Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states

Zero-temperature quantum phase transitions and their associated quantum critical points are believed to underpin the exotic finite-temperature behaviours of many strongly correlated electronic systems, but identifying the microscopic origins of these transitions can be challenging and controversial; Iftikhar et al. (see also the related paper by Keller et al. ) show how such behaviours can be engineered into nanoelectronic quantum dots, which permit both precise experimental control of the quantum critical behaviour and its exact theoretical characterization. Two-channel Kondo physics goes critical Zero-temperature quantum phase transitions and their associated quantum critical points are believed to underpin the exotic finite-temperature behaviours of many strongly correlated electronic systems, such as heavy fermion materials and maybe even high-temperature superconductors. But identifying the microscopic origins of these transitions can be challenging and controversial. In two complementary papers, Zubair Iftikhar et al . and Andrew Keller et al . show how such behaviours can be engineered into nanoelectronic quantum dots, thereby permitting both exquisite experimental control of the quantum critical behaviour and its exact theoretical characterization. Many-body correlations and macroscopic quantum behaviours are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo effect 1 , 2 , which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems 3 , 4 , 5 and can be explored with tunable nanostructures 6 , 7 , 8 , 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 , 12 , 13 , 14 . Here we demonstrate the previously elusive ‘charge’ Kondo effect in a hybrid metal–semiconductor implementation of a single-electron transistor, with a quantum pseudospin of 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 unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics 1 , 4 , 21 , 22 . U