Unconventional ordering phenomena in magnets and superconductors

Jeremy A. Strockoz

doi:10.17918/00010816

In this work, we study theoretical models of strongly correlated materials which exhibit long-range order in the form of magnetism and superconductivity. First, a quantum phase transition between a paramagnetic state and a rotation symmetry breaking magnetically ordered state is studied on the triangular, honeycomb, and face-centered cubic lattices. This phase transition is determined to occur in two steps, with a Potts-nematic intermediate phase defined by broken Z₃ rotation symmetry, but no long-range magnetic order. Next, Kondo lattice magnets are investigated in the strong-coupling limit. This means that the Kondo coupling J_K is the largest energy scale. A systematic expansion in 1/S and t/J_K is developed via a canonical Schrieffer-Wolff transformation of the Kondo lattice Hamiltonian. The resulting effective Hamiltonian is expressed in terms of the natural degrees of freedom of the problem: the transformed bosons correspond to spin wave excitations of the total spin at a given site and the transformed fermions create or annihilate electrons in a total spin S ± 1/2 state. The edge states of topological superconductors are then characterized. First, numerical calculations of superconductors with open boundary conditions are performed for multiple pairing functions. Through qualitative comparisons to experimental observations along with additional evidence from collaborators, the results suggest that Sn/Si(111) is a topological superconductor with chiral d-wave pairing. In order to make more robust and quantitative comparisons with future experiments, the edge state energy and wavefunction are calculated exactly as a function of the Hamiltonian parameters for all allowed chiral pairing functions on the square and triangular lattices. From these expressions, experimentally measurable quantities such as the density of states and edge state decay length are determined as a function of the Hamiltonian parameters. This allows for a direct comparison between theory and experiment. Finally, the generic phase diagram is established for noncentrosymmetric topological Dirac semimetals in three dimensions. We identify the noncentrosymmetric crystallographic point groups required to stabilize fourfold degenerate band crossings and derive model Hamiltonians for all distinct types of band inversions allowed by symmetry. Using these model Hamiltonians, we demonstrate that the phase diagram generically includes phases with coexistent Weyl point nodes or Weyl line nodes.

Unconventional ordering phenomena in magnets and superconductors

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Unconventional ordering phenomena in magnets and superconductors

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