A subtle relation between Quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin type Hamiltonians that arise in (p_{x}+ip_{y}) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive non-commuting (p_{x}+ip_{y})-type pairing Hamiltonians. For the Laughlin sequence, it is observed that this problem is frustration free and zero energy ground states lie in the common null space of all of these non-commuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a "squeezing principle" that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) "incompressible filling factors" for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasi-hole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the Quantum Hall systems precise.
Hund's pairing refers to Cooper pairing generated by onsite interactions that become attractive due to large Hund's exchange $J$. This is possible in multiorbital systems even when all local bare interactions are repulsive, since attraction in specific channels are given by certain linear combinations of interaction parameters. On the other hand, pairing processes such as the exchange of spin fluctuations, are also present. We compare these two mechanisms on an equal footing using electronic bands appropriate for different classes of multiorbital systems over a wide range of interaction parame…
Fermion systems with flat bands can boost superconductivity by enhancing the density of states at the Fermi level. We use quasiexact numerical methods to show that repulsive interactions between spinless fermions in a one-dimensional (1D) flat-band system, the Creutz ladder, give a finite pairing energy that increases with repulsion, though charge quasi-order (QO) remains dominant. Adding an attractive component shifts the balance in favor of superconductivity and the interplay of two flat bands further yields a remarkable enhancement of superconductivity, well outside of known paradigms for 1…
We study mesoscopic pairing in the one dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type,…
We study the pairing of fermions by an interaction consisting of a Hubbard repulsion, mimicking a screened Coulomb potential, and a dynamical phonon-mediated attraction. For such interaction, the gap equation allows even- and odd-frequency solutions $Δ_e$ and $Δ_o$. We show that odd-frequency pairing does not develop within the Eliashberg approximation due to over-critical pair-breaking from the self-energy. When vertex corrections are included, the pairing interaction gets stronger, and $Δ_o$ can develop. We argue that even in this case keeping the self-energy is still a must as it cancels ou…
We demonstrate the stability of a spin-triplet paired s-wave (with an admixture of extended s-wave) state for the case of purely repulsive interactions in a degenerate two-band Hubbard model. We further show that near half-filling the considered kind of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the so-called statistically consistent Gutzwiller approximation for the case of a square lattice. The absence of a stable paired state when analyzed in the Hartree-Fock-BCS approximation allows us to claim that the electron correlations…
We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermion interacting with repulsive pairing forces in a two dimensional square lattice. Inspite of the repulsive pairing force the exact results show attractive pair correlations.
Exact thermal studies of small (4-site, 5-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, in particular, pairing fluctuations away from half filling (near optimal doping). These exact calculations, carried out in canonical (i.e. for fixed electron number N) and grand canonical (i.e. fixed chemical potential $μ$) ensembles, monitoring variations in temperature T and magnetic field h, show rich phase diagrams in a T-$μ$ space consisting of pairing fluctuations and signatures of conde…
An overview is given on how superconductivity with anisotropic pairing can be realised from repulsive electron-electron interaction. (i) We start from the physics in one dimension, where the Tomonaga-Luttinger theory predicts that, while there is no superconducting phase for the repulsive case for a single chain, the phase does exists in ladders with the number of legs equal to or greater than two, as shown both by analytically (renormalisation) and numerically (quantum Monte Carlo). (ii) We then show how this pairing has a natural extension to the two-dimensional case, where anisotropic (usua…
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.
We study repulsive Hubbard and t-J type systems on a square lattice (long believed to capture certain quintessential aspects of the high temperature superconductors). These models (alongside the parent compounds of the high temperature superconductors) are antiferromagnetic in the absence of hole doping. As we illustrate, a unifying underlying principle for the dynamics of holes introduced by doping rationalizes the emergence of nonuniform electronic structures- "stripes" and possible pairing tendencies therein. Specifically, our analysis invokes the following (numerically verified) sublattice…
We consider a fractional quantum Hall bilayer system with an interface between quantum Hall states of filling fractions $(ν_{\text{top}},ν_{\text{bottom}})=(1,1)$ and $(1/3,2)$, motivated by a recent approach to engineering artificial edges~\cite{2018NatPh..14..411R}. We show that random tunneling and strong repulsive interactions within one of the layers will drive the system to a stable fixed point with two counterpropagating charge modes which have attractive interactions. As a result, slowly decaying correlations on the edge become predominantly superconducting. We discuss the resulting ob…
We consider a collection of fermions in a strong magnetic field coupled by a purely three body repulsive interaction, and predict the formation of composite fermions, leading to a remarkably rich phase diagram containing a host of fractional quantum Hall states, a composite fermion Fermi sea, and a pairing transition. This is entirely unexpected, because the appearance of composite fermions and fractional quantum Hall effect is ordinarily thought to be a result of strong two-body repulsion. Recent theoretical and experimental breakthroughs in ultra-cold atoms and molecules have facilitated the…
We study unconventional superconductivity induced by weak repulsive interactions in 2D electronic systems at Van Hove singularity (VHS) where density of states is logarithmically divergent. We define two types of VHS. For systems at type-I VHS, weak repulsive interactions generically induce unconventional singlet pairing. However and more interestingly, for type-II VHS renormalization group (RG) analysis shows that weak repulsive interactions favor triplet pairing (e.g. p-wave) when the Fermi surface is not sufficiently nested. For type-II VHS systems respecting tetragonal symmetry, topologica…
In two-dimensional systems possessing a high degree of symmetry, the repulsive electron-electron interaction produces a pairing force; the mechanism would fail in the presence of strong distortions. We have studied this in the one-band and three-band Hubbard Model. From partially occupied orbitals one obtains pair eigenstates of the Hamiltonian with no on-site repulsion (the W=0 pairs). The concept of W=0 pairs allows to make qualitative and quantitative predictions about the behaviour of interacting many-body systems, a quite remarkable and unusual situation. Exact numerical solutions for clu…
The Kohn-Luttinger mechanism for unconventional superconductivity (SC) driven by weak repulsive electron-electron interactions on a periodic lattice is generalized to the quasicrystal (QC) via a real-space perturbative approach. The repulsive Hubbard model on the Penrose lattice is studied as an example, on which a classification of the pairing symmetries is performed and a pairing phase diagram is obtained. Two remarkable properties of these pairing states are revealed, due to the combination of the presence of the point-group symmetry and the lack of translation symmetry on this lattice. Fir…
We present a scheme comprised of a one-dimensional system with repulsive interactions, in which the formation of bound pairs can take place in an easily tunable fashion.By capacitively coupling a primary electronic quantum wire of interest to a secondary strongly-correlated fermionic system, the intrinsic electron-electron repulsion may be overcome, promoting the formation of bound electron pairs in the primary wire. The intrinsic repulsive interactions tend to favor the formation of charge density waves of these pairs, yet we find that superconducting correlations are dominant in a limited pa…
We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at ν=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.
Unconventional symmetries of the order parameter allowed some researchers to maintain that a purely repulsive interaction between electrons provides superconductivity without phonons in a number of high-temperature superconductors. It is shown that the Cooper pairing in p and d states is not possible with the realistic Coulomb repulsion between fermions at relevant temperatures in any dimension.
Stimulated by the recent finding of Na$_{0.35}$CoO$_2$.1.3H$_2$O superconductor, we investigate superconducting instabilities on a 2D triangular lattice in the repulsive Hubbard model. Using the third-order perturbation expansion with respect to the on-site repulsion $U$, we evaluate the linearized Dyson-Gor'kov equation. We find that an $f$-wave spin-triplet pairing is the most stable in a wide range of the next nearest neighbor hopping integral $t'$ and an electron number density $n$. The introduction of $t'$ is crucial to adjust the van Hove singularities to the neighborhood of the Fermi su…
We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ν=1/m$ (with $m$ an odd integer). This setup can be utilized to create non-Abelian parafermion zero-modes if the coupling to the superconductor opens an energy gap in the counter-propagating modes. However, when the coupling to the superconductor is weak an energy gap is opened only in the presence of sufficiently strong attractive interactions between the edge modes, which do not commonly occur in solid state experime…
Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at $q_c$ inversely proportional to the characteristic length-scale in real space, the soft-core radius $r_c$. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with novel super…
Studies of systems with two fermionic bands with repulsive interaction strength U have a long history, with the Periodic Anderson Model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use Quantum Monte Carlo to study analogous issues for attractive interactions. As in the Periodic Anderson Model, we focus on a case where one band is uncorrelated (U=0), and focus on the effect of hybridization V between the bands on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are able to explore the physics of doped multi…
Electron pairing is a rare phenomenon appearing only in a few unique physical systems; e.g., superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected, but robust, electron "pairing" in the integer quantum Hall effect (IQHE) regime. The pairing takes place within an interfering edge channel circulating in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, $2<ν _B<5$. The main observations are: (a) High visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity $Δϕ=φ_0/2=h/2e$ (instead of the ubiquitous $h/e$), with …
We study bilayer fermionic cold atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth and first Haldane pseudopotentials, at total Landau level filling factor 1/2. Our numerical results on the TCTP model indicates that Haldane-Rezayi state describes the critical point between strong and weak d-wave pairing quantum Hall phases. Further increasing the attractive zeroth pseudopotentials, the system transits from the strong-pairing phase to a stripe phase, and then to a cluster phase (or phase separation). The dipolar in…
We theoretically investigate the nature of the state at quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to $f$-wave pairing of composite fermions. This state is topologically distinct from the familiar $p$-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.
Pairing from repulsive interactions in twisted WSe2 from functional renormalization
Max Planck Institute for Solid State Research（马克斯·普朗克固体的研究学会）；Technische Universität München（慕尼黑工业大学）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·皮尔斯理论物理中心）；Princeton University（普林斯顿大学）；Donostia International Physics Center (DIPC)（多诺西亚国际物理中心）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）；School of Applied and Engineering Physics, Cornell University（康奈尔大学应用与工程物理学院）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构与动力学研究所）
The normal-state behavior of the temperature-dependent Hall coefficient in cuprate superconductors is investigated using linear response theory. The Hall conductivity is of paramount importance in that its sign and magnitude directly reflect the sign of the charge carriers and the size of particle-hole asymmetry effects. Here we apply a strong-pairing fluctuation theory that incorporates pseudogap effects known to be important in cuprate transport. As a result, in the vicinity of the transition temperature our theoretical approach goes beyond the conventional superconducting fluctuation formal…
The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is su…
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $ν=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is li…
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…
A profound problem in modern condensed matter physics is discovering and understanding the nature of the fluctuations and their coupling to fermions in cuprates which lead to high temperature superconductivity and the invariably associated strange metal state. Here we report the quantitative determination of the normal and pairing self-energies, made possible by laser-based angle-resolved photoemission measurements with unprecedented accuracy and stability. Through a precise inversion procedure, both the effective interactions in the attractive d-wave symmetry and the repulsive part in the ful…
We investigate a microscopic model for strongly correlated electrons with both on-site and nearest neighbor Coulomb repulsion on a 2D square lattice. This exhibits a state in which electrons undergo a ``somersault'' in their internal spin-space (spin-flux) as they traverse a closed loop in external coordinate space. When this spin-1/2 antiferromagnetic (AFM) insulator is doped, the ground state is a liquid of charged, bosonic meron-vortices, which for topological reasons are created in vortex-antivortex pairs. The magnetic exchange energy of the distorted AFM background leads to a logarithmic …
To address the issue of electron correlation driven superconductivity in graphene, we perform a systematic quantum Monte Carlo study of the pairing correlation in the t-U-V Hubbard model on a honeycomb lattice. For V=0 and close to half filling, we find that pairing with d+id symmetry dominates pairing with extended-s symmetry. However, as the system size or the on-site Coulomb interaction increases, the long-range part of the d+id pairing correlation decreases and tends to vanish in the thermodynamic limit. An inclusion of nearest-neighbor interaction V, either repulsive or attractive, has a …
Under the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we argue that the pairing symmetry in all measured iron-based superconductors is universally consistent with the A_{1g} s-wave. The robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high T_c superconducting mechanisms: (1) the correspondence principle: the short range magnetic exchange interactions and the Fermi surfaces act collaboratively to achieve high T_c superconduc…
A repulsive interaction model of superconductivity (SC) is studied for tight-binding models with three-fold degenerate molecular orbitals. Taking a weak-coupling approach, we derive dimensionless coupling constants for various symmetries of SC pairs. In addition to anisotropic SC pairs, the s-wave pairing ($A_g$) can also be formed. With the purely repulsive interaction, however, the $A_g$ pair is not the most stable in both bcc and fcc lattices. The most stable SC pair for the bcc lattice has the $T_g$ symmetry, which is favored by a strongly nesting Fermi surface. In the fcc lattice, various…
Using the functional renormalization group technique we demonstrate a route for potentially high-temperature odd-parity superconductivity in ferromagnetic materials caused by repulsive electron interactions, where the superconducting pairing is driven by charge-density wave fluctuations. Our model is directly applicable to a lightly cobalt-doped LaNiO$_3$ bilayer grown in the (111) direction. As the on-site repulsive interaction grows, a charge-density wave state with a charge pattern that respects all point-group symmetries of the bilayer is replaced by a superconducting state with an f-wave …
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 propose a paring mechanism between holes in the dilute limit of doped frustrated Mott insulators. Hole pairing arises from a hole-hole-magnon three-body bound state. This pairing mechanism has its roots on single-hole kinetic energy frustration, which favors antiferromagnetic (AFM) correlations around the hole. We demonstrate that the AFM polaron (hole-magnon bound state) produced by a single-hole propagating on a field-induced polarized background is strong enough to bind a a second hole. The effective interaction between these three-body bound states is repulsive, implying that this pairi…
We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the en…
We discuss a many-electron Hamiltonian with Hubbard-like repulsive interaction and linear coupling to the phonon branches, having the Cu-O plane of the superconducting cuprates as a paradigm. A canonical transformation extracts an effective two-body problem from the many-body theory. As a prototype system we study the $\cu$ cluster, which yields electronic pairing in the Hubbard model; moreover, a standard treatment of the Jahn-Teller effect predicts distortions that destroy electronic pairing. Remarkably, calculations that keep all the electronic spectrum into account show that vibrations are…
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…
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…
We study interacting GaAs bilayer hole systems, with very small interlayer tunneling, in a counterflow geometry where equal currents are passed in opposite directions in the two, independently contacted layers. At low temperatures, both the longitudinal and Hall counterflow resistances tend to vanish in the quantum Hall state at total bilayer filling $ν=1$, demonstrating the pairing of oppositely charged carriers in opposite layers. The temperature dependence of the counterflow Hall resistance is anomalous compared to the other transport coefficients: even at relatively high temperatures ($\si…
In iron selenide superconductors only electron-like Fermi pockets survive, challenging the $S^{\pm}$ pairing based on the quasi-nesting between the electron and hole Fermi pockets (as in iron arsenides). By functional renormalization group study we show that an in-phase $S$-wave pairing on the electron pockets ($S^{++}_{ee}$) is realized. The pairing mechanism involves two competing driving forces: The strong C-type spin fluctuations cause attractive pair scattering between and within electron pockets via Cooperon excitations on the virtual hole pockets, while the G-type spin fluctuations caus…
A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. Two canonically dual pairing gap functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due to the correlation holes. We find that the ground state is the Moore-Read pfaffian in the long wavelength limit for weak Coulomb interactions, a new pfaffian of an oscillatory pairing function for intermedi…
Intertwining of spin, charge and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wavefunctions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective pairing interactions are identified, they are strongly fragmented in several modes including d-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field w…
