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Register a new userVortices, zero modes and fractionalization in bilayer-graphene exciton condensate
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B. Seradjeh
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A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.
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We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. At each superlattice point, we place a locally superconducting puddle which can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic incommensurate fillings, with the superconductivity being `interrupted by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. These features are consistent with experimental observations in magic-angle twisted bilayer graphenes despite the distinct microscopic details. We further study the full phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.
We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at non-integer fillings. Adding a phonon-mediated inter-valley retarded attractive interaction, we obtain strong-coupling superconducting domes, whose structure is in qualitative agreement with experiments. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic structure determine the phase diagram. It also explains how subtle differences between devices may lead to the different behaviors observed experimentally. A similar model can be applied with minor modifications to other moir{e} systems, such as twisted trilayer graphene.
We calculate the interactions between the Wannier functions of the 8-orbital model for twisted bilayer graphene (TBG). In this model, two orbitals per valley centered at the AA regions, the AA-p orbitals, account for the most part of the spectral weight of the flats bands. Exchange and assisted-hopping terms between these orbitals are found to be small. Therefore, the low energy properties of TBG will be determined by the density-density interactions. These interactions decay with the distance much faster than in the two orbital model, following a 1/r law in the absence of gates. The magnitude of the largest interaction in the model, the onsite term between the flat band orbitals, is controlled by the size of the AA regions and is estimated to be ~ 40 meV. To screen this interaction, the metallic gates have to be placed at a distance smaller than 5 nm. For larger distances only the long-range part of the interaction is substantially screened. The model reproduces the band deformation induced by doping found in other approaches within the Hartree approximation. Such deformation reveals the presence of other orbitals in the flat bands and is sensitive to the inclusion of the interactions involving them.
We propose an alternative route to engineer Majorana zero modes (MZMs), which relies on inducing shift or spin vortex defects in magnetic textures which microscopically coexist or are in proximity to a superconductor. The present idea applies to a variety of superconducting materials and hybrid structures, irrespectively of their spin-singlet, -triplet, or mixed type of pairing, as long as their bulk energy spectrum contains robust point nodes. Our mechanism provides a new framework to understand the recent observations of pairs of MZMs in superconductor - magnetic adatom systems. Moreover, it can inspire the experimental development of new platforms, consisting of nanowires in proximity to conventional superconductors with strong Rashba spin-orbit coupling.
Twisted bilayer graphene exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well isolated electronic bands near magic-angle. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron-electron (phonon) interactions and non-trivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus here on an interplay of two independent interaction-induced phenomena on superconductivity. We analyze the combined effects of Coulomb interaction driven band-flattening and phonon-mediated attraction due to the exchange of multiple electron-phonon umklapp processes, as a function of filling and twist angle. The former leads to a filling-dependent enhancement of the renormalized density of states, which contributes to a robust increase in the tendency towards pairing in a range of angles near magic-angle. In addition, the minimal spatial extent associated with the Wannier functions develops a non-trivial enhancement as a result of these many-body renormalizations, which can further contribute towards stabilizing the superconducting state over a wider range of fillings and twist-angles.
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