Exotic phases in strongly correlated materials

Zhang, Guanghua
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In strongly correlated materials, the electron-electron interaction is much stronger than the kinetic energy and plays a determining role in the properties of such materials. The strong electron-electron interaction often gives rise to exotic physical phenomena, such as high-temperature superconductivity, quantum Hall effects, Mott insulators, heavy fermion systems, and quantum criticality. There is no unified and effective approach to understand the physics in different materials, however, many of the same techniques generalize to different scenarios. In this thesis, we will discuss two types of exotic phases: the nematic order above the double-stripe magnetism, and hastatic order which originates from two-channel Kondo effect in a cubic environment.

Chapter 2 presents a fundamental tool to understand phase transitions: Landau theory, which associates each phase with an order parameter and describe mean-field phase transitions; and Ginzburg-Landau theory, which accounts for the spatial fluctuations of order parameters. We also discuss the spin-driven nematicity in both single-stripe magnetism and double-stripe magnetism, and possible experimental realizations.

In Chapter 3, we argue that the low-temperature state of the recently discovered superconductor BaTi2Sb2O is a strong candidate for a more exotic form of spin-driven nematic order, in which fluctuations occurring in four Neel sublattices promote both nearest- and next-nearest neighbor bond order. We develop a low energy effective field theory of this state and show that it can have, as a function of temperature, up to two separate bond-order phase transitions -- namely, one that breaks rotation symmetry and one that breaks reflection and translation symmetries of the lattice. First principles calculations by our collaborators confirm that the model is applicable to BaTi2Sb2O.

In Chapter 4, we extend the work in Chapter 3 to quasi-two dimensions, where magnetism comes into play. We find that all three transitions - two Ising bond orders and one magnetic order are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.

In Chapter 5, we will investigate the Kondo effect resulting from magnetic impurities in metallic materials. The physics with dense concentration of impurities can be captured by the Kondo lattice model. When the degree of freedom of the local moments and the number of the conduction electron channels differ, a multi-channel Kondo effect can take place in place of the normal single-channel Kondo effect. By the end, we give a microscopic description of the two-channel Kondo effect, and possible candidates of its realization.

Chapter 6 provides a survey of cubic hastatic order motivated by the Pr-based materials.

We employ an SU(N) fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields. The experimental signatures of these phases are also discussed.