Momentum Dependence of the Nematic Order Parameter in Iron-Based Superconductors
H. Pfau, S. D. Chen, M. Yi, M. Hashimoto, C. R. Rotundu, J. C. Palmstrom, T. Chen, P. -C. Dai, J. Straquadine, A. Hristov, R. J. Birgeneau, I. R. Fisher, D. Lu, Z. -X. Shen
The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy (ARPES) with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe$_2$As$_2$ without interference from either twinning or magnetic order. We find that the nematic order parameter exhibits the same momentum dependence in both compounds with a sign change between the Brillouin center and the corner. This suggests that the same microscopic mechanism drives the nematic order in spite of the very different phase diagrams.
In several families of iron-based superconducting materials, a d-wave pairing instability may compete with the leading s-wave instability. Here we show that when both states have comparable free energies, superconducting and nematic degrees of freedom are strongly coupled. While nematic order causes a sharp non-analytic increase in $T_{c}$, nematic fluctuations can change the character of the s-wave to d-wave transition, favoring an intermediate state that does not break time-reversal symmetry but does break tetragonal symmetry. The coupling between superconductivity and nematicity is also man…
We report Raman scattering measurement of charge nematic fluctuations in the tetragonal phase of BaFe$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (x=0.04) single crystals. In both systems, the observed nematic fluctuations are found to exhibit divergent Curie-Weiss like behavior with very similar characteristic temperature scales, indicating a universal tendency towards charge nematic order in 122 iron-based superconductors.
Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quant…
In this paper we study an effective model for the normal state of iron-based superconductors. It has separate, but interacting itinerant and localized degrees of freedom, originating from the d_xz and d_yz, and from d_xy iron orbitals respectively. At low temperatures, below a mean-field phase transition, these different states condense together in an excitonic order parameter. We show that at even lower temperature, after another phase transition, this ordered state can spontaneously break the C_4 lattice symmetry and become nematic. We propose this mechanism as an explanation of the tendency…
In a fully-gapped superconductor the electronic Raman response has a pair-breaking peak at twice the superconducting gap $Δ$, if the Bogoliubov excitations are uncorrelated. Motivated by the iron based superconductors, we study how this peak is modified if the superconducting phase hosts a nematic-structural quantum critical point. We show that, upon approaching this point by tuning, e.g., doping, the growth of nematic correlations between the quasiparticles transforms the pair-breaking peak into a nematic resonance. The mode energy is below 2$Δ$, and stays finite at the quantum critical point…
Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong ele…
Electron correlations produce a rich phase diagram in the iron pnictides. Earlier theoretical studies on the correlation effect demonstrated how quantum fluctuations weaken and concurrently suppress a $C_2$-symmetric single-Q antiferromagnetic order and a nematic order. Here we examine the emergent phases near the quantum phase transition. For a $C_4$-symmetric collinear double-Q antiferromagnetic order, we show that it is accompanied by both a charge order and an enhanced nematic susceptibility. Our results provide understanding for several intriguing recent experiments in hole-doped iron ars…
Motivated by growing indications for a distinct form of nematic correlations in the extremely hole doped iron pnictide compounds $A$Fe$_2$As$_2$ ($A$=K,Rb,Cs), we consider spin-driven nematic order in the general case of incommensurate magnetic fluctuations. We classify the nematic order parameters by broken mirror symmetries of the tetragonal $D_{4h}$ point group, and use this scheme to construct a general Ginzburg-Landau theory that links the nematic order to spatial pattern of magnetic fluctuations. Our analysis points to incommensurate magnetic fluctuations of wavevector $(q,q)$ as underly…
We propose that impurity-induced electronic nematic state is realized above the orthorhombic structure transition temperature $T_S$ in iron-pnictide superconductors. In the presence of strong orbital fluctuations near $T_S$, it is theoretically revealed that a single impurity induces non-local orbital order with $C_2$-symmetry, consistently with recent STM/STS measurements. Each impurity-induced $C_2$ orbital order aligns along a-axis by applying tiny uniaxial pressure along b-axis. In this impurity-induced nematic phase, the resistivity shows sizable in-plane anisotropy ($ρ_b/ρ_a \sim 2$) eve…
In a magnetically driven electronic nematic state, an externally applied uniaxial strain rounds the nematic transition and increases the magnetic transition temperature. We study both effects in a simple classical model of the iron-pnictides expressed in terms of local SO(N) spins (with N = 3) which we solve to leading order in 1=N. The magnetic transition temperature is shown to increase linearly in response to an external strain while a sharp crossover, which is a remnant of the nematic transition, can only be identified for extremely small strain. We show that these results can reasonably a…
The theoretical understanding of the nematic state of iron-based superconductors and especially of FeSe is still a puzzling problem. Although a number of experiments calls for a prominent role of local correlations and place iron superconductors at the entrance of a Hund metal state, the effect of the electronic correlations on the nematic state has been theoretically poorly investigated. In this work we study the nematic phase of iron superconductors accounting for local correlations, including the effect of the Hund's coupling. We show that Hund's physics strongly affects the nematic propert…
We review the recent developments in electronic Raman scattering measurements of charge nematic fluctuations in iron-based superconductors. A simple theoretical framework of a $d$-wave Pomeranchuk transition is proposed in order to capture the salient features of the spectra. We discuss the available Raman data in the normal state of 122 iron-based systems, particularly Co doped BaFe$_2$As$_2$, and we show that the low energy quasi-elastic peak, the extracted nematic susceptibility and the scattering rates are consistent with an electronic driven structural phase transition. In the superconduc…
Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive …
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
The role of nematic fluctuations for unconventional superconductivity has been subject of intense discussions for many years. In iron-based superconductors, the most established probe for electronic-nematic fluctuations, i.e. the elastoresistivity seems to imply that superconductivity is reinforced by electronic-nematic fluctuations, since the elastoresistivity amplitude peaks at or close to optimal $T_C$. However, on the over-doped side of the superconducting dome, the diminishing elastoresistivity suggests a negligible importance in the mechanism of superconductivity. Here we introduce the N…
Using a variational Monte Carlo method, we investigate the nematic state in iron-base superconductors based on a three-band Hubbard model. Our results demonstrate that the nematic state, formed by introducing an anisotropic hopping order into the projected wave function, can arise in the underdoped regime when a realistic off-site Coulomb interaction $V$ is considered. {\color {red} We demonstrate that the off-site Coulomb interaction $V$, which is neglected so far in the analysis of iron-base superconductors, make a dominant contribution to the stabilization of nematic state. We calculate the…
Quantum criticality in iron pnictides involves both the nematic and antiferromagnetic degrees of freedom, but the relationship between the two types of fluctuations has yet to be clarified. Here we study this problem in the presence of a small external uniaxial potential, which breaks the $C_4$-symmetry in the B$_{1g}$ sector. We establish an identity that connects the spin excitation anisotropy, which is the difference of the dynamical spin susceptibilities at $\vec{Q}_1=\left(π,0\right)$ and $\vec{Q}_2=\left(0,π\right)$, with the dynamical magnetic susceptibility and static nematic susceptib…
We show that the interference between scattering by impurities and by critical spin fluctuations gives rise to anisotropic transport in the Ising-nematic state of the iron pnictides. The effect is closely related to the non-Fermi liquid behavior of the resistivity near an antiferromagnetic quantum critical point. Our theory not only explains the observed sign of the resistivity anisotropy $Δρ$ in electron doped systems, but also predicts a sign change of $Δρ$ upon sufficient hole doping. Furthermore, our model naturally addresses the changes in $Δρ$ upon sample annealing and alkaline-earth sub…
Mechanical strain is a powerful technique for tuning electronic structure and interactions in quantum materials. In a system with tetragonal symmetry, a tunable uniaxial in-plane strain can be used to probe nematic correlations in the same way that a tunable magnetic field is used to probe magnetic correlations. Here, we present a new spectroscopic scanned probe technique that provides atomic-resolution insight into the effect of anisotropic strain on the electronic structure. We use this technique to study nematic fluctuations and nematic order across the phase diagram of a prototypical iron-…
We investigate how emergent nematic order and nematic fluctuations affect several macroscopic properties of both the normal and superconducting states of the iron pnictides. Due to its magnetic origin, long-range nematic order enhances magnetic fluctuations, leaving distinctive signatures in the spin-lattice relaxation rate, the spin-spin correlation function, and the uniform magnetic susceptibility. This enhancement of magnetic excitations is also manifested in the electronic spectral function, where a pseudogap can open at the hot spots of the Fermi surface. In the nematic phase, electrons a…
To understand the interplay between nematic fluctuation and superconductivity in iron-based superconductors, we performed a systematic study of the realistic two-orbital Hubbard model by using the constrained-path quantum Monte Carlo method. Our numerical results showed that the on-site nematic interaction induces a strong enhancement of nematic fluctuations at various momentums, especially at ($π$,$π$). Simultaneously, it was found that the on-site nematic interaction suppresses the ($π$,0)/(0,$π$) antiferromagnetic order and long-range electron pairing correlations for dominant pairing chann…
Nematic order in the iron-based superconductors is closely tied to a lattice distortion and a structural transition from tetragonal to orthorhombic symmetry. External stress of the appropriate symmetry acts as a conjugate field of the nematic order parameter and can be utilized to detwin nematic domains but also smears an otherwise sharp nematic transition. On the other hand, applying stress in proper symmetry channels allows one to tune the nematic phase transition. Recent experiments analyzed the stress-induced changes of the nematic and magnetic phase transition temperature. Here we show th…
Electronic nematics, an electron orientational order which breaks the underlying rotational symmetry, have been observed in iron pnictide superconductors several years after their discovery. However, the universality of the doping dependence of this phase and its relation to other symmetry-breaking orders (such as superconductivity) in distinct families of iron pnictides, remain outstanding questions. Here we use torque magnetometry as a probe to study the rotational symmetry breaking in EuFe$_2$(As$_{1-x}$P$_x$)$_2$ without introducing external pressure. The nematic phase is found to prolifer…
Strongly interacting electrons can exhibit novel collective phases, among which the electronic nematic phases are perhaps the most surprising as they spontaneously break rotational symmetry of the underlying crystal lattice. The electron nematicity has been recently observed in the iron-pnictide and cuprate high-temperature superconductors. Whether such a tendency of electrons to self-organise unidirectionally has a common feature in these superconductors is, however, a highly controversial issue. In the cuprates, the nematicity has been suggested as a possible source of the pseudogap phase, w…
Although the existence of nematic order in iron-based superconductors is now a well-established experimental fact, its origin remains controversial. Nematic order breaks the discrete lattice rotational symmetry by making the $x$ and $y$ directions in the Fe plane non-equivalent. This can happen because of (i) a tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking of an orbital symmetry, or (iii) a spontaneous development of an Ising-type spin-nematic order - a magnetic state that breaks rotational symmetry but preserves time-reversal symmetry. The Landau theory of phas…
The extent to which quantum criticality drives the physics of iron pnictides is a central question in the field. Earlier theoretical considerations were based on an effective field theory, and the proposed realization in P-doped iron arsenides has received extensive experimental evidence. To connect the quantum critical behavior with the underlying electronic physics, it is important to analyze it within microscopic models. Here, we do so for a multi-orbital model containing both Hubbard and Hund's interactions, by a variational Monte Carlo method based on Jastrow-Slater wave functions that al…
In the newly discovered iron-based superconductors, many experiments have demonstrated the existence of the rotational symmetry breaking nematic order, which has been a prevailing phenomenon in many correlated electronic systems. In this paper, we review nematic behaviors in iron-pnictides and the mechanism behind the development of the nematic order. We discuss evidences that support the spin-driven nematicity in iron-pnictides. Theories, results and predictions will be discussed based on this picture. We also briefly discuss the generalization of this theory to the nematicity in iron-chalcog…
Charge-$4e$ superconductivity as a novel phase of matter remains elusive so far. Here we show that charge-$4e$ phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect -- nematic vortex -- is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-$4e$ phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-…
We demonstrate that the changes in the elastic properties of the FeAs systems, as seen in our resonant ultrasound spectroscopy data, can be naturally understood in terms of fluctuations of emerging nematic degrees of freedom. Both the softening of the lattice in the normal, tetragonal phase as well as its hardening in the superconducting phase are consistently described by our model. Our results confirm the view that structural order is induced by magnetic fluctuations.
We use scanning tunneling microscopy to investigate the doping dependence of quasiparticle interference (QPI) in NaFe1-xCoxAs iron-based superconductors. The goal is to study the relation between nematic fluctuations and Cooper pairing. In the parent and underdoped compounds, where four-fold rotational symmetry is broken macroscopically, the QPI patterns reveal strong rotational anisotropy. At optimal doping, however, the QPI patterns are always four-fold symmetric. We argue this implies small nematic susceptibility and hence insignificant nematic fluctuation in optimally doped iron pnictides.…
A nematic superconductor can in principle support a vestigial order phase above its superconducting transition temperature, with rotational symmetry spontaneously broken while remain nonsuperconducting. We examine the condition for this vestigial nematic order to occur, within a Ginzburg-Landau theory with order parameter fluctuations included. Contrary to prior theoretical results, we found that this vestigial order actually requires very stringent conditions to be met: the material must be sufficiently deep in the nematic regime (i.e. far away from the boundary separating the nematic and chi…
Nematic phase intertwines closely with high-Tc superconductivity in iron-based superconductors. Its mechanism, which is closely related to the pairing mechanism of superconductivity, still remains controversial. Comprehensive characterization of how the electronic state reconstructs in the nematic phase is thus crucial. However, most experiments focus only on the reconstruction of band dispersions. Another important characteristic of electronic state, the spectral weight, has not been studied in details so far. Here, we studied the spectral weight transfer in the nematic phase of FeSe$_{0.9}$S…
Starting from a microscopic itinerant model, we derive and analyze the effective low-energy model for collective magnetic excitations in the iron pnictides. We show that the stripe magnetic order is generally preempted by an Ising-nematic order which breaks $C_{4}$ lattice symmetry but preserves O(3) spin-rotational symmetry. This leads to a rich phase diagram as function of doping, pressure, and elastic moduli, displaying split magnetic and nematic tri-critical points. The nematic transition may instantly bring the system to the verge of a magnetic transition, or it may occur first, being fol…
The low-energy electronic states of the iron-based superconductors are strongly affected by both spin-orbit coupling and, when present, by the nematic order. These two effects have different physical origins, yet they can lead to similar gap features in the electronic spectrum. Here we show how to disentangle them experimentally in the iron superconductors with one Fe plane per unit cell. Although the splitting of the low energy doublet at the Brillouin zone center ($Γ$-point) can be due to either the spin-orbit coupling or the nematic order, or both, the degeneracy of each of the doublet stat…
Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length $ξ$ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe$_{0.97}$Co$_{0.03}$)$_2$As$_2$ and optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. In all cases, we find that $ξ$ is well described by a power law $(T-T_0)^{-1/2}$ extending over a wide temperature range. We attributed this mean-field behavior and the extended fluctuation regime to a sizable nem…
In copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
Nematicity in the heavily hole-doped iron pnictide superconductors remains controversial. Sizeable nematic fluctuations and even nematic orders far from a magnetic instability were declared in RbFe$_2$As$_2$ and its sister compounds. Here we report a systematic elastoresistance study of series of isovalent- and electron-doped KFe$_2$As$_2$ crystals. We found divergent elastoresistance upon cooling for all the crystals along their [110] direction. The amplitude of elastoresistivity diverges if K is substituted with larger ions or if the system is driven towards a Lifshitz transition. However, w…
In this paper, instabilities of the isotropic metallic phase in iron pnictides are investigated. The relevant quartic fermionic interaction terms in the model are identified using phase space arguments. Using the functional integral formalism, a Hubbard-Stratonovich transformation is used to decouple these quartic terms. This procedure introduces several bosonic fields which describe the low-energy collective modes of the system. By studying the behavior of these collective modes, a possible instability is found in the forward scattering channel of the isotropic phase driven by magnetic fluctu…
The origin of the electronic nematicity and its remarkable material-dependence are famous longstanding unsolved issues in Fe-based superconductors. To attack these issues, we focus on the in-plane anisotropy of the resistivity: In the nematic state in FeSe, the relation $ρ_x>ρ_y$ holds, where $ρ_{x(y)}$ is the resistivity along the longer (shorter) Fe-Fe axis. In contrast, the opposite anisotropy $ρ_x<ρ_y$ is realized in other undoped Fe-based superconductors. Such nontrivial material dependence is naturally explained in terms of the strongly orbital-dependent inelastic quasiparticle scatterin…
We consider the role of potential scatterers in the nematic phase of Fe-based superconductors above the transition temperature to the (pi,0) magnetic state but below the orthorhombic structural transition. The anisotropic spin fluctuations in this region can be frozen by disorder, to create elongated magnetic droplets whose anisotropy grows as the magnetic transition is approached. Such states act as strong anisotropic defect potentials which scatter with much higher probability perpendicular to their length than parallel, although the actual crystal symmetry breaking is tiny. We calculate the…
Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr$_{1-x}$Na$_x$Fe$_2$As$_2$ measured via inelastic X-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped ($x=0.36$) sample, which harbors a magnetically-ordered tetragonal phase, we find it hosts a short nematic correlation length $ξ$ ~ 10 $Å$ and a large nematic susceptibility $χ_{\rm ne…
The origin of diverse nematicity and their order parameters in Fe-based superconductors have been attracting increasing attention. Recently, a new type of nematic order has been discovered in heavily hole-doped ($n_d=5.5$) compound AFe$_2$As$_2$ (A=Cs, Rb). The discovered nematicity has $B_{2g}$ (=$d_{xy}$) symmetry, rotated by $45^\circ$ from the $B_{1g}$ (=$d_{x^2-y^2}$) nematicity in usual compounds with $n_d\approx6$. We predict that the "nematic bond order", which is the symmetry-breaking of the correlated hopping, is responsible for the $B_{2g}$ nematic order in AFe$_2$As$_2$. The Dirac …
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…
The emergence of the nematic order and fluctuations has been discussed as a central issue in Fe-based superconductors. To clarify the origin of the nematicity, we focus on the shear modulus $C_{66}$ and the Raman quadrupole susceptibility $χ_{x^2-y^2}^{Raman}$. Due to the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhances both $1/C_{66}$ and $χ_{x^2-y^2}^{Raman}$ strongly. However, $χ_{x^2-y^2}^{Raman}$ remains finite even at the structure transition temperature $T_S$, because of the absence of the band Jahn-Teller effect and the Pauli (=in…
We perform a non-perturbative analysis of the strong interaction between gapless nodal fermions and the nematic order parameter in two-dimensional d_{x^2-y^2} superconductors. We predict that the critical nematic fluctuation can generate a dynamical nodal gap if the fermion flavor N is smaller than a threshold N_c. Such gap generation leads to an additional is-wave Cooper pairing instability, which induces a fully gapped d_{x^2-y^2}+is superconducting dome in the vicinity of the nematic quantum critical point. The opening of a dynamical gap has important consequences, including the saturation …
We examine the quantum theory of the spontaneous breaking of lattice rotation symmetry in d-wave superconductors on the square lattice. This is described by a field theory of an Ising nematic order parameter coupled to the gapless fermionic quasiparticles. We determine the structure of the renormalization group to all orders in a 1/N_f expansion, where N_f is the number of fermion spin components. Asymptotically exact results are obtained for the quantum critical theory in which, as in the large N_f theory, the nematic order has a large anomalous dimension, and the fermion spectral functions a…
We analyze the scattering rate for 2D fermions interacting via soft nematic fluctuations. The ground state is an s-wave superconductor, but other pairing channels are almost equally attractive. This strongly alters the scattering rate: At energies beyond the pairing gap $Δ$, it is renormalized by contributions from all pairing channels. At energies of order $Δ$, it is determined by the competition between scattering into a gapped continuum and dispersing nematic resonance. The outcome is a "peak-peak-dip-hump" spectrum, similar, but not identical, to the "peak-dip-hump" structure in the cuprat…
A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effect on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization gro…
Motivated by the recent experiments suggesting the importance of nematicity in the phase diagrams of ironbased and cuprate high-Tc superconductors, we study the influence of nematicity on the collective modes inside the superconducting state in a non-equilibrium. In particular, we consider the signatures of collective modes in short-time dynamics of a system with competing nematic and s- and d-wave superconducting orders. In the rotationally symmetric state, we show that the Bardasis-Schrieffer mode, corresponding to the subdominant pairing, hybridizes with the nematic collective mode and merg…
We consider the impact of the competition among superconductivity, spin density wave, and nematic order in iron pnictides, and show that the ordering competition substantially reshapes the global phase diagram. We perform a detailed renormalization group analysis of an effective field theory of iron pnictides and derive the flow equations of all the physical parameters. Using these results, we find that superconductivity can be strongly suppressed by the ordering competition, and also extract the $T$-dependence of superfluid density. Moreover, the phase transitions may become first order. Inte…
The electronic nematic responses in Fe-based superconductors have been observed ubiquitously in various experimental probes. One novel nematic character is the d-wave {\it bond} orbital-relevant nematic charge order which was firstly proposed by symmetry analysis and then conformed by angle-resolved photoemission spectroscopy. In this paper, we present a mechanism that the driving force of the orbital-relevant nematic charge order is the reduction of the large Hubbard energy in the particle-hole charge channel by virtual hopping processes. This is one scenario from strong-coupling consideratio…
In this paper, we study theoretically the behaviors of the magnetic excitations(MEs) in the normal and nematic phases of iron pnictides. The normal state MEs exhibit commensurability to diamond and to square-like structure transition with the increase of energy. This structure transition persists in the spin and orbital scenarios of nematic phases, although the MEs show anisotropic behaviors due to the C4 symmetry breaking induced by the nematic orders. The MEs exhibit distinct energy evolution behaviors between the spin and orbital scenarios of nematicity. For the spinnematic scenario, the an…
Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic $d$-$p$ Hubbard model. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform ($q = 0$) charge modulation on the $p_x$ and $p_y$ orbitals, which possesses the d-symmetry. This uniform nematic order triggers another nem…
An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using nois…
Spin-driven nematic order that has been proposed for iron-based superconductors is generated by pronounced fluctuations of a striped density wave state. On the other hand it is a well known fact that nematic order parameter couples bilinearly to the strain, which supresses the fluctuations of the nematic order parameter itself and lowers the upper critical dimension, yielding mean-field behaviour of the nematic degrees of freedom for $d>2$. This is consistent with the measured Currie-Weiss behaviour of the nematic susceptibility. Here we reconcile this apparent contradiction between pronounced…
Recent experiments suggest that besides of antiferromagnetic fluctuations nematic fluctuations may contribute to the occurrence of superconductivity in iron pnictides. Motivated by this observation we study superconductivity from nematic fluctuations in a minimal two-band model. The employed band parameters are appropriate for iron pnictides and lead to four pockets for the Fermi line. It is shown that low-energy, long-wavelength nematic fluctuations within the pockets give rise to strong-coupling superconductivity whereas the large momenta density fluctuations between pockets are rather irrel…
