  Impurities or boundaries often impose nontrivial boundary conditions on a
gapless bulk, resulting in distinct boundary universality classes for a given
bulk, phase transitions, and non-Fermi liquids in diverse systems. The
underlying boundary states however remain largely unexplored. This is related
with a fundamental issue how a Kondo cloud spatially forms to screen a magnetic
impurity in a metal. Here we predict the quantum-coherent spatial and energy
structure of multichannel Kondo clouds, representative boundary states
involving competing non-Fermi liquids, by studying quantum entanglement between
the impurity and the channels. Entanglement shells of distinct non-Fermi
liquids coexist in the structure, depending on the channels. As temperature
increases, the shells become suppressed one by one from the outside, and the
remaining outermost shell determines the thermal phase of each channel.
Detection of the entanglement shells is experimentally feasible. Our findings
suggest a guide to studying other boundary states and boundary-bulk
entanglement.
