Theory of hastatic order and its defect states
Date
2023-08
Authors
Kornjača, Milan
Major Professor
Advisor
Flint, Rebecca A
Orth, Peter P
Canfield, Paul C
Tuchin, Kirill
Kovnir, Kirill
Iadecola, Thomas
Committee Member
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Abstract
We explore the physics of hastatic order, a novel symmetry-breaking heavy Fermi liquid state arising in two-channel Kondo lattices. The macroscopic Landau-Ginzburg theory of antiferrohastatic order captures its unconventional spinorial signatures through multiple order parameters. The predictions of the theory are shown to be realized in a mean-field treatment of a concrete microscopic model for a candidate hastatic material, URu2Si2, allowing us to propose a hastatic theory unifying discrepant experimental observations. We extended our study of the two-channel Kondo lattice to one dimension, showing that hastatic order is indeed competitive quantum ground state and how the predictions of hastatic theory materialize. We study the physics of hastatic order defects, discovering that they host sought-after Majorana zero modes.
In chapter 2, the phenomenological Landau-Ginzburg theory of the antiferrohastatic order is proposed. Our theory can explain all the symmetries broken by hastatic order, including double-time-reversal, by considering two distinct gauge invariant order parameters. We apply the theory to the candidate material, URu2Si2, disentangling the experimental signatures of different order parameters through a hierarchy of energy scales. We consider the effect of fluctuations and disorder on the tetragonal symmetry breaking in the material, explaining the absence of in-plane moments in URu2Si2 and predicting a new transition in the transverse field.
In chapter 3, we present a concrete, multi-band microscopic model of URu2Si2 candidate material and treat the hastatic order within a large-N mean-field approach. Symmetry-breaking results are explained within the previously developed Landau theory framework. Parameter region reproducing the experimental URu2Si2 phase diagram is found, allowing the tuning between two distinct experimental phases with pressure analog and magnetic field. This complex multi-band model presents the Ising heavy-fermion physics seen in experiments, as shown by developing an effective model of hastatic Fermi surfaces.
In chapter 4, we study a one-dimensional two-channel Kondo lattice using the density matrix renormalization group technique to obtain the exact ground states of the model. We report the presence of several algebraic hastatic density wave phases. These are heavy Tomonaga-Luttinger liquids with heavy Fermi wave-vectors captured by hastatic large-N mean-field theory. We also detect algebraic correlations of the secondary order parameter, confirming Landau theory predictions.
In chapter 5, we consider defects of hastatic order, specifically, of the two-channel antiferrohastatic Kondo insulator phase. We show that these defects host localized states, which in the case of topological hastatic skyrmions, have Majorana character stemming from effective two-channel Kondo impurity physics. These states are protected by the insulating gap and may be adiabatically braided, providing the novel possibility of realizing topological quantum computation in heavy fermion material.
Chapter 6 provides a short review of the main results described in the thesis and a discussion of future research directions that they motivate.
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dissertation