Purcell-like enhancement of electron-phonon interactions in moire superlattices: Linear-T resistivity and cooling power

Tunable flat-band systems in moire superstructures, e.g., twisted bilayer graphene, show rich correlated phases such as superconductivity, Mott insulator, and ferromagnetism. In these materials, the nearly-flat band appears at the Fermi level when the twist angle between the two layers is at a certain angle called “magic angle.” Strong electron-electron interaction is naturally expected at the magic angle because of the narrow bandwidth. On the other hand, recent experiments also found evidence for enhanced electron-phonon interaction, such as the large T-linear resistivity in a wide range of twist angles, including the magic angle. The enhanced resistivity is an order of magnitude larger than those predicted in theoretical calculations. However, the mechanism of this enhancement remains controversial.

Drawing inspiration from the Purcell effect in quantum optics, we discuss that a well-localized Wannier orbital realized in twisted bilayer graphene boosts the electron-phonon interactions. Recent electronic state calculation of twisted bilayer graphene finds that the nearly-flat band has a compact Wannier function, namely the Wannier function is localized in a small area of the Brillouin zone. This situation resembles the Purcell effect in quantum optics, in which the confinement of electrons to a quantum dot (or photons confined in a cavity) increases the electron-photon interaction. Similarly, we find that the localized Wannier orbitals in twisted bilayer graphene have a prominent effect on the electron-phonon interaction. In particular, reducing the effective orbital volume leads to enhancing the electron-phonon coupling strength, yielding values considerably larger than those known for monolayer graphene. The enhanced coupling boosts the electron-phonon scattering rates, pushing them above the values predicted from the enhanced spectral density of electronic excitations. The enhanced scattering rate manifests in the observables such as the electron-lattice cooling and the resistivity, showing an enhancement as large as tenfold [1]. Strengthening interactions by the reshaped Wannier orbitals provides unique means to control the electron-phonon interaction in moire bands.