Emulating moir\'e materials with quasiperiodic circuit quantum electrodynamics

Topological bandstructures interfering with moir\'e superstructures give rise to a plethora of emergent phenomena, which are pivotal for correlated insulating and superconducting states of twisttronics materials. While quasiperiodicity was up to now a notion mostly reserved for solid-state materials and cold atoms, we here demonstrate the capacity of conventional superconducting circuits to emulate moir\'e physics in charge space. With two examples, we show that Hofstadter's butterfly and the magic-angle effect, are directly visible in spectroscopic transport measurements. Importantly, these features survive in the presence of harmonic trapping potentials due to parasitic linear capacitances. Our proposed platform benefits from unprecedented tuning capabilities, and opens the door to probe incommensurate physics in virtually any spatial dimension.Comment: 11 pages, 5 figure

Middle-infrared absorption and electron paramagnetic resonance of copper associates in zinc sulfide

After firing in sulphur atmosphere, ZnS crystals show at low temperature an absorption multiplet in the middle-infrared (MIR) region near v ≃ 800 cm-1. An unpolarized main line is assigned to the transition (E, T2)-3T1 (F) ← A1- 3T1(F) of Cu3 +(3d8) ions on Td lattice sites whose symmetry is reduced to C3v by association with a neighboured defect X. Five polarized satellites refer likewise to associates [Cu3+, X] of symmetry Cs, the copper residing in a hexagonal environment in that case. Under UV irradiation at T ≃ 4 K, the configuration of the copper ion is changed into d9 so that a complex [Cu2+, X] emerges which, in EPR experiments, figures as the Cu-« M »-centre known from an earlier study (Holton et al., 1969). This state of the crystal is characterized by an additional MIR absorption at v ≃ 868 cm-1 and by a modified NIR emission spectrum.Après traitement thermique dans une atmosphère de soufre des cristaux de ZnS présentent, à basse température, un multiplet d'absorption dans l'infrarouge moyen (IRM) à v ≃ 800 cm-1. Une raie principale non polarisée est attribuée à la transition (E, T2)-3T 1 (F) ← A1-3T1(F) des ions Cu 3+(3d8) sur des sites Td dont la symétrie est réduite à C3v par association avec un défaut X voisin. Par analogie, cinq satellites appartiennent aux complexes [Cu3+, X] de la symétrie Cs; dans ce cas, le Cu est situé dans un environnement hexagonal. Par irradiation UV à T ≃ 4 K, la configuration de l'ion Cu est modifiée en d 9 en formant un complexe [Cu2+, X] qui, dans des expériences RPE est apparu comme le centre appelé Cu-« M » présenté dans un travail précédent (Holton et al., 1969). Cet état du cristal est caractérisé par une absorption IRM à v = 868 cm-1 et dans l'infrarouge proche par un spectre d' émission modifié

Emulating moir\'e materials with quasiperiodic circuit quantum electrodynamics

Topological bandstructures interfering with moir\'e superstructures give rise to a plethora of emergent phenomena, which are pivotal for correlated insulating and superconducting states of twisttronics materials. While quasiperiodicity was up to now a notion mostly reserved for solid-state materials and cold atoms, we here demonstrate the capacity of conventional superconducting circuits to emulate moir\'e physics in charge space. With two examples, we show that Hofstadter's butterfly and the magic-angle effect, are directly visible in spectroscopic transport measurements. Importantly, these features survive in the presence of harmonic trapping potentials due to parasitic linear capacitances. Our proposed platform benefits from unprecedented tuning capabilities, and opens the door to probe incommensurate physics in virtually any spatial dimension