The newly discovered high temperature superconductor SmFeAs(O1-xFx) shows a clear nematic transition where the square lattice of Fe ions has a rectangular distortion. Similar nematic ordering has also been observed in the cuprate superconductors. We provide a detailed theory of experimental observables near such a nematic transition: we calculate the scaling of specific heat, local density of states (LDOS) and NMR relaxation rate 1/T_1T.
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…
The large in-plane anisotropy of the resistivity is a hallmark of the nematic state of the iron pnictides. Solving the Boltzmann transport equation, we show that the prominent doping dependence as well as the large values of the anisotropy can be well explained by momentum-dependent spin-fluctuation scattering without assuming anisotropic impurity states. Due to the forward-scattering corrections, the hot spots contribute to the resistive anisotropy even in the case of strong spin fluctuations, which makes large values of the anisotropy possible. The ellipticity of the electron pockets plays a…
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…
We compare the one-loop functional renormalization group results for the cuprates and the iron pnictides. Interestingly a coherent picture suggesting that antiferromagnetic correlation causes pairing for both materials emerges.
We establish a relation between the Raman response function in the $B_{1g}$ channel and the electronic contribution to the nematic susceptibility within the spin-driven approach to electron nematicity of the iron based superconductors. The spin-driven nematic phase, characterized by the broken $C_4$ symmetry, but unbroken $O(3$) spin-rotational symmetry, is generated by the presence of magnetic fluctuations associated with the striped phase. It occurs as a separate phase between $T_N$ and $T_s$ in systems where the structural and magnetic phase transitions are separated. Detecting the presence…
The nature of the normal state and the mechanism of superconductivity in two families of high-temperature superconductors, cuprates and pnictides, remain a matter of intense discussions. According to band-structure calculations, confirmed by ARPES data, the electronic structure of pnictides differs considerably from that of cuprates. However, in spite of these differences, it looks like in both cases there exists some general and fairly "coarse" mechanism independent of fine details of the band structure and responsible for superconductive pairing in these materials. Here, we suggest a qualita…
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations in directions perpendicular and parallel to the ordering wave-vector even above the magnetic transition temperature $T_N$, we study the frustrated Heisenberg model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the $C_4$ symmetry e…
We explore energy scales, features in the normal state transport, relevant interactions and constraints for the pairing mechanisms in the high-Tc cuprates and Fe-pnictides. Based on this analysis we attempt to identify a number of attributes of superconductors with a higher T_c. Expanded version of the article published in Nature Physics, 7, 271 (2011).
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…
The iron pnictides and the cuprates represent two families of materials, where strong antiferromagnetic correlation drives three other distinct ordering tendencies: (1) superconducting pairing, (2) Fermi surface distortion, and (3) orbital current order. We propose that (1)-(3) and the antiferromagnetic correlation are the hallmarks of a class of strongly correlated materials to which the cuprates and pnictides belong. In this paper we present the results of the functional renormalization group studies to support the above claim. In addition, we show that as a function of the interlayer hoppin…
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…
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…
The role of Coulomb correlations in the iron pnictide LaFeAsO is studied by generalizing exact diagonalization dynamical mean field theory to five orbitals. For rotationally invariant Hund's rule coupling a continuous transition from a paramagnetic Fermi-liquid phase to a non-Fermi-liquid metallic phase exhibiting frozen moments is found at moderate Coulomb energies. For Ising-like exchange, this transition is first order and occurs at a lower critical Coulomb energy. The correlation-induced scattering rate as a function of doping relative to half-filling, i.e., delta = n/5-1, where n=6 for th…
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…
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-…
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…
The nematic state of the iron-based superconductors is studied in the undoped limit of the three-orbital ($xz$, $yz$, $xy$) spin-fermion model via the introduction of lattice degrees of freedom. Monte Carlo simulations show that in order to stabilize the experimentally observed lattice distortion and nematic order, and to reproduce photoemission experiments, {\it both} the spin-lattice and orbital-lattice couplings are needed. The interplay between their respective coupling strengths regulates the separation between the structural and Néel transition temperatures. Experimental results for the …
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…
The recent experimental evidence in favor of stripe ordering in ferropnictides [Chuang {\it et. al.}, Science {\bf 327},181 (2010)] points to the new field of study for strongly correlated systems. Here we argue that due to the smallness of the chemical potential in ferropnictides the effects of stripe modulation are likely to be much more pronounced than in the cuprates leading to stronger degree of one-dimensionality. This may allow to treat the striped pnictides as an array of coupled one-dimensional spin liquids making them a good testing ground for various ideas concerning strongly correl…
We compare the position of an ordering transition in a metal to that in a superconductor. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |Delta|, where Delta is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the ~ |Delta|^2 shift predicted by theories of competing orders which ignore Fermi surface effects. For Ising-nematic order, the shift from Fermi surface effects remains of order |Delta|^2. We discuss implications of these results for the phase diagrams of …
We study the in-plane anisotropy of the thermoelectric power and electrical resistivity on detwinned single crystals of isovalent substituted EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_2$. Compared to the resistivity anisotropy the thermopower anisotropy is more pronounced and clearly visible already at temperatures much above the structural and magnetic phase transitions. Most remarkably, the thermopower anisotropy changes sign below the structural transition. This is associated with the interplay of two contributions due to anisotropic scattering and orbital polarization, which dominate at high- and low…
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…
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…
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…
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…
Nematic order has manifested itself in a variety of materials in the cuprate family. We propose an effective field theory of a layered system with incommensurate, intertwined spin- and charge-density wave (SDW and CDW) orders, each of which consists of two components related by $C_4$ rotations. Using a variational method (which is exact in a large $N$ limit), we study the development of nematicity from partially melting those density waves by either increasing temperature or adding quenched disorder. As temperature decreases we first find a transition to a nematic phase, but depending on the r…
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…
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…
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…
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…
One of the major puzzles regarding unconventional superconductivity is how some of the most interesting superconductors are related to an insulating phase that lies in close proximity. Here we report scanning tunneling microscopy studies of the local electronic structure of Cu doped NaFeAs across the superconductor to insulator transition. We find that in the highly insulating regime the electronic spectrum develops an energy gap with diminishing density of state at the Fermi level. The overall lineshape and strong spatial variations of the spectra are strikingly similar to that of lightly dop…
How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba$_{1-x}$Sr$_{x}$Ni$_{2}$As$_{2}$ (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a six-fold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at $x_c=0.7$). The superconductivity is, however, anomalous, with the resistive transition for $0.4 < x< x_c$ occurring at a higher temperature than the specific heat anomaly. Using x-ray scattering, we discovered a new charge density w…
We construct a 2-leg ladder model of an Fe-pnictide superconductor and discuss its properties and relationship with the familiar 2-leg cuprate model. Our results suggest that the underlying pairing mechanism for the Fe-pnictide superconductors is similar to that for the cuprates.
Numerous contemporary investigations in condensed matter physics are devoted to high temperature (high-$T_c$ ) cuprate superconductors. Despite its unique effulgence among research subjects, the enigma of the high-$T_c$ mechanism still persists. One way to advance its understanding is to discover and study new analogous systems. Here we begin a novel exploration of the natural mineral murunskite, K$_2$FeCu$_3$S$_4$, as an interpolation compound between cuprates and ferropnictides, the only known high-$T_c$ superconductors at ambient pressure. Because in-depth studies can be carried out only on…
We report a high magnetic field study up to 55 T of the nearly optimally doped iron-pnictide superconductor Ca$_{10}$(Pt$_{3}$As$_{8}$) ((Fe$_{1-x}$Pt$_{x}$)$_{2}$As$_{2}$)$_{5}$ (x=0.078(6)) with a Tc 10 K using magnetic torque, tunnel diode oscillator technique and transport measurements. We determine the superconducting phase diagram, revealing an anisotropy of the irreversibility field up to a factor of 10 near Tc and signatures of multiband superconductivity. Unexpectedly, we find a spin-flop like anomaly in magnetic torque at 22 T, when the magnetic field is applied perpendicular to the …
Using cluster-perturbation theory, we calculate the spectral density A(k,w) for a nematic phase of models describing pnictide superconductors, where very short-range magnetic correlations choose the ordering vector (pi,0) over the equivalent (0,pi) and thus break the fourfold rotation symmetry of the underlying lattice without inducing long-range magnetic order. In excellent agreement with angle resolved photo-emission spectroscopy (ARPES), we find that the yz bands at X move to higher energies. When onsite Coulomb repulsion brings the system close to a spin--density-wave (SDW) and renormalize…
Many of the iron pnictides have strongly anisotropic normal-state characteristics, important for the exotic magnetic and superconducting behavior these materials exhibit. Yet, the origin of the observed anisotropy is unclear. Electronically driven nematicity has been suggested, but distinguishing this as an independent degree of freedom from magnetic and structural orders is difficult, as these couple together to break the same tetragonal symmetry. Here we use time-resolved polarimetry to reveal critical nematic fluctuations in unstrained Ba(Fe_(1-x)Co_x)_2As_2. The femtosecond anisotropic res…
The SQCRAMscope is a recently realized Scanning Quantum CRyogenic Atom Microscope that utilizes an atomic Bose-Einstein condensate to measure magnetic fields emanating from solid-state samples. The quantum sensor does so with unprecedented DC sensitivity at micron resolution from room-to-cryogenic temperatures. An additional advantage of the SQCRAMscope is the preservation of optical access to the sample: Magnetometry imaging of, e.g., electron transport may be performed in concert with other imaging techniques. This multimodal imaging capability can be brought to bear with great effect in the…
The main driven force of the electronic nematic phase in iron-based superconductors is still under debate. Here, we report a comprehensive study on the nematic fluctuations in a non-superconducting iron pnictide system BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$ by electronic transport, angle-resolved photoemission spectroscopy (ARPES) and inelastic neutron scattering (INS) measurements. Previous neutron diffraction and transport measurements suggested that the collinear antiferromagnetism persists to $x=0.8$, with similar Néel temperature $T_N$ and structural transition temperature $T_s$ around …
Single- and multi-band Hubbard models have been found to describe many of the complex phenomena that are observed in the cuprate and iron-based high-temperature superconductors. Simulations of these models therefore provide an ideal framework to study and understand the superconducting properties of these systems and the mechanisms responsible for them. Here we review recent dynamic cluster quantum Monte Carlo simulations of these models, which provide an unbiased view of the leading correlations in the system. In particular, we discuss what these simulations tell us about superconductivity in…
Modern theories of quantum magnetism predict exotic multipolar states in weakly interacting strongly frustrated spin-1/2 Heisenberg chains with ferromagnetic nearest neighbor (NN) inchain exchange in high magnetic fields. Experimentally these states remained elusive so far. Here we report the evidence for a long-sought magnetic field-induced nematic state arising above a field of $\sim 13$ T in the edge-sharing chain cuprate LiSbCuO$_4$ $\equiv$ LiCuSbO$_4$. This interpretation is based on the observation of a field induced spin-gap in the measurements of the $^7$Li NMR spin relaxation rate $T…
During the last decade, translational and rotational symmetry-breaking phases -- density wave order and electronic nematicity -- have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant x-ray scattering in a cuprate high-temperature superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ (Nd-LSCO) to navigate the cuprate phase diagram, probing the rel…
The interplay of structural and electronic phases in iron-based superconductors is a central theme in the search for the superconducting pairing mechanism. While electronic nematicity, defined as the breaking of four-fold symmetry triggered by electronic degrees of freedom, is competing with superconductivity, the effect of purely structural orthorhombic order is unexplored. Here, using x-ray diffraction (XRD), we reveal a new structural orthorhombic phase with an exceptionally high onset temperature ($T_\mathrm{ort} \sim 250$ K), which coexists with superconductivity ($T_\mathrm{c} = 25$ K), …
There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodal-antinodal dichotomy in the structure of the single-particle spectral functions. In this context, we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting "nodal points" and the nematic "cold-spots" on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angle-resolved photoemi…
The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the superconducting dome. In this review, we critically examine these claims and highlight significant diffe…
Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-$d$ and O-$p$ orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the $p$-orbitals inevitably generate a biquadratic coupling between the spins of the $d$-orbitals. The key point revealed by our classical Monte Carlo simu…
Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, we report the obser…
The twin issues of the nature of the normal state and competing order(s) in the iron arsenides are central to understanding their unconventional, high-Tc superconductivity. We use a combination of transport anisotropy measurements on detwinned Sr(Fe(1-x)Co(x))2As2 single crystals and local density approximation plus dynamical mean field theory (LDA + DMFT) calculations to revisit these issues. The peculiar resistivity anisotropy and its evolution with x are naturally interpreted in terms of an underlying orbital-selective Mott transition (OSMT) that gaps out the dxz or dyz states. Further, we …
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…
To address the issues of superconducting and charge properties in high-T$_c$ cuprates, we perform a quantum Monte Carlo study of an extended three-band Emery model, which explicitly includes attractive interaction $V_{OO}$ between oxygen orbitals. In the physically relevant parameter range, we find that $V_{OO}$ acts to strongly enhance the long-range part of d-wave pairing correlation, with a clear tendency to form long-range superconducting order in the thermodynamic limit. Simultaneously, increasing $|V_{OO}|$ renders a rapid increase of the nematic charge structure factor at most of waveve…
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…
The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a spin density wave order in the presence of a magnetic field. We show that a cooperation of the nematicity and the magnetic field induces a finite coupling between the spin density wave and spin-triplet staggered flux orders. As a consequence of such a coupling, the magnon gap decreases as the magnetic field increases, and it eventually condenses beyond a crit…
We present a microscopic derivation of the nematic charge-density-wave (CDW) formation in cuprate superconductors based on the three-orbital d-p Hubbard model, by introducing the vertex correction (VC) into the charge susceptibility. The CDW instability at $q=(Δ_{FS},0)$, $(0,Δ_{FS})$ appears when the spin fluctuations are strong, due to the strong charge-spin interference represented by the VC. Here, $Δ_{FS}$ is the wavenumber between the neighboring hot spots. The obtained spin-fluctuation-driven CDW is expressed as the "intra-unit-cell orbital order" accompanied by the charge transfer betwe…
