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The metallic delafossites host ultra-high mobility carriers in the bulk, while at their polar surfaces, intrinsic electronic reconstructions stabilise markedly distinct electronic phases, from charge-disproportionated insulators, to Rashba-split heavy-hole gases and ferromagnetic metals. The understanding of these phases has been strongly informed by surface spectroscopic measurements, but previous studies have been complicated by the presence of spatially varying terminations of the material surface. Here, we demonstrate the potential of microscopic-area angle-resolved photoemission to overcome these challenges. Our measurements of the model compound PdCoO$_2$ yield extremely high-quality spectra of the electronic structure, which allows us to place new experimental constraints on the weak electron-phonon coupling in the bulk of PdCoO$_2$, while revealing much stronger interactions at its surfaces. While the CoO$_2$-terminated surface exhibits a conventional weak-coupling behavior, our measurements reveal surprising spectroscopic signatures of polaron formation at the Pd-terminated surface, despite its pronounced metallicity. Together, our findings reveal how mode and symmetry-selective couplings can markedly tune the electron-phonon interactions in a single host material, here opening routes to stabilise surprisingly persistent polaronic quasiparticles., Comment: 17 pages including supplementary information

Doping of a Mott insulator gives rise to a wide variety of exotic emergent states, from high-temperature superconductivity to charge, spin, and orbital orders. The physics underpinning their evolution is, however, poorly understood. A major challenge is the chemical complexity associated with traditional routes to doping. Here, we study the Mott insulating CrO$_2$ layer of the delafossite PdCrO$_2$, where an intrinsic polar catastrophe provides a clean route to doping of the surface. From scanning tunnelling microscopy and angle-resolved photoemission, we find that the surface stays insulating accompanied by a short-range ordered state. From density functional theory, we demonstrate how the formation of charge disproportionation results in an insulating ground state of the surface that is disparate from the hidden Mott insulator in the bulk. We demonstrate that voltage pulses induce local modifications to this state which relax over tens of minutes, pointing to a glassy nature of the charge order., Comment: published paper and supplementary, 28 pages in total, 4 figures in the main text and 15 in the supplementary