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Register a new userFlat band in topological matter: possible route to room-temperature superconductivity
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G. E. Volovik
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Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. In gapless topological media, the bulk-surface and bulk-vortex correspondence produce topologically protected gapless fermions without dispersion - the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and this property may give rise in particular to surface superconductivity which in principle could exist even at room temperature.
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It was recently suggested that the topology of magic-angle twisted bilayer graphenes (MATBG) flat bands could provide a novel mechanism for superconductivity distinct from both weakly-coupled BCS theory and the $d$-wave phenomenology of the high-$T_c$ cuprates. In this work, we examine this possibility using a density matrix renormalization group (DMRG) study of a model which captures the essential features of MATBGs symmetry and topology. Using large scale cylinder-DMRG calculations to obtain the ground state and its excitations as a function of the electron doping, we find clear evidence for superconductivity driven by the binding of electrons into charge-$2e$ skyrmions. Remarkably, this binding is observed even in the regime where the unscreened Coulomb repulsion is by-far the largest energy scale, demonstrating the robustness of this topological, all-electronic pairing mechanism.
We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the pi-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor u=1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave--spin-wave) coupling.
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.
Topological magnon is a vibrant research field gaining more and more attention in the past few years. Among many theoretical proposals and limited experimental studies, ferromagnetic Kagome lattice emerges as one of the most elucidating systems. Here we report neutron scattering studies of YMn6Sn6, a metallic system consisting of ferromagnetic Kagome planes. This system undergoes a commensurate-to-incommensurate antiferromagnetic phase transition upon cooling with the incommensurability along the out-of-plane direction. We observe magnon band gap opening at the symmetry-protected K points and ascribe this feature to the antisymmetric Dzyaloshinskii-Moriya (DM) interactions. Our observation supports the existence of topological Dirac magnons in both the commensurate collinear and incommensurate coplanar magnetic orders, which is further corroborated by symmetry analysis. This finding places YMn6Sn6 as a promising candidate for room-temperature magnon spintronics applications.
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.
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