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Register a new userSuperconducting Transitions in Flat Band Systems
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The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with unequal number of sites in each sublattice must have nonzero spin S at half-filling. Recently, there has been interest in Lieb geometries due to the possibility of novel topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using Determinant Quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems.
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Existing Quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO$_2$) lattice interacting with an on-site, or near-neighbor electron-electron coupling. Attention has focused on the interplay of such interactions with the macroscopic degeneracy of local zero energy modes, from which Bloch states can be formed to produce a flat band in which energy is independent of momentum. The resulting high density of states, in combination with the Stoner criterion, suggests that there should be pronounced instabilities to ordered phases. Indeed, a theorem by Lieb rigorously establishes the existence of ferrimagnetic order. Here we study the charge density wave phases induced by electron-phonon coupling on the Lieb lattice, as opposed to previous work on electron-electron interactions. Our key result is the demonstration of charge density wave (CDW) phases at one-third and two-thirds fillings, characterized by long-range density density correlations between doubly occupied sites on the minority or majority sublattice, and an accompanying gap. We also compute the transition temperature to the ordered phase as a function of the electron-phonon coupling.
Electronic flat bands represent a paradigmatic platform to realize strongly correlated matter due to their associated divergent density of states. In common instances, including electron-electron interactions leads to magnetic instabilities for repulsive interactions and superconductivity for attractive interactions. Nevertheless, interactions of Kondo nature in flat band systems have remained relatively unexplored. Here we address the emergence of interacting states mediated by Kondo lattice coupled to a flat band system. Combining dynamical mean-field theory and tensor networks methods to solve flat band Kondo lattice models in one and two dimensions, we show the emergence of a robust underscreened regime leading to a magnetically ordered state in the flat band. Our results put forward flat band Kondo lattice models as a platform to explore the genuine interplay between flat band physics and many-body Kondo screening.
It is known that a system which exhibits a half filled lowest flat band and the localized one-particle Wannier states on the flat band satisfy the connectivity conditions, is always ferromagnetic. Without the connectivity conditions on the flat band, the system is non-magnetic. We show that this is not always true. The reason is connected to a peculiar behavior of the band situated just above the flat band.
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $thetasim1.05^circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling ($n=pm2$).
We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion $U$, the Hunds coupling $J$, the crystal field splitting, and the number of electrons per site $n$. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by $Delta>0$ with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling ($n=3$), as the Hubbard interaction $U$ is increased. This leads to orbital selective Mott transitions where either the higher energy band (for $4>n>3$) or the lower energy degenerate bands ($2<n<3$) become insulating for $U$ larger than a critical interaction $U_{c}(n)$. Away from the half-filled case $|n-3|gtrsim 0.3$ there is a wide range of parameters for $U<U_c(n)$ where the system presents a Hunds metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the $n=2$ Hunds metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hunds metal regime to crystal fields due to the opposing effects of $J$ and the crystal field splittings on the charge distribution between the bands.
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