Many-body correlations and macroscopic quantum behaviors are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo model 1,2 which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems 3-5 and can be explored with tunable nanostructures 6-9 . Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments 10 , theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum 4,11-14 . Here we demonstrate the previously elusive 'charge' Kondo effect in a hybrid metal-semiconductor implementation of a singleelectron transistor, with a quantum pseudospin-1 2 constituted by two degenerate macroscopic charge states of a metallic island 11,[15][16][17][18][19][20] . In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel 11 , thereby providing an unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics 1,4,21,22 . Using a weakly coupled probe, we reveal the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point 4,21 . Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality 17 .In previous experimental investigations, the Kondo quantum impurity was of microscopic nature and mostly associated with spin 6,7,9,23-25 , orbital 8,26 , or possibly structural degrees of freedom 4,27 . In the 'charge' Kondo effect 11,16,17 , it is a pseudospin-1 2 constituted of two degenerate states of a macroscopic quantum variable, the electrical charge of a metallic island comprising several billions of electrons. The role of the electrons' spin (↑↓) in the original spin Kondo problem 10 is played by the electrons' location, in the island (↑) or elsewhere (↓). Accordingly, the charge pseudospin flips when electrons are transferred in and out of the island. The Kondo channels, each coupling the Kondo impurity (pseudo)spin with a distinct electron continuum, directly equate with the different electrical conduction channels connected to the island (distinguishing between those associated with different values of the real electron spin). In contrast, * e-mail: frederic.pierre@lpn.cnrs.fr Hybrid metal-semiconductor singleelectron transistor. a, Colorized picture of the sample (schematic in inset) constituted of a central metallic island (bright) connected to large electrodes (white circles) through the quantum point contacts QPC1,2 formed in a buried 2D electron gas (darker gray). The lateral continuous gates and QPCp are used, respectively, to characterize the 'intrinsic...

Quantum phase transitions (QPTs) are ubiquitous in strongly correlated materials. However, the microscopic complexity of these systems impedes the quantitative understanding of QPTs. We observed and thoroughly analyzed the rich strongly correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. An unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly correlated phenomena.