Spin and Orbital Physics in Novel Correlated Materials

Electrons in metals interact via their mutual Coulomb repulsion. When these interactions become large, the electrons rearrange themselves into new quantum states of order. Such 'quantum materials' include ferro- and antiferromagnets, high temperature superconductors, and materials in which the electronic wavefunction acquires topological order. The scientific insights into these phenomena gained from research into their underlying physics is vital for their future applications as materials for new device, memory, communication and energy applications. Of particular interest to this science, are the transformative effects of the magnetic moments and the orbital motion of the electrons.

One focus of the research are the effects of electron interactions on topological Quantum Materials. Research over the past ten years has revealed a class of topological quantum materials in which the wave function of the electrons acquires a topological twist: like a Mobius strip, this twist can not be undone in a smooth fashion, and the presence of the twist transforms the physics of the electronic ground-state, giving rise to new kinds of properties, such as robust conducting surface states. The simplest examples of such interacting topological materials are called Topological Kondo insulators. In these materials, magnetic interactions amongst the atoms cause the low temperature transformation of the material from a metal into an insulator with novel conducting surface states. Recent discoveries suggest that under some circumstances, electron interactions can transform the bulk properties of these materials, generating new kinds of neutral excitations. The proposed research will develop new mathematical tools to describe the effect of charge or 'valence' fluctuations of the magnetic ions on these unusual quantum states.

A second thrust of the research will examine the effects of interactions and orbital physics on high temperature iron-based and transition-metal superconductors, with a particular emphasis on exploring the implications of topology and strong Hund's interactions in these superconductors. When a magnetic field is applied to this superconductors, it generates a lattice of superconducting vortices. One of the proposed effects of topology that we will explore, is the development of a new kind of propagating excitation, called a Majorana Fermion inside the core of these vortices. We will develop a detailed model of this physics, making predictions for future experiments. In combination with this work, we will be examining the effect of the 'Hund's interactions' on the electrons. When strong Coulomb interactions act on electrons in different atomic orbitals, they give rise to a strong ferromagnetic forces between the electrons, called Hund's interactions. Recent experiments suggest that the driving force for pairing in iron-based superconductors may be local, driven by these Hund's interactions. The research will examine whether these Hund's interactions have the capability to drive superconducting pairing in iron-based superconductors.

A final thrust of the research will examine the physics of low dimensional antiferromagnets and conductors. The effects of electron interactions become strongest in materials with low dimensional structures (such as planes or chains) , making them ideal platforms to explore the effects of electron interactions. There is in fact, a close relationship between quantum mechanics in one dimension and classical statistical mechanics in two dimensions which allows use of statistical mechanics in 2D to gain new insights into 1D quantum physics. By using the mathematics that maps 2D classical magnetism into 1D conductors we will develop a geometrically based description of how the electron physics of complex one dimensional conductors scales with distance.