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![Universal scaling of the BS localization length λBS as a function of the CLSs overlap |α| for 1D and 2D lattices based on Eqs. (32) and (34), respectively (in the common case that only nearest-neighbour CLSs overlap). Here, |α| = 1/2 and |α| = 1/4 are the maximum allowed values of |α|, respectively in 1D and 2D, consistent with the hypothesis that only nearest-neighbour CLSs overlap. In 2D, the behaviour is the sum of two decaying exponentials with localization lengths λ2D and λ ′ 2D [cf. Eq. (34)].](profile/Enrico_Di_Benedetto2/publication/381108902/figure/fig3/AS:11431281248721224@1717386330904/Universal-scaling-of-the-BS-localization-length-lBS-as-a-function-of-the-CLSs-overlap-a.png)
Universal scaling of the BS localization length λBS as a function of the CLSs overlap |α| for 1D and 2D lattices based on Eqs. (32) and (34), respectively (in the common case that only nearest-neighbour CLSs overlap). Here, |α| = 1/2 and |α| = 1/4 are the maximum allowed values of |α|, respectively in 1D and 2D, consistent with the hypothesis that only nearest-neighbour CLSs overlap. In 2D, the behaviour is the sum of two decaying exponentials with localization lengths λ2D and λ ′ 2D [cf. Eq. (34)].
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Flat bands (FBs) are energy bands with zero group velocity, which in electronic systems were shown to favor strongly correlated phenomena. Indeed, a FB can be spanned with a basis of strictly localized states, the so called "compact localized states" (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions...
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Context 1
... settsech(x) the inverse function of the hyperbolic secant. Therefore, ξ nn ′ decays exponentially with |n − n ′ | with a characteristic length λ 1D which is a growing function of the non-orthogonality coefficient α [see Fig. 4 Fig. ...
Context 2
... is subject to the constraint |α| ≤ 1/4). Thus, in this case the decay results from the superposition of two exponential functions with localization length λ 2D and λ ′ 2D , respectively. As in 1D, both localization lengths grow with |α| (see Fig. 4(b)]. Differently from 1D, however, when α approaches its maximum value 1/4 only λ 2D diverges while λ ′ 2D instead saturates to the finite value λ ′ 2D (α → 1/4) ≃ 0.567 (for α → −1/4, λ 2D saturates to the same value while λ ′ 2D diverges). This means that in this limiting case the weight function ξ nn ′ is a single exponential having ...
Context 3
... settsech(x) the inverse function of the hyperbolic secant. Therefore, ξ nn ′ decays exponentially with |n − n ′ | with a characteristic length λ 1D which is a growing function of the non-orthogonality coefficient α [see Fig. 4 Fig. ...
Context 4
... is subject to the constraint |α| ≤ 1/4). Thus, in this case the decay results from the superposition of two exponential functions with localization length λ 2D and λ ′ 2D , respectively. As in 1D, both localization lengths grow with |α| (see Fig. 4(b)]. Differently from 1D, however, when α approaches its maximum value 1/4 only λ 2D diverges while λ ′ 2D instead saturates to the finite value λ ′ 2D (α → 1/4) ≃ 0.567 (for α → −1/4, λ 2D saturates to the same value while λ ′ 2D diverges). This means that in this limiting case the weight function ξ nn ′ is a single exponential having ...
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Flat bands (FBs) are energy bands with zero group velocity, which in electronic systems were shown to favor strongly correlated phenomena. Indeed, a FB can be spanned with a basis of strictly localized states, the so called compact localized states (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions be...
