Due to its extremely rich phase diagram, the two-dimensional electron gas exposed to perpendicular magnetic field has been the subject of intense and sustained study. One particularly interesting problem in this system is that of the half-filled Landau level, where the Fermi sea of composite fermions, a fractional quantum Hall state arising from a pairing instability of the composite fermions, and the quantum Hall nematic were observed in the half-filled $N=0$, $N=1$, and $N \geq 2$ Landau levels, respectively. Thus different ground states developed in different half-filled Landau levels. This situation has recently changed, when evidence for both the paired fractional quantum Hall state and the quantum Hall nematic was reported in the half-filled $N=1$ Landau level. Furthermore, a direct quantum phase transition between these two ordered states was found. These results highlight an intimate connection between pairing and nematicity, a topic of current interest in several strongly correlated systems, in a well-understood and low disorder environment.
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 propose utilizing the Cooper pair to induce magnetic frustration in systems of two-dimensional (2D) magnetic adatom lattices on s-wave superconducting surfaces. The competition between singlet electron correlations and the RKKY coupling is shown to lead to a variety of hidden order states that break the point-group symmetry of the 2D adatom lattice at finite temperature. The phase diagram is constructed using a newly developed effective bond theory [M. Schecter et al., Phys. Rev. Lett. 119, 157202 (2017)], and exhibits broad regions of long-range vestigial nematic order.
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…
The physical properties of high-$T_c$ superconductors are affected by spatial inhomogeneities introduced by impurities. In addition, superconductivity and electronic nematicity seem intertwined in these materials. To address these questions, we apply inhomogeneous cluster dynamical mean field theory to the study of superconductivity in the Hubbard model, in the presence of a repeated impurity, at zero temperature. We find that the superconducting phase is shifted slightly away from half-filling due to the presence of the impurity. This can be explained by a competition with the Mott insulating…
Strongly interacting electrons in solid-state systems often display tendency towards multiple broken symmetries in the ground state. The complex interplay between different order parameters can give rise to a rich phase diagram. Here, we report on the identification of intertwined phases with broken rotational symmetry in magic-angle twisted bilayer graphene (TBG). Using transverse resistance measurements, we find a strongly anisotropic phase located in a 'wedge' above the underdoped region of the superconducting dome. Upon crossing the superconducting dome, a reduction of the critical tempera…
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…
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 investigate the effect of interchain repulsive interaction on the pairing symmetry competition in quasi-one-dimensional organic superconductors (TMTSF)$_2$X by applying random phase approximation and quantum Monte Carlo calculation to an extended Hubbard model. We find that interchain repulsive interaction enhances the $2k_F$ charge fluctuations, thereby making the possibility of spin-triplet $f$-wave pairing dominating over spin-singlet d-wave pairing realistic.
To shed light into the pairing mechanism of possible spin-triplet superconductors (TMTSF)$_2$X and Sr$_2$RuO$_4$, we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model (TMTSF)$_2$X by a quarter-filled quasi-one dimensional (quasi-1D) Hubbard model,and the $γ$ band of Sr$_2$RuO$_4$ by a two dimensional (2D) Hubbard model with a band filling of $\sim 4/3$. For the quasi-1D system, we find that triplet $f$-wave pairing not only dominates over…
A review is given on theoretical studies concerning the pairing symmetry in organic superconductors. In particular, we focus on (TMTSF)$_2$X and $κ$-(BEDT-TTF)$_2$X, in which the pairing symmetry has been extensively studied both experimentally and theoretically. Possibilities of various pairing symmetry candidates and their possible microscopic origin are discussed. Also some tests for determining the actual pairing symmtery are surveyed.
We discuss the pairing symmetry of a cobaltate superconductor Na$_x$CoO$_2\cdot y$ H$_2$O by adopting an effective single band model that takes into account the $e_g'$ hole pockets, as discussed in our previous paper [to appear in Phys. Rev. Lett.] Here we consider the off-site repulsions in addition to the on-site repulsion considered in our previous study. We show that the spin-triplet f-wave pairing proposed in our previous study is robust to some extent even in the presence of off-site repulsions. However, f-wave pairing gives way to singlet pairings for sufficiently large values of off-si…
Within a multicomponent BCS-like framework we study the coexistence and competition of various CDW and SC order parameters in the presence of a strong ferromagnetic background. We find that the competition of unconventional CDW, also called orbital antiferromagnet, with SC at finite momentum (${\bf Q}$-triplet pairing) shows unique characteristics like an extreme sensitivity on the deviations from nesting. We argue that pressure in UGe$_2$ creates deviations from the nesting and report a phase diagram in qualitative agreement with the observed behavior of UGe$_2$.
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 …
As the number of legs n of an n-leg, t-J ladder increases, density matrix renormalization group calculations have shown that the doped state tends to be characterized by a static array of domain walls and that pairing correlations are suppressed. Here we present results for a t-t'-J model in which a diagonal, single particle, next-near-neighbor hopping t' is introduced. We find that this can suppress the formation of stripes and, for t' positive, enhance the d_{x^2-y^2}-like pairing correlations. The effect of t' > 0 is to cause the stripes to evaporate into pairs and for t' < 0 to evaporate i…
We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity s-wave and odd-parity p-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as Cooper triple by solving the corresponding in-medium variational equations. We further feature the phase diagram consisting of the s- and p-wave Cooper pairing phase, and Cooper tripling phase, in the plane of s- and p-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both s- and p-wave inter…
The electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe the expected electron pocket at the $Y$ point in the 1-Fe Brillouin zone. It has been speculated that this pocket, essential for an understanding of the superconducting state, is either absent or incoherent. Here, we perform a theoretical study of the preferred nematic order originating from nearest-neighbor Coulomb interactions in an electronic model relevant for FeSe. We find that at low temperatures the dominating nematic components are of inter-orbit…
Correlation-driven enhancement of pairing in a nematic Hund's metal
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN-BME-BCE Quantum Technology Research Group（匈牙利研究与创新网络-布达佩斯技术与经济大学-布达佩斯理工大学量子技术研究组）；Istituto dei Sistemi Complessi (ISC-CNR)（复杂系统研究所）
The Holstein Model (HM) describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits, but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We qu…
Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context we study the phase diagram of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the s…
Ru based perovskites demonstrate an amazing richness in their magnetic properties, including 3D and quasi-2D ferromagnetism, antiferromagnetism, and unconventional superconductivity. Tendency to ferromagnetism, stemming from the unusually large involvement of O in magnetism in ruthenates, leads to ferromagnetic spin fluctuations in Sr2RuO4 and eventually to p-wave superconductivity. A related compound Ca2RuO4 was measured to be antiferromagnetic, suggesting a possibility of antiferromagnetic fluctuations in Sr2RuO4 as well. Here we report first principles calculations that demonstrate that in …
Electron correlations play a central role in iron-based superconductors. In these systems, multiple Fe $3d$-orbitals are active in the low-energy physics, and they are not all degenerate. For these reasons, the role of orbital-selective correlations has been an active topic in the study of the iron-based systems. In this paper, we survey the recent developments on the subject. For the normal state, we emphasize the orbital-selective Mott physics that has been extensively studied, especially in the iron chalcogenides, in the case of electron filling $n \sim 6$. In addition, the interplay betwee…
Topological insulator quantum wells with induced attractive interactions between electrons are candidate systems for the realization of novel vortex lattice states with time-reversal symmetry, and incompressible quantum vortex liquids with fractional excitations. We analyze the competition between different pairing channels stimulated by the superconducting proximity effect in these quantum wells, and calculate the helical triplet pairing instability that can produce the mentioned phases using perturbation theory. We discuss the phase diagram tunable by gate voltage.
In kagome metals AV3Sb5 (A = K, Rb, Cs), three-dimensional charge order (3D-CO) is the primary instability that sets the stage for other collective orders to emerge, including unidirectional stripe order, orbital flux order, electronic nematicity, and superconductivity. Here, we use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order (3D-CO) in AV3Sb5 and its interplay with superconductivity. Our approach is based on identifying an unusual splitting of kagome bands induced by 3D-CO, which provides a sensitive way to…
We show that the competition between magnetism and superconductivity can be used to determine the pairing state in the iron arsenides. To this end we demonstrate that the itinerant antiferromagnetic phase (AFM) and the unconventional $s^{+-}$ sign-changing superconducting state (SC) are near the borderline of microscopic coexistence and macroscopic phase separation, explaining the experimentally observed competition of both ordered states. In contrast, conventional $s^{++}$ pairing is not able to coexist with magnetism. Expanding the microscopic free energy of the system with competing orders …
We propose a simple picture for the occurrence of superconductivity and the pressure dependence of the superconducting critical temperature, T_{SC}, in ZrZn_2. According to our hypothesis the pairing potential is independent of pressure, but the exchange splitting, E_{xc}, leads to a pressure dependence in the (spin dependent) density of states at the Fermi level, D_σ(ε_F). Assuming p-wave pairing T_{SC} is dependent on D_σ(ε_F) which ensures that, in the absence of non-magnetic impurities, T_{SC} decreases as pressure is applied until it reaches a minimum in the paramagnetic state. Disorder r…
We describe a quantum simulator for the Hubbard--Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing, and Berezinskii--Kosterlitz--Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed: (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon i…
Electronic nematicity has been commonly observed in juxtaposition with unconventional superconductivity. Understanding the nature of the nematic state, as well as its consequence on the electronic band structure and superconductivity, has become a pivotal focus in condensed matter physics. Here we use spectroscopic imaging-scanning tunneling microscopy to visualize how the interacting quasiparticles organize themselves in the nematic state of kagome superconductor CsV$_{3-x}$Ti$_x$Sb$_5$, in which twofold symmetric (C$_2$) quasiparticle scattering interference of the vanadium kagome bands emer…
We study transient effects in a setup, where the quantum dot (QD) is abruptly sandwiched between the metallic and superconducting leads. Focusing on the proximity-induced electron pairing, manifested by the in-gap bound states, we determine characteristic time-scale needed for these quasiparticles to develop. In particular, we derive analytic expressions for (i) charge occupancy of the QD, (ii) amplitude of the induced electron pairing, and (iii) the transient currents under equilibrium and nonequilibrium conditions. We also investigate the correlation effects within the Hartree-Fock-Bogolubov…
The competition between spin-triplet and singlet pairings is studied theoretically for the tight-binding $α$-$β$ bands in Sr$_2$RuO$_4$, which arise from two sets of quasi-one dimensional Fermi surfaces. Using multiband FLEX approximation, where we incorporate an anisotropy in the spin fluctuations as suggested from experiments, we show that (i) the triplet can dominate over the singlet (which turns out to be extended s), and (ii) the triplet gap function optimized in the Eliashberg equation has an unusual, very non-sinusoidal form, whose time-reversal-broken combination exhibits a crib-shaped…
The ground-state phase diagram is numerically studied for an electronic model consisting of the spin exchange term (J) and the correlated hopping term (t_3: the three-site term). This model has no single-particle hopping and the ratio of the two terms is controlled by a parameter α\equiv 4 t_3 / J. The case of α=1 corresponds to complete suppression of single-particle hopping in the strong-coupling limit of the Hubbard model. In one dimension, phase separation takes place below a critical value α_c = 0.36-0.63 which depends on the electron density. Spin gap opens in the whole region except the…
Using a dynamic cluster quantum Monte Carlo approximation, we study a two-dimensional Hubbard model with a small orthorhombic distortion in the nearest neighbor hopping integrals. We find a large nematic response in the low-frequency single-particle scattering rate which develops with decreasing temperature and doping as the pseudogap region is entered. At the same time, the d-wave superconducting gap function develops an s-wave component and its amplitude becomes anisotropic. The strength of the pairing correlations, however, is found to be unaffected by the strong anisotropy, indicating that…
Motivated by the presence of various charge inhomogeneities in strongly correlated systems of coupled ladders, a model of spatially separated bosonic and fermionic degrees of freedom is numerically studied. In this model, bosonic chains are connected to fermionic chains by two types of generalized Andreev couplings. It is shown that for both types of couplings the long-distance pairing correlations are enhanced. Near quarter filling, this effect is much larger for the splitting of a pair in electrons which go to the two neighboring fermionic chains than for a pair hopping process. It is argued…
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) $s$-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular …
We analyze Cooper pairing instabilities in strongly driven electron-phonon systems. The light-induced non-equilibrium state of phonons results in a simultaneous increase of the superconducting coupling constant and the electron scattering. We demonstrate that the competition between these effects leads to an enhanced superconducting transition temperature in a broad range of parameters. Our results may explain the observed transient enhancement of superconductivity in several classes of materials upon irradiation with high intensity pulses of terahertz light, and may pave new ways for engineer…
We study the competition between long- and short-range interactions among charge carriers in strongly-correlated electronic systems employing a new method which combines the density-matrix renormalization-group technique with a self-consistent treatment of the long-range interactions. We apply the method to an extended t-J model which exhibits ``stripe'' order. The Coulomb interactions, while not destroying stripes, induce large transverse stripe fluctuations with associated charge delocalization. This leads to a substantial Coulomb-repulsion-induced {\it enhancement} of long-range superconduc…
We study two effective models developed for description of superconductors with short-coherence length: (i) the extended Hubbard model with on-site attraction and intersite repulsion, (ii) the model of hard-core charged bosons on a lattice. The analysis is concentrated on the problem of phase separations and competition between superconductivity (SS) and charge-density-wave (CDW) orderings. The phase diagrams of the systems are shown to consist of at least seven different states, including 3 types of phase separated (PS) states: CDW-SS (PS1), CDW-normal (PS2) and the state of electron droplets…
We study the non-local superconducting pairing of two interacting Anderson impurities, which has an instability near the quantum critical point from the competition between the Kondo effect and an antiferromagnetic inter-impurity spin exchange interaction. As revealed by the dynamics over the whole energy range, the superconducting pairing fluctuations acquire considerable strength from an energy scale much higher than the characteristic spin fluctuation scale while the low energy behaviors follow those of the staggered spin susceptibility. We argue that the glue to the superconducting pairing…
We propose a model for high-Tc superconductors that includes both the spin fluctuations of the Cu++ magnetic ions and of the spins of O-- doped holes (spinons). The charge of the dopants (holons) is associated to quantum skyrmion excitations of the Cu++ spin background. The quantum skyrmion effective interaction potential is evaluated as a function of doping and temperature, indicating that Cooper pair formation is determined by the competition between these two types of spin fluctuations. The superconducting transition occurs when the effective potential allows for skyrmion bound states. Our …
Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for d-wave superconductivity in the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest neighbor hopping $t'$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable $t'$ is necessary to obtain a sizable pairing gap.
We analyze a possibility for odd-frequency pairing near a quantum critical point(QCP) in a metal. We consider a model with dynamical pairing interaction $V(Ω_n)\sim 1/|Ω_n|^γ$ (the $γ$-model). This interaction gives rise to a non-Fermi liquid in the normal state and is attractive for pairing. The two trends compete with each other. We search for odd-frequency solutions for the pairing gap $Δ(ω_m)= -Δ(ω_m)$. We show that for $γ<1$, odd-frequency superconductivity looses the competition with a non-Fermi liquid and does not develop. We show that the pairing does develop in the extended model in w…
Different models for doping of two-orbital chains with mobile $S=1/2$ fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the pr…
We theoretically study the competition among different electronic phases in molecular conductors $κ$-(BEDT-TTF)$_2$X. The ground-state properties of a 3/4-filled extended Hubbard model with the $κ$-type geometry are investigated by a variational Monte Carlo method. We find various competing phases: dimer-Mott insulator, polar charge-ordered insulator, 3-fold charge-ordered metal, and superconductivity, whose pairing symmetry is an "extended-$s$+$d_{x^2-y^2}$"-wave type. Our results show that the superconducting phase is stabilized not on the verge of the Mott metal-insulator transition but nea…
When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity ($σ^f_{xy}$) controls the degeneracy of topologically protected, fermion zero-modes, localized on…
