We study the coexistence of antiferromagnetism and unconventional superconductivity on the Creutz lattice which shows strictly flat bands in the noninteracting regime. The famous renormalized mean-field theory is used to deal with strong electron–electron repulsive Hubbard interaction in the effective low-energy t–J model, the superfluid weight of the unconventional superconducting state has been calculated via the linear response theory. An unconventional superconducting state with both spin-singlet and staggered spin-triplet pairs emerges beyond a critical antiferromagnetic coupling interaction, while antiferromagnetism accompanies this state. The superconducting state with only spin-singlet pairs is dominant with paramagnetic phase. The A phase is analogous to the pseudogap phase, which shows that electrons go to form pairs but do not cause a supercurrent. We also show the superfluid behavior of the unconventional superconducting state and its critical temperature. It is proven directly that the flat band can effectively raise the critical temperature of superconductivity. It is implementable to simulate and control strongly-correlated electrons’ behavior on the Creutz lattice in the ultracold atoms experiment or other artificial structures. Our results may help the understanding of the interplay between unconventional superconductivity and magnetism.
We study the coexistence of antiferromagnetism and unconventional superconductivity on the Creutz lattice which shows strictly flat bands in the noninteracting regime. The famous renormalized mean-field theory is used to deal with strong electron–electron repulsive Hubbard interaction in the effective low-energy t–J model, the superfluid weight of the unconventional superconducting state has been calculated via the linear response theory. An unconventional superconducting state with both spin-singlet and staggered spin-triplet pairs emerges beyond a critical antiferromagnetic coupling interaction, while antiferromagnetism accompanies this state. The superconducting state with only spin-singlet pairs is dominant with paramagnetic phase. The A phase is analogous to the pseudogap phase, which shows that electrons go to form pairs but do not cause a supercurrent. We also show the superfluid behavior of the unconventional superconducting state and its critical temperature. It is proven directly that the flat band can effectively raise the critical temperature of superconductivity. It is implementable to simulate and control strongly-correlated electrons’ behavior on the Creutz lattice in the ultracold atoms experiment or other artificial structures. Our results may help the understanding of the interplay between unconventional superconductivity and magnetism.
Abstract Flat-band systems provide an ideal platform for studying strong electron correlations, in which multiple quasi-degenerate charge orders frequently coexist. Motivated by this context, we investigate the pair-density-wave (PDW) superconducting state in a quasi-one-dimensional Creutz lattice featuring two strictly flat bands. Using a renormalized mean-field approach for the strongly correlated t - J model, we obtain self-consistent solutions that demonstrate a PDW phase—characterized by finite-center-of-mass-momentum Cooper pairing—coexisting with charge density wave (CDW) and bond density wave (BDW) orders. Physically, this coexistence phenomenon originates from the perfect band nesting inherent to the flat-band system, which allows for changes in the particle momentum distributions without energy cost. Here, a pure PDW solution without CDW and BDW orders emerges in the underdoped regime when magnetic effects are neglected, while strong Hubbard correlations favor a pure CDW phase. We conclude that a robust PDW phase, accompanied by CDW and BDW orders, occupies the majority of the parameter space. Furthermore, both the PDW order parameter and its critical temperature scale linearly with the superexchange coupling strength—a hallmark of flat-band superconductivity. Overall, our results reveal that a PDW superconducting state can be realized on the Creutz lattice with strong correlations.
We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely, the Creutz lattice, where we investigate the role of local attractive interactions in the U<0 Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.
We study the interplay between on-site disorder and fermion pairing on the quasi-one-dimensional flat-band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat-band superconductivity is robust against disorder: The critical disorder strength Wc required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength U and is proportional to the superconducting weight Ds of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that Wc can be accurately determined by using an appropriate scaling function.
In this thesis, superconductivity of fermions in two-dimensional Hubbard lattice models is theoretically studied. Each of the studied lattice structures features intriguing properties that provide valuable insight to understand superconductivity in general. While real condensed matter systems are too complicated to tackle with theoretical tools, the Hubbard model is one of the simplest quantum many-body models to possess a wide spectrum of physically relevant phenomena, from superconductivity to magnetism and topological order. Hubbard models are also interesting as they can be experimentally realized and accurately controlled by utilizing ultracold gases.
The first part of the thesis explains the required theoretical background of superconductivity in the level of mean-field and linear response theories. Specifically, we primarily focus on the superfluid weight which implies the existence of the Meissner effect and dissipationless current, defining properties of superconductors. We further discuss how the Berezinskii-Kosterlitz-Thouless (BKT) transition, related to the loss of superconductivity due to the thermal fluctuations of the superconducting order parameter in high enough temperatures, can be accessed via the superfluid weight.
In the second part, the main results are discussed. We show how the superconductivity of lattice models featuring dispersionless Bloch bands, so-called flat bands, can be large and originating from the quantum geometric properties of the Bloch states of the flat bands. This is in contrast to conventional dispersive bands where superconductivity is determined by the effective mass of the particles, i.e. by the dispersion relation of the Bloch bands alone and not by the Bloch states. This is well demonstrated in the Lieb lattice geometry, studied in Publication I, which features both a strictly flat and two dispersive Bloch bands, allowing direct comparison of superconductivity in dispersive and flat bands. We show how the superconductivity of the flat band is more robust than that of the dispersive bands and how the superfluid weight behaves non-monotonically as a function of the interaction strength. This non-monotonic behavior should be experimentally accessible. Flat band superconductivity is also the topic of Publication III, where the experimentally realized twisted bilayer graphene (TBG) is studied with local and non-local attractive interactions. We predict qualitative differences between local and non-local interaction schemes which could be distinguished experimentally and reveal the quantum geometric origin of superconductivity in TBG systems in case of both the assumed interaction schemes.
Exotic Fulde-Ferrell (FF) superfluid phases, characterized by the non-zero momentum of Cooper pairs, were explored in Publication II. We show how the FF phases can be stabilized against thermal fluctuations in the presence of spin-orbit coupling (SOC) and that topologically non-trivial FF states, created with SOC and Zeeman fields, can be found at finite temperatures.; Tassa…
We study the pairing and superconducting properties of the attractive Hubbard model in two quasi-one-dimensional topological lattices---the Creutz and sawtooth lattices---which share two peculiar properties: each of their band structures exhibits a flat band with a nontrivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, due to a chiral (sublattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use a multiband mean field and exact density matrix renormalization group in our work. Our three main results are as follows: (a) For both lattice systems, the superconducting weight, Ds, is linear in the coupling strength, U, for low values of U. (b) For small U,Ds is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent. We have therefore extended the approach to this more complex situation and found an excellent agreement with the numerical results. (c) At moderate and large U, the conventional BCS mean field is no longer appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multiband mean-field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean-field parameters.
Materials with strongly correlated electrons show a multitude of unconventional phenomena, such as superconductivity or magnetism, that cannot be explained in a single-particle picture and necessitate to take many-body effects into account. A route to explain the origin of these phenomena consists in constructing effective models for these materials that are then solved, often using numerical techniques. Paradigmatic models for two different classes of strongly correlated electron systems are investigated in this thesis: The Hubbard model is a paradigmatic model to describe the Mott metal-insulator transition (MIT) and the Kondo lattice model describes the low-energy physics in heavy fermion compounds. Both models are analyzed numerically using different variations of a quantum cluster technique, the variational cluster approximation (VCA). The first part focuses on the MIT, as it is investigated experimentally in quasi-two-dimensional charge-transfer salts. Its nature and associated universality class are still heavily discussed and both experiments and theoretical approaches come to different conclusions. In this thesis, the Mott transition is investigated on an anisotropic two-dimensional Hubbard model at half-filling. By using a control parameter, which induces this anisotropy, strong evidence for Mott quantum criticality is found in weakly coupled Hubbard chains. The results at zero temperature show that the second-order critical end point Tc of the interaction-driven metal-insulator transition can be tuned down to zero at strong anisotropy. Further results for the antiferromagnetic phase suggest a similar picture and motivate adding the anisotropy as a new axis in the phase diagram to account for a low-temperature critical end point of the Mott transition. The second part of this thesis focuses on unconventional phases that emerge in a paradigmatic model for heavy fermion systems, the Kondo lattice model. Using the VCA, the two-dimensional Kondo lattice model is investigated in the paramagnetic phase as well as in phases with broken symmetry. An antiferromagnetic phase at weak coupling and a phase with Kondo-singlet formation at strong coupling are analyzed. Within the antiferromagnetically ordered region, two phases with different Fermi-surface topology, which are separated by a discontinuous transition, are identified. The model is also tested for s-wave superconductivity as found recently using dynamical mean-field theory, but no indications for robust local pairing are seen within VCA. Instead, nodal d-wave superconductivity is found and analyzed in a large range of couplings and electron fillings, and its interplay with antiferromagnetic order at weak coupling is discussed. This motivates further studies on extended models that might allow for a close comparison with experiments on heavy fermion systems. Understanding the formation of unconventional phases in strongly correlated electron systems is not only of fundamental interest, but it is also essential for designing new functional materials. Although the results of approximate cluster techniques have to be handled with care, the new aspects presented in this thesis pave the way for further investigations in this direction.