Metallic islands in quantum Hall devices: from quantum impurities to synthetic quantum matter

The surprisingly rich physics of a single Coulomb-blockaded metallic island coupled to quantum Hall edge channels, is now well established -- giving rise to charge fractionalization and multi-channel quantum impurity behavior. In this talk I will describe qualitatively new physics that emerges in arrays of such elements. I will consider a 1D chain of  metallic islands, focusing on thermodynamic signatures such as quantized entropy and anomalous thermal conductance. Universal and robust behavior emerges for energy scales smaller than the charging energy of the islands. In particular, I will demonstrate that for bulk filling factor 1 the islands can support a finite heat flow without temperature difference between them. Upon pinching the array with a quantum point contact, there is an entropy change that scales with the number of islands and suggests the emergence of a novel type of fractional excitations in the array.