photoemission spectroscopy, revealing a remarkable degeneracy of dxz and dyz bands at the Brillouin zone center, but a significant band separation at the zone corner. This momentum-dependent nematicity demonstrates that nematicity in FeSe/STO originates from the Pomeranchuk instability, offering insights into the relationship between nematicity and superconductivity. Our results establish two-dimensional FeSe thin film as a powerful platform for investigating quantum physics under complex intertwinement.
We study the competition between the nematic and the hexatic phases of a two-dimensional spinless Fermi fluid near Pomeranchuk instabilities. We show that the general phase diagram of this theory contains a bicritical point where two second order lines and a first order nematic/hexatic phase transition meet together. We found that at criticality, and deep inside the associated symmetry broken phases, the low energy theory is governed by a dissipative cubic mode, even near the bicritical point where nematic and hexatic fluctuations cannot be distinguished due to very strong dynamical couplings.
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 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.
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…
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…
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…
We investigate the evolution of the Fermi surfaces and electronic interactions across the nematic phase transition in single crystals of FeSe1-xSx using Shubnikov-de Haas oscillations in high magnetic fields up to 45 tesla in the low temperature regime. The unusually small and strongly elongated Fermi surface of FeSe increases monotonically with chemical pressure, x, due to the suppression of the in-plane anisotropy except for the smallest orbit which suffers a Lifshitz-like transition once nematicity disappears. Even outside the nematic phase the Fermi surface continues to increase, in stark …
We analyze a two-dimensional Pomeranchuk-Nematic instability, trigger by the Landau parameter $F_2<0$, in the presence of a small magnetic field. Using Landau Fermi liquid theory in the isotropic phase, we analyze the collective modes near the quantum critical point $F_2=-1,ω_c=0$ (where $ω_c$ is the cyclotron frequency). We focus on the effects of parity symmetry breaking on the Fermi surface deformation. We show that, for studying the critical regime, the linear response approximation of the Landau-Silin equation is not sufficient and it is necessary to compute corrections at least of order …
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 …
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…
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.
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…
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 …
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 high-pressure $^{77}$Se NMR studies on FeSe single crystals that reveal a prominent inhomogeneous NMR linewidth broadening upon cooling, with the magnetic field applied along the tetragonal [110] direction. The data indicate the existence of short-range-ordered, inhomogeneous electronic nematicity, which has surprisingly long time scales over milliseconds. The short-range order survives temperatures up to $8$ times the structural transition temperature, and remains robust against pressure, in contrast to the strong pressure-dependence of the orbital ordering, structural transition, a…
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…
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…
Crystalline FeSe is known to display strong nematic order below a weak tetragonal-orthorhombic structural transition around $T_s\sim 90$K, and a superconducting transition at $T_c\sim 9K$. Recently, it was shown that electron irradiation, which creates pointlike potential scattering defects, has the surprising effect of enhancing $T_c$ while suppressing $T_s$. Here we discuss a possible scenario for such an effect, which postulates a competition between $s_\pm$ superconductivity and nematic order. The transition to the nematic state is modeled by a mean field theory of a $d$-wave Pomeranchuk i…
The origin of the high-temperature superconducting state observed in FeSe thin films, whose phase diagram displays no sign of magnetic order, remains a hotly debated topic. Here we investigate whether fluctuations arising due to the proximity to a nematic phase, which is observed in the phase diagram of this material, can promote superconductivity. We find that nematic fluctuations alone promote a highly degenerate pairing state, in which both $s$-wave and $d$-wave symmetries are equally favored, and $T_{c}$ is consequently suppressed. However, the presence of a sizable spin-orbit coupling or …
The iron-based superconductor FeSe has attracted much recent attention because of its simple crystal structure, distinct electronic structure and rich physics exhibited by itself and its derivatives. Determination of its intrinsic electronic structure is crucial to understand its physical properties and superconductivity mechanism. Both theoretical and experimental studies so far have provided a picture that FeSe consists of one hole-like Fermi surface around the Brillouin zone center in its nematic state. Here we report direct observation of two hole-like Fermi surface sheets around the Brill…
FeSe is arguably the simplest, yet the most enigmatic, iron-based superconductor. Its nematic but non-magnetic ground state is unprecedented in this class of materials and stands out as a current puzzle. Here, our NMR measurements in the nematic state of mechanically detwinned FeSe reveal that both the Knight shift and the spin-lattice relaxation rate 1/T_1 possess an in-plane anisotropy opposite to that of the iron pnictides LaFeAsO and BaFe2As2. Using a microscopic electron model that includes spin-orbit coupling, our calculations show that an opposite quasiparticle weight ratio between the …
We have performed high-resolution angle-resolved photoemission spectroscopy on FeSe superconductor (Tc ~ 8 K), which exhibits a tetragonal-to-orthorhombic structural transition at Ts ~ 90 K. At low temperature we found splitting of the energy bands as large as 50 meV at the M point in the Brillouin zone, likely caused by the formation of electronically driven nematic states. This band splitting persists up to T ~ 110 K, slightly above Ts, suggesting that the structural transition is triggered by the electronic nematicity. We have also revealed that at low temperature the band splitting gives r…
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 report the evolution of the electronic nematic susceptibility in FeSe via Raman scattering as a function of hydrostatic pressure up to 5.8 GPa where the superconducting transition temperature $T_{c}$ reaches its maximum. The critical nematic fluctuations observed at low pressure vanish above 1.6 GPa, indicating they play a marginal role in the four-fold enhancement of $T_{c}$ at higher pressures. The collapse of nematic fluctuations appears to be linked to a suppression of low energy electronic excitations which manifests itself by optical phonon anomalies at around 2 GPa, in agreement with…
To elucidate the origin of nematic order in Fe-based superconductors, we report a Raman scattering study of lattice dynamics, which quantify the extent of $C_4$-symmetry breaking, in BaFe$_2$As$_2$ and FeSe. FeSe possesses a nematic ordering temperature $T_\mathrm{s}$ and orbital-related band-energy split below $T_\mathrm{s}$ that are similar to those in BaFe$_2$As$_2$, but unlike BaFe$_2$As$_2$ it has no long-range magnetic order. We find that the $E_g$ phonon-energy split in FeSe sets in only well below $T_\mathrm{s}$, and its saturated value is substantially smaller than that in BaFe$_2$As$…
We provide evidence that spin ferroquadrupolar (FQ) order is the likely ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By studying the variational mean-field phase diagram of a bilinear-biquadratic Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close proximity to the columnar antiferromagnet commonly realized in iron-based superconductors; the stability of FQ phase is further verified by the density matrix renormalization group. The dynamical spin structure factor in the FQ state is calculated with flavor-wave theory, which yields a qualitativel…
We use scanning tunneling microscopy (STM) and quasiparticle interference (QPI) imaging to investigate the low-energy orbital texture of single-layer FeSe/SrTiO$_3$. We develop a $T$-matrix model of multi-orbital QPI to disentangle scattering intensities from Fe $3d_{xz}$ and $3d_{yz}$ bands, enabling the use of STM as a nanoscale detection tool of nematicity. By sampling multiple spatial regions of a single-layer FeSe/SrTiO$_3$ film, we quantitatively exclude static $xz/yz$ orbital ordering with domain size larger than $δr^2$ = 20 nm $\times$ 20 nm, $xz/yz$ Fermi wave vector difference larger…
FeSe exhibits a novel ground state in which superconductivity coexists with a nematic order in the absence of any long-range magnetic order. Here we report an angle-resolved photoemission study on the superconducting gap structure in the nematic state of FeSe$_{0.93}$S$_{0.07}$, without the complication caused by Fermi surface reconstruction induced by magnetic order. We found that the superconducting gap shows a pronounced 2-fold anisotropy around the elliptical hole pocket near the Z point of the Brillouin zone, with gap minima at the endpoints of its major axis, while no detectable gap was …
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…
The interplay between electronic orders and superconductivity is central to the physics of unconventional superconductors, and is particularly pronounced in the iron-based superconductors. Motivated by recent experiments on FeSe, we study the superconducting pairing in its nematic phase in a multiorbital model with frustrated spin-exchange interactions. The electron correlations in the presence of the nematic order give rise to an enhanced orbital selectivity in the superconducting pairing amplitudes. This orbital-selective pairing produces a large gap anisotropy on the Fermi surface. Our resu…
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 offer an explanation for the recently observed pressure-induced magnetic state in the iron-chalcogenide FeSe based on \textit{ab initio} estimates for the pressure evolution of the most important Coulomb interaction parameters. We find that an increase of pressure leads to an overall decrease mostly in the nearest-neighbor Coulomb repulsion, which in turn leads to a reduction of the nematic order and the generation of magnetic stripe order. We treat the concomitant effects of band renormalization and the induced interplay of nematic and magnetic order in a self-consistent way and determine …
Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system.…
We report the evolution of nematic fluctuations in FeSe$_{1-x}$S$_x$ single crystals as a function of Sulfur content $x$ across the nematic quantum critical point (QCP) $x_c\sim$ 0.17 via Raman scattering. The Raman spectra in the $B_{1g}$ nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie-Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling which shifts the location of the nematic QCP. We argue that this lattice-induce…
The origin of the electronic nematicity in FeSe is one of the most important unresolved puzzles in the study of iron-based superconductors. In both spin- and orbital-nematic models, the intrinsic magnetic excitations at $\mathbf{Q}_1=(1, 0)$ and $\mathbf{Q}_2=(0, 1)$ of twin-free FeSe are expected to provide decisive criteria for clarifying this issue. Although a spin-fluctuation anisotropy below 10 meV between $\mathbf{Q}_1$ and $\mathbf{Q}_2$ has been observed by inelastic neutron scattering around $T_c\sim 9$ K ($<<T_s\sim 90$ K), it remains unclear whether such an anisotropy also persists …
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 (…
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$3.3 GPa. From the…
The emergence of high transition temperature ($T_c$) superconductivity in bulk FeSe under pressure is associated with the tuning of nematicity and magnetism. However, sorting out the relative contributions from magnetic and nematic fluctuations to the enhancement of $T_c$ remains challenging. Here, we design and conduct a series of high-pressure experiments on FeSe thin flakes. We find that, as the thickness decreases, the nematic phase boundary on temperature-pressure phase diagrams remains robust while the magnetic order is significantly weakened. A local maximum of $T_c$ is observed outside…
Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter $F_{\ell} \le -1$ in the angular momentum $\ell=2$ channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters $F_\ell$ of the composite fermion Fermi liquid with a finite layer width. We consider $F_{\ell}$ in different Landau levels $n=0,1,2$ as a f…
Despite its seemingly simple composition and structure, the pairing mechanism of FeSe remains an open problem due to several striking phenomena. Among them are nematic order without magnetic order, nodeless gap and unusual inelastic neutron spectra with a broad continuum, and gap anisotropy consistent with orbital selection of unknown origin. Here we propose a microscopic description of a nematic quantum spin liquid that reproduces key features of neutron spectra. We then study how the spin fluctuations of the local moments lead to pairing within a spin-fermion model. We find the resulting sup…
When a symmetry-breaking phase of matter is suppressed to a quantum critical point (QCP) at absolute zero, quantum-mechanical fluctuations proliferate. Such fluctuations can lead to unconventional superconductivity, as evidenced by the superconducting domes often found near magnetic QCPs in correlated materials. However, it remains unclear whether this superconductivity mechanism holds for QCPs of the electronic nematic phase, characterized by rotational symmetry breaking. Here, we demonstrate from systematic elastoresistivity measurements that nonmagnetic FeSe$_{1-x}$Te$_{x}$ exhibits an elec…
Nematic state, where the system is translationally invariant but breaks the rotational symmetry, has drawn great attentions recently due to experimental observations of such a state in both cuprates and iron-based superconductors. The mechanism of nematicity that is likely tied to the pairing mechanism of high-Tc, however, still remains controversial. Here, we studied the electronic structure of multilayer FeSe film by angle-resolved photoemission spectroscopy (ARPES). We found that the FeSe film enters the nematic state around 125 K, while the electronic signature of long range magnetic order…
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 $…
One of central issues in iron-based superconductors is the role of structural change to the superconducting transition temperature (T_c). It was found in FeSe that the lattice strain leads to a drastic increase in T_c, accompanied by suppression of nematic order. By angle-resolved photoemission spectroscopy on tensile- or compressive-strained and strain-free FeSe, we experimentally show that the in-plane strain causes a marked change in the energy overlap (DeltaE_{h-e}) between the hole and electron pockets in the normal state. The change in DeltaE_{h-e} modifies the Fermi-surface volume, lead…
We report the results of our in-depth analysis of spectroscopic and thermodynamic properties of a multi-orbital metal, like FeSe, which first develops a nematic order and then undergoes a transition into a superconducting state, which co-exists with nematicity. We analyze the angular dependence of the gap function and specific heat $C_V (T)$ of such nematic superconductor. We specifically address three issues: (i) angular dependence of the gap in light of the competition between nematicity-induced $s$-$d$ mixture and orbital transmutation of low-energy excitations in the nematic state, (ii) th…
A very fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of {\it two} other instabilities. Apart from a tendency towards magnetic order, these Fe-based systems have a propensity for nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stage for superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spin degrees of freedom. Here we report a very clear splitting of NMR resonance lines in FeSe at $T_{nem}$ =…
Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing. Nematic order breaks fourfold rotational symmetry in the iron plane, which is believed to be driven by either orbital or spin degrees of freedom. However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult. Here, we use neutron scattering to study structura…
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…
Despite having the simplest atomic structure, bulk FeSe has an observed electronic structure with the largest deviation from the band theory predictions among all Fe-based superconductors and exhibits a low temperature nematic electronic state without intervening magnetic order. We show that the Fe-Fe interatomic Coulomb repulsion $V$ offers a natural explanation for the puzzling electron correlation effects in FeSe superconductors. It produces a strongly renormalized low-energy band structure where the van Hove singularity sits remarkably close to Fermi level in the high-temperature electron …
Clarifying the origin of nematic state in FeSe is one of urgent problems in the field of iron-based superconductivity. Motivated by the discovery of a nematic solution in the density-functional theory implemented by on-site Coulomb interaction (DFT+$U$) [npj Quantum Mater. \textbf{5}, 50 (2020)], we reexamine the $U$ dependence of electronic states in the nonmagnetic normal state of FeSe and perform full multipolar analyses for the nematic state. We find that with increasing $U$ the normal state experiences a topological change in the Fermi surfaces before the emergence of a nematic ground sta…
