π-tons — generic optical excitations of correlated systems A. Kauch a,∗ , P. Pudleiner a,b,∗ , K. Astleithner a , T. Ribic a , and K. Held a a Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria and b Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria ∗ (Dated: July 17, 2022) The interaction of light with solids gives rise to new bosonic quasiparticles, with the exciton being—undoubtedly—the most famous of these polaritons. While excitons are the generic polaritons of semiconductors, we show that for strongly correlated systems another polariton is prevalent— originating from the dominant antiferromagnetic or charge density wave fluctuations in these sys- tems. As these are usually associated with a wave vector (π,π,...) or close to it, we propose to call the derived polaritons π-tons. These π-tons yield the leading vertex correction to the opti- cal conductivity in all correlated models studied: the Hubbard, the extended Hubbard model, the Falicov-Kimball, and the Pariser-Parr-Pople model, both in the insulating and in the metallic phase. Since the springtime of modern physics, the interac- tion of solids with light has been of prime interest. The arguably simplest kind of interaction is Einstein’s Noble prize winning photoelectric effect [1], where the photon excites an electron across the band gap. More involved processes beyond a mere electron-hole excitation can be described in general by effective bosonic quasiparticles, coined polaritons since a polar excitation is needed to couple the solid to light. The prime example of a polariton is the exciton [2, 3], where the excited electron-hole pair is bound due to the Coulomb attraction between electron and hole. This in- teraction is visualized in Fig. 1 (a). Since it is an attrac- tive interaction, an exciton requires the exciton binding energy less than an unbound electron-hole pair. Other polaritons describe the coupling of the photon to surface plasmons, magnons or phonons. Fig. 1 (b) describes the exciton in terms of Feynman diagrams: the incoming photon creates the electron- hole pair (distinguishable by the different [time] direc- tion of the arrows) which interact with each other re- peatedly and finally recombine emitting a photon. Since the energy-momentum relation of light is very steep com- pared to the electronic bandstructure of a solid, the trans- ferred momentum from the photon is negligibly small q = 0. Thus, electron and hole have the same momen- tum. For semiconductors this is often the preferable mo- mentum transfer as well, connecting the bottom of the conductance with the top of the valence band as in Fig. 1 (a). In this paper we show that the generic polaritons for strongly correlated systems are strikingly different. While semiconductors are band insulators with a filled valence and empty conduction band, strongly correlated systems are typically closer to a half-filled (or in general integer filled) band which is split into two Hubbard bands by strong electronic correlations as visualized in Fig. 1 (c) for a Mott insulator. (In case of a metallic system there is an additional quasiparticle band). Both metal and insulator are prone to strong antiferromagnetic (AFM) q=0 k k´ k´ q=0 k 0 k a) b) c) d) q=0 k k´ k´ q=0 k k-k´»p 0 p k FIG. 1. (Color online) Sketch of the physical processes (top) and Feynman diagrams (bottom) behind an exciton (left) and a π-ton (right). The yellow wiggled line symbolizes the incom- ing (and outgoing) photon which creates an electron-hole pair denoted by open and filled circles, respectively. The Coulomb interaction between the particles is symbolized by a red wig- gled line; dashed line indicates the recombination of the par- ticle and hole; dotted line denotes the creation of a second particle-hole pair (right); black lines the underlying band- structure (top panels). or charge density wave (CDW) fluctuations with a wave vector close to q =(π,π,...)[4, 5]. Indeed these fluctu- ations can be described by the central part of the Feyn- man diagram Fig. 1 (b), where the bare ladder diagrams correspond to the random phase approximation (RPA). However the wave vector q =(π,π,...) cannot directly couple to light, which only transfers q = 0. Hence an exciton-like polariton as displayed in Fig. 1 (b) is not possible for AFM or CDW fluctuations. As we will show in this paper, the (π,π,...) fluctu- ations nonetheless constitute the dominant vertex cor- rections beyond a bare (bubble) particle-hole excitation. This is possible through a process where the central part of the Feynman diagram Fig. 1 (b), i.e., the (π,π,...) fluctuations, are rotated (and flipped) as sketched in arXiv:1902.09342v1 [cond-mat.str-el] 25 Feb 2019