Abstract
We demonstrate how self-sourced collective modes – of which the plasmon is a prominent example due to its relevance in modern technological applications – are identified in strongly correlated systems described by holographic Maxwell theories. The characteristic \omega \propto \sqrt{k}ω∝k plasmon dispersion for 2D materials, such as graphene, naturally emerges from this formalism. We also demonstrate this by constructing the first holographic model containing this feature. This provides new insight into modeling such systems from a holographic point of view, bottom-up and top-down alike. Beyond that, this method provides a general framework to compute the dynamical charge response of strange metals, which has recently become experimentally accessible due to the novel technique of momentum-resolved electron energy-loss spectroscopy (M-EELS). This framework therefore opens up the exciting possibility of testing holographic models for strange metals against actual experimental data.
Highlights
Holography is a powerful framework for computing the response functions of strongly correlated matter, where, due to the absence of long-lived quasi-particles, perturbation theory is not applicable
We find that for isotropic systems there are boundary conditions that translate the necessary features from the boundary theory into the bulk, (12) and (13) for longitudinal and transverse collective modes, respectively
We point out that, in the case of holographic Maxwell theories, poles of the screened correlator χsc, corresponding to quasi-normal modes (QNMs), are not collective modes as they require non-vanishing external fields, and represent driven excitations of the system. We demonstrate that this method of relating the physical set-up in the boundary theory to the boundary conditions on the equations of motion in the bulk is instructive and intuitive, and a powerful tool when regarding other types of Maxwell theories, such as codimension one materials
Summary
Holography is a powerful framework for computing the response functions of strongly correlated matter, where, due to the absence of long-lived quasi-particles, perturbation theory is not applicable. we will extend previous work [3] to illustrate how collective modes, both in the longitudinal and transverse sectors, correspond to specific choices of boundary conditions This identification is consistent with the notion that these modes are, in condensed matter theory (CMT), usually identified with the vanishing of the dielectric function. to lay out how these insights have to be incorporated into an effective holographic description of a strongly correlated codimension one system, like graphene, since the relative number of dimensions in which the charge carriers can move compared to the number of dimensions the potential permeates is an essential point Based on these considerations, we argue in sec. Within the large parameter space of the holographic model, we will elaborate on the detailed agreement with results in regions where conventional condensed matter approaches are applicable
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