The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two dimensional Holstein model are computed using determinant quantum Monte Carlo (DQMC), and compared with results computed using the Migdal-Eliashberg (ME) approach. We access temperatures as low as 25 times less than the Fermi energy, EF , which are still above the SC transition. We find that the SC susceptibility at low T agrees quantitatively with the ME theory up to a dimensionless electronphonon coupling λ0 ≈ 0.4 but deviates dramatically for larger λ0. We find that for large λ0 and small phonon frequency ω0 EF CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.

Ultrafast spectroscopies have become an important tool for elucidating the microscopic description and dynamical properties of quantum materials. In particular, by tracking the dynamics of non-thermal electrons, a material's dominant scattering processes -and thus the many-body interactions between electrons and collective excitations -can be revealed. Here we present a new method for extracting the electron-phonon coupling strength in the time domain, by means of time and angle-resolved photoemission spectroscopy (TR-ARPES). This method is demonstrated in graphite, where we investigate the 1 arXiv:1902.05572v3 [cond-mat.str-el] 1 Aug 2019 dynamics of photo-injected electrons at the K point, detecting quantized energyloss processes that correspond to the emission of strongly-coupled optical phonons.We show that the observed characteristic timescale for spectral-weight-transfer mediated by phonon-scattering processes allows for the direct quantitative extraction of electron-phonon matrix elements, for specific modes, and with unprecedented sensitivity.The concept of the electronic quasiparticle as proposed by Landau, i.e. the dressing of an electron with many-body and collective excitations (1), is essential to the modern understanding of condensed matter physics. Among the plethora of interactions relevant to solid-state systems, electron-phonon coupling (EPC) has been a persistent subject of great interest, related as it is to the emergence of disparate physical phenomena, from resistivity in normal metals to conventional (BCS) superconductivity and charge-ordered phases (2,3). While strong EPC is desirable in systems like BCS superconductors (4, 5), it is deleterious for conductivity in normal metals, curtailing the application of several compounds as room-temperature electronic devices (6).Given the important role of the electron-phonon interaction in relation to both conventional and quantum materials, extensive theoretical and experimental efforts have been devoted towards determining the strength and anisotropy of EPC. While ab-initio calculations are powerful, they rely on complex approximations which require precise experimental data to benchmark their validity (7). Inelastic scattering experiments -such as Raman spectroscopy (8), electron energy loss spectroscopy (9), inelastic x-ray (10), and neutron scattering (11) -are able to access EPC for specific phonon modes, yet integrated over all electronic states. Angle-resolved photoemission spectroscopy (ARPES), on the converse, can access the strength of EPC via phononmediated renormalization effects for specific momentum-resolved electronic states, as revealed by "kinks" in the electronic band dispersion (12-16). However, extraction of EPC strength from these kinks requires accurate modelling of the bare band dispersion and of the electronic

van der Waals heterostructures, vertical stacks of layered materials, offer new opportunities for novel quantum phenomena which are absent in their constituent components. Here we report the emergence of polaron quasiparticles at the interface of graphene/hexagonal boron nitride (h-BN) heterostructures. Using nanospot angle-resolved photoemission spectroscopy, we observe zone-corner replicas of h-BN valence band maxima, with energy spacing coincident with the highest phonon energy of the heterostructure, an indication of Fröhlich polaron formation due to forward-scattering electron-phonon coupling. Parabolic fitting of the h-BN bands yields an effective mass enhancement of ∼2.3, suggesting an intermediate coupling strength. Our theoretical simulations based on Migdal-Eliashberg theory corroborate the experimental results, allowing the extraction of microscopic physical parameters. Moreover, renormalization of graphene π-band is observed due to the hybridization with the h-BN band. Our work generalizes the polaron study from transition metal oxides to van der Waals heterostructures with higher material flexibility, highlighting interlayer coupling as an extra degree of freedom to explore emergent phenomena.