The standard theory of electrons in metals, Landau’s Fermi liquid theory from 1956 has been very successful in predicting the low-temperature properties of many metals. Its greatest success was its ability to describe many heavy fermion metals, whose name comes from the huge apparent masses acquired by their conduction electrons. However increasingly many metals have been synthesized where Fermi-liquid predictions fail. They are called non-Fermi liquid (NFL) or exotic metals. Prominent examples are certain heavy fermion compounds and high-temperature superconductors. These materials are of interest because of the emergence of new properties that could be used in future technologies. In most cases NFL behaviors lack the understanding, as only a handful of solvable, microscopic models describe NFL phenomena. To make strides I will construct a novel class of NFL quantum impurity models. Quantum impurity models describe the interaction between local degrees of freedom, like a spin, and the surrounding conduction electrons. The simplest NFL quantum impurity model was considered to be the so-called two-channel Kondo model (2CKM). One of the new quantum impurity models—which I call the one-and-a-half-channel Kondo model and whose low-energy solution gives the topological Kondo effect—has less degrees of freedom and is, in this sense, simpler than the 2CKM, yet it also exhibits NFL behavior. Generally, this new family of NFL quantum impurity models includes all those overscreened Kondo-type models where the number of conduction electron species are not integer multiples of the number of impurity states. I will study the new quantum impurity models using Wilson’s numerical renormalization group method (recognized by the 1982 Nobel Prize). My further aims are to experimentally realize the corresponding NFL behavior, i.e. create new states of matter in bulk materials, and also to theoretically explore alternative realizations of the novel NFL physics in quantum dot devices.
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