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Extreme confinement of electromagnetic energy by phonon polaritons holds the promise of strong and new forms of control over the dynamics of matter. To bring such control to the atomic-scale limit, it is important to consider phonon polaritons in two-dimensional (2D) systems. Recent studies have pointed out that in 2D, splitting between longitudinal and transverse optical (LO and TO) phonons is absent at the $Gamma$ point, even for polar materials. Does this lack of LO--TO splitting imply the absence of a phonon polariton in polar monolayers? Here, we derive a first-principles expression for the conductivity of a polar monolayer specified by the wavevector-dependent LO and TO phonon dispersions. In the long-wavelength (local) limit, we find a universal form for the conductivity in terms of the LO phonon frequency at the $Gamma$ point, its lifetime, and the group velocity of the LO phonon. Our analysis reveals that the phonon polariton of 2D is simply the LO phonon of the 2D system. For the specific example of hexagonal boron nitride (hBN), we estimate the confinement and propagation losses of the LO phonons, finding that high confinement and reasonable propagation quality factors coincide in regions which may be difficult to detect with current near-field optical microscopy techniques. Finally, we study the interaction of external emitters with two-dimensional hBN nanostructures, finding extreme enhancement of spontaneous emission due to coupling with localized 2D phonon polaritons, and the possibility of multi-mode strong and ultra-strong coupling between an external emitter and hBN phonons. This may lead to the design of new hybrid states of electrons and phonons based on strong coupling.
We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation within the Callaway model, we derive a 2D Guyer-Krumhansl-like equation describing non-local hydrodynamic phonon transport, ta
We demonstrate how weak hybridization can lead to apparent heavy doping of 2d materials even in case of physisorptive binding. Combining ab-intio calculations and a generic model we show that strong reshaping of Fermi surfaces and changes in Fermi vo
We propose an optical method of shining circularly polarized and spatially periodic laser fields to imprint superlattice structures in two-dimensional electronic systems. By changing the configuration of the optical field, we synthesize various latti
We propose a robust and efficient way of controlling the optical spectra of two-dimensional materials and van der Waals heterostructures by quantum cavity embedding. The cavity light-matter coupling leads to the formation of exciton-polaritons, a sup
Exciton problem is solved in the two-dimensional Dirac model with allowance for strong electron-hole attraction. The exciton binding energy is assumed smaller than but comparable to the band gap. The exciton wavefunction is found in the momentum spac