Electron pairing and ferromagnetism in various cluster geometries are studied with emphasis on tetrahedron and square pyramid under variation of interaction strength, electron doping and temperature. These exact calculations of charge and spin collective excitations and pseudogaps yield intriguing insights into level crossing degeneracies, phase separation and condensation. Criteria for spin-charge separation and reconciliation driven by interaction strength, next nearest coupling and temperature are found. Phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen recently in high T$_c$ cuprates, manganites and CMR nanomaterials.
The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and ferromagnetism in nanoclusters. The phase diagram off half filling strongly suggests the existence of subsequent transitions from electron pairing into unsaturated and saturated ferromagnetic Mott-Hubbard like insulators, driven by electron repulsion. Rigorous criteria for the existence of quantum critical points in the ground state and corresponding crossovers at f…
Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in $U>0$ Hubbard model including the {\it next nearest neighbor coupling} are calculated with the emphasis on the two-dimensional (square) lattices generated by 8- and 10-site Betts unit cells. The exact theory yields insights into the nature of quantum critical points, continuous transitions, dramatic phase separation instabilities and electron condensation in spatially inhomogeneous systems. The picture of coupled anti-parallel (singlet) spins and paired charged holes sugges…
Exact calculations of collective excitations and charge/spin (pseudo)gaps in an ensemble of bipartite and nonbipartite clusters yield level crossing degeneracies, spin-charge separation, condensation and recombination of electron charge and spin, driven by interaction strength, inter-site couplings and temperature. Near crossing degeneracies, the electron configurations of the lowest energies control the physics of electronic pairing, phase separation and magnetic transitions. Rigorous conditions are found for the smooth and dramatic phase transitions with competing stable and unstable inhomog…
We have performed Diffusion Quantum Monte Carlo simulations of Li clusters showing that Resonating-Valence-Bond (RVB) pairing correlations between electrons provide a substantial contribution to the cohesive energy. The RVB effects are identified in terms of electron transfers from s- to p-like character, constituting a possible explanation for the breakdown of the Fermi liquid picture observed in recent high resolution Compton scattering experiments for bulk Li.
Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band-filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density wave order. Away from half filling, f-wave triplet pairing and d+id singlet pairing instabilities are found to emerge out of density-wave regimes.
There is growing evidence that the unconventional spatial inhomogeneities in the doped high-Tc superconductors are accompanied by the pairing of electrons, subsequent quantum phase transitions (QPTs), and condensation in coherent states. We show that these superconducting states can be obtained from phase separation instabilities near the quantum critical points. We examine electron coherent and incoherent pairing instabilities using our results on exact diagonalization in pyramidal and octahedron Hubbard-like clusters under variation of chemical potential (or doping), interaction strength, te…
Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations and both intrachain and interchain repulsive interactions. We find a close proximity of spin-density- and charge-density-wave phases, singlet d-wave and triplet f-wave superconducting phases. There is a striking correspondence between our results and recent puzzling experimental findings in the Bechgaard salts, including the coexistence of spin-density-wave and charge-density-wave phases and the possibility of a trip…
The interplay of non-Fermi liquid and superconductivity born out of strong dynamical interactions is at the heart of the physics of unconventional superconductivity. As a solvable platform of the strongly correlated superconductors, we study the pairing instabilities of the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model, which describes spin-1/2 fermions coupled to bosons by the random, all-to-all, spin-independent and dependent Yukawa interactions. In contrast to the previously studied models, the random Yukawa couplings are sampled from a collection of Gaussian ensembles whose variances follow …
Using finite-temperature determinantal quantum Monte Carlo calculations, we re-examine the pairing susceptibilities in the Hubbard model on the honeycomb lattice, focusing on doping levels onto and away from the van Hove singularity (VHS) filling. For this purpose, electronic densities of $0.75$ (at the hole-doping VHS) and $0.4$ (well below the VHS) are considered in detail, where due to a severe sign problem at strong coupling strengths, we focus on the weak interaction region of the Hubbard model Hamiltonian. From analyzing the temperature dependence of pairing susceptibilities in various s…
We studied the electronic Raman spectra of (Li$_{1-x}$Fe$_x$)OHFeSe as a function of light polarization and temperature. In the B$_{1g}$ spectra alone we observe the redistribution of spectral weight expected for a superconductor and two well-resolved peaks below T$_c$. The nearly resolution-limited peak at 110 cm$^{-1}$ (13.6 meV) is identified as a collective mode. The peak at 190 cm$^{-1}$ (23.6 meV) is presumably another collective mode since the line is symmetric and its energy is significantly below the gap energy observed by single-particle spectroscopies. Given the experimental band st…
In the recently discovered Co-oxide superconductor Na_xCoO_2*yH_2O, the edge-shared CoO6 octahedra are trigonally contracted along the c-axis in the CoO2-plane. We study how this CoO6 distortion affects the magnetic properties and superconductivity in this compound by analyzing the multiorbital Hubbard model using the fluctuation-exchange approximation. It is shown that through generating the trigonal crystal field, the distortion pushes the Co e'g bands up and consequently gives rise to the hole-pocket Fermi surfaces, which have been predicted in the band calculations. As the distortion incre…
Cooper pairs featuring a nonzero center-of-mass crystal momentum ${\boldsymbol Q}=(π,π, \dots)$ and an off-diagonal long-range order ($η$-pairing states) constitute exact eigenstates of a Hubbard model [C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989)]. Here we show that the $η$-pairing states are rendered dynamically unstable via coupling to dynamical electromagnetic fields. The instability is caused by "tachyonic" electromagnetic fields and unstable plasma modes for attractive and repulsive interactions, respectively. The typical time scale of the growth of the instability is of the order of fem…
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.
We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon increasing the particle density in the latter regime …
Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground-state degeneracy. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry-broken phases, which lift the ground-state degeneracy. We examine the instabilities of the flat-band edge states of d_{xy}-wave superconductors by performing a mean-field analysis in the Majorana basis of the edge s…
The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D t-t' Hubbard model. We find significant deviations from pure s-, d-, or p-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate t'. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended s-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besi…
We apply the fermion renormalization group method, implemented numerically by Honerkamp et.al., to a two-band model of FeAs-based materials. At half filling we find the $(π,0)$ or $(0,π)$ spin density wave order and a sub-dominant superconducting pairing tendency. Due to a topological reason, the spin density wave gap has nodes on the fermi surfaces. Away from half filling we find an unconventional s-wave and a sub-dominant $d_{x^2-y^2}$ pairing instability. The former has $s$ symmetry around the hole fermi surface but exhibits $s+d_{x^2-y^2}$ symmetry around the electron pockets where the 90 …
We study the quantum many-body instabilities of the $t -J_{\mathrm{K}} - J_{\mathrm{H}}$ Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-$1/2$ model is believed to describe the magnetic properties of the layered transition-metal oxide Na$_2$IrO$_3$. We determine the ground-state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow-equations adapted to the lack of full spin-rotational invariance in the fermionic …
Building on previous work [N. Read, Phys. Rev. B 58, Z. Dong and T. Senthil, 16262 (1998); Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $ν= 1$, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and applying the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. Th…
The recent discovery of AV$_3$Sb$_5$ (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple with multiple van Hove singularities close to the Fermi level for AV$_3$Sb$_5$, we provide a random phase…
Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, pro…
We study a one-dimensional electron liquid embedded in a 2D antiferromagnetic insulator, and coupled to it via a weak antiferromagnetic spin exchange interaction. We argue that this model may qualitatively capture the physics of a single charge stripe in the cuprates on length- and time scales shorter than those set by its fluctuation dynamics. Using a local mean-field approach we identify the low-energy effective theory that describes the electronic spin sector of the stripe as that of a sine-Gordon model. We determine its phases via a perturbative renormalization group analysis. For realisti…
Recent experiments on the organic compound κ-(ET)_2Cu_2(CN)_3 have provided a promising example of a two dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular-momentum/spin-triplet channels. Implications to experiments are discussed.
Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations and both intrachain and interchain repulsive interactions. d-wave superconductivity, which dominates over the spin-density-wave (SDW) phase at large nesting deviations, becomes unstable to the benefit of a triplet $f$-wave phase for a weak repulsive interchain backscattering term $g_1^\perp>0$, despite the persistence of dominant SDW correlations in the normal state. Antiferromagnetism becomes unstable against the fo…
The superconductor Sr2RuO4 has been the subject of enormous interest over more than two decades, but until now the form of its order parameter has not been determined. Since groundbreaking NMR experiments revealed that the pairs are of dominant spin-singlet character, attention has focused on time-reversal symmetry breaking linear combinations of $s$-, $d$- and $g$-wave one-dimensional (1D) irreducible representations. However, a state of the form $d_{xz}+id_{yz}$ has also been proposed. We present a systematic study of the stability of various superconducting candidate states, assuming that p…
The effect of interactions near the coincidence of two Landau levels with opposite spins at filling factor 1/2 is investigated. By mapping to Composite Fermions it is shown that the fluctuations of the gauge field induces an effective attractive Fermion interaction. This can lead to a spin-singlet ground state that is separated from the excited states by a gap. The magnitude of the gap is evaluated. The results are consistent with the recently observed half-polarized states in the FQHE at a fixed filling factor. It is suggested that similar anomalies exist for other spin configurations in dege…
We perform a theoretical study of the leading pairing instabilities and the associated superconducting gap functions within the spin-fluctuation mediated pairing scenario in the presence of spin-orbit coupling (SOC). Focussing on iron-based superconductors (FeSCs), our model Hamiltonian consists of a realistic density functional theory (DFT)-derived ten-band hopping term, spin-orbit coupling, and electron-electron interactions included via the multi-orbital Hubbard-Hund Hamiltonian. We perform an extensive parameter sweep and investigate different doping regimes including cases with only hole-…
Superconductivity is an emergent phenomena in the sense that the energy scale associated with Cooper pairing is generically much lower than the typical kinetic energy of electrons. Addressing the mechanism of Cooper pairing amounts to determine the effective interaction that operates at low energies. Deriving such an interaction from a bottom-up approach has not been possible for any superconductor, especially strongly correlated ones. Top-down approaches, where one assumes an effective interaction, is plagued with the difficulty of extracting the implied electronic instabilities without uncon…
The one-band extended Hubbard model in two dimensions near band-filling 1/2 is solved in the fluctuation exchange approximation, including the long-range (1/r) part of the Coulomb interaction, up to 4th neighbor distance. Our results suggest that d_(x^2 - y^2) pairing in the Hubbard model is robust against the inclusion of long-range Coulomb interactions with moderate 1st neighbor repulsion strength V_1. d_(x^2 - y^2) pairing is suppressed only at large V_1 (>~ 0.25U-0.4U), due to incipient charge density wave instabilities.
The unconventional superconductivity in Sr$_2$RuO$_4$ continues to attract considerable interest. While many measurements can be interpreted on the basis of chiral $p$-wave pairing with intriguing topological character, a number of exceptions hinder an unambiguous verification of such pairing. The pairing mechanism also remains under debate. In this paper, with effects of the sizable spin-orbit coupling accounted for, we reexamine the superconducting instabilities in Sr$_2$RuO$_4$ through systematic microscopic analysis within random phase approximation. Our calculations show that the odd-pari…
In certain unconventional superconductors with sizable electronic correlations, the availability of closely competing pairing channels leads to characteristic soft collective fluctuations of the order parameters, which leave fingerprints in many observables and allow to scrutinize the phase competition. Superconducting layered materials, where electron-electron interactions are enhanced with decreasing thickness, are promising candidates to display these correlation effects. In this work, we report the existence of a soft collective mode in single-layer NbSe$_2$, observed as a characteristic r…
We study the spin-density-wave instabilities in the quasi-one-dimensional conductor (TMTSF)_2ClO_4. The orientational order of the anions ClO_4 doubles the unit cell and leads to the presence of two electrnic bands at the Fermi level. From the Ginzburg-Landau expansion of the free energy, we determine the low-temperature phase diagram as a function of the strength of the Coulomb potential due to the anions. Upon increasing the anion potential, we first find a SDW phase corresponding to an interband pairing. This SDW phase is rapidly supressed, the metallic phase being then stable down to zero …
We discuss the low energy theory of two-dimensional metals near the onset of spin density wave order. It is well known that such a metal has a superconducting instability induced by the formation of spin-singlet pairs of electrons, with the pairing amplitude changing sign between regions of the Fermi surface connected by the spin density wave ordering wavevector. Here we review recent arguments that there is an additional instability which is nearly as strong: towards the onset of a modulated bond order which is locally an Ising-nematic order. This new instability is a consequence of an emerge…
Motivated by the recent finding of superconductivity in layered CoO_2 compounds, we investigate superconducting and magnetic instabilities of interacting electrons on the two-dimensional triangular lattice. Using a one-loop renormalization group scheme for weak to moderate coupling strengths, we find that for purely local interactions U>0 and small Fermi surfaces the renormalization group flow remains bounded down to very low scales and no superconducting or other instabilities can be detected. Antiferromagnetic exchange interactions J generate a wide density region with a d_{x^2-y^2}+id_{xy}-…
Superconductivity in many strongly correlated materials appears in proximity to a density-wave or nematic order and is believed to be mediated by quantum-critical (QC) fluctuations of the corresponding order parameter. We argue that fingerprints of QC pairing can be extracted from the angular dependence of the gap $Δ(θ)$. We consider pairing by QC nematic fluctuations and show that there exist multiple pairing instabilities within the same symmetry ($s-$wave in our case), with closely spaced transition temperatures $T_{c,n}$. The corresponding $Δ_n (θ)$ change sign $8n$ times along the FS. Onl…
We study the electronic instabilities of near 1/4 electron doped graphene using the functional renormalization group (FRG) and variational Monte-Carlo method. A modified FRG implementation is utilized to improve the treatment of the von Hove singularity. At 1/4 doping the system is a chiral spin density wave state exhibiting the anomalous quantized Hall effect, or equivalently a Chern insulator. When the doping deviates from 1/4, the $d_{x^2-y^2}+i d_{xy}$ Cooper pairing becomes the leading instability. Our results suggest near 1/4 electron or hole doped graphene is a fertile playground for th…
We studied the pairing instabilities in K$_x$Fe$_{2-y}$Se$_2$ using a two stage functional renormalization group (FRG) method. Our results suggest the leading and subleading pairing symmetries are nodeless $d_{x^2-y^2}$ and nodal extended $s$ respectively. In addition, despite having no Fermi surfaces we find the buried hole bands make important contributions to the final effective interaction. From the bandstructure, spin susceptibility and the FRG results we conclude that the low energy effective interaction in K$_x$Fe$_{2-y}$Se$_2$ is well described by a $J_1-J_2$ model with dominant neares…
Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet to $p+ip$ triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) a…
We study the superconducting pairing instabilities and gap functions for prototypical two-dimensional (2D) transition-metal dichalcogenides (TMDCs) WS$_2$, MoTe$_2$, and MoS$_2$ in the 2H phase under both hole and electron doping at 10 K. Our first-principles quantum many-body Green's function approach allows us to treat the full $d$ and $p$ manifold of orbitals with strong spin-orbit coupling, yielding pairing predictions with material specific detail. The resulting gap functions exhibit a variety of mixed-parity superconducting states, including $s$, $p$, $d$, $f$, $d\pm id$, and $p\pm ip$ p…
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group…
The superconducting symmetry of Sr$_2$RuO$_4$ remains a puzzle. Time-reversal symmetry breaking $d_{x^2-y^2} + ig_{xy(x^2-y^2)}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in Sr$_2$RuO$_4$, including the effects of spin-orbit coupling (SOC), in the presence of both local and longer-range interactions within a random phase approximation. We show that the inclusion of second nearest neighbor repulsions, together with non-local SOC in the $B_{2g}$ channel or orbi…
The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit $d_{r^2-3z^2}$ anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibili…
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…
Heavily electron-doped and single-layer FeSe superconduct at much higher temperatures than bulk FeSe. There have been a number of proposals attempting to explain the origin of the enhanced transition temperature, including the proximity to magnetic, nematic and antiferro-orbital critical points, as well as possible strong interfacial phonon coupling in the case of single-layer FeSe. In this paper, we examine the effect of the various mechanisms in an effective two-band model. Within our model, the fluctuations associated with these instabilities contribute to different parts of the effective m…
Superconducting pnictides are widely found to feature spin-singlet pairing in the vicinity of an antiferromagnetic phase, for which nesting between electron and hole Fermi surfaces is crucial. LiFeAs differs from the other pnictides by (i) poor nesting properties and (ii) unusually shallow hole pockets. Investigating magnetic and pairing instabilities in an electronic model that incorporates these differences, we find antiferromagnetic order to be absent. Instead we observe almost ferromagnetic fluctuations which drive an instability toward spin-triplet p-wave superconductivity.
We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and the one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an intermediate fixed point which belongs to the universality class of chirally stabilized liquids. Using a Toulouse point approach, the universal properties of the models are determined as well as the identification of the leading instabilities. It is shown that these models exhibit a non-Fermi liquid behavior with strong enhanced composite pairing correlations.
The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band and interaction parameters. We map out the phase diagrams within a random phase approximation (RPA) spin- and charge-fluctuation approach, and find that while $B_{1g}$ ($d_{x^2-y^2}$) and $B_{2g}$ ($d_{xy}$) pairing dominates in the absence of repulsive longer-range Coulomb interactions $V_{\rm NN}$, the latter induces pairing in other symmetry channels, including e.g $A_{2g}$ ($g$-wave), nodal $A_{1g}$ (e…
It has recently been pointed out that Fermi surfaces can remain even in the superconductors under the symmetric spin-orbit interaction and broken time-reversal symmetry. Using the linear response theory, we study the instability of such systems toward ordering, which is an intrinsic property of the Fermi surfaces. The ordered states are classified into diagonal and offdiagonal ones, each of which respectively indicates the Pomeranchuk instability and Cooper pairing not of original electron but of Bogoliubov particles (bogolons). The corresponding order parameters are expanded by multipole mome…
We investigate the microscopic mechanism of charge instabilities and the formation of inhomogeneous states in systems with strong electron correlations. It is demonstrated that within a strong coupling expansion the single-band Hubbard model shows an instability towards phase separation and extend the approach also for an analysis of phase separation in the Hubbard-Kanamori hamiltonian as a prototypical multiband model. We study the pairing fluctuations on top of an inhomogeneous stripe state where superconducting correlations in the extended s-wave and d-wave channels correspond to (anti)boun…
We derive an efficient and unbiased method for computing order parameters in correlated electron systems with competing instabilities. Charge, magnetic and pairing fluctuations above the energy scale of spontaneous symmetry breaking are taken into account by a functional renormalization group flow, while the formation of order below that scale is treated in mean-field theory. The method captures fluctuation driven instabilities such as $d$-wave superconductivity. As a first application we study the competition between antiferromagnetism and superconductivity in the ground state of the two-dime…
We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large N techniques. We focus on developing a systematic approach to studying the BCS instability, including careful treatment of the enhanced log^2 and log^3 singularities which appear already at 1-loop. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales Lambda_{BCS} and Lambda_{CDW} of the onset of the instabilities in different p…
We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the Ångström scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this p…
We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.
We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability oc…
We investigate the many-body instabilities of electrons interacting near Van Hove singularities arising in monolayer and twisted bilayer graphene. We show that a pairing instability must be dominant over the tendency to magnetic order as the Fermi level is tuned to the Van Hove singularity in the conduction band of graphene. As a result of the extended character of the saddle points in the dispersion, we find that the pairing of the electrons takes place preferentially in a channel of f-wave symmetry, with an order parameter vanishing at the position of the saddle points along the Fermi line. …
