Electron-electron interactions in t2g two-dimensional electron gases




Tolsma, John Robert

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In this thesis I discuss the effects of electron-electron interactions on the properties of recently created two dimensional conducting layers which form near the surface or interface of transition-metal oxides, most commonly SrTiO3. Although these systems typically contain far fewer than one conduction band electron per unit cell, and are therefore most appropriately described using two-dimensional electron gas (2DEG) models, they are distinct from previous 2DEGs in that unique single-particle characteristics ({\it e.g} multiple occupied bands at the Fermi energy, strong band-anisotropy, varying band-edge energy differences) are inherited from the t2g d-orbitals which form the low-energy bands. The interplay of the long-range Coulomb interaction with these unique single-particle characteristics leads to many novel results and is the central theme of this thesis.

The contents of this dissertation are separated into two complimentary parts.. In the first part I propose a model intended to qualitatively capture the electron-electron interaction physics of two-dimensional electron gases formed near transition-metal oxide heterojunctions containing t2g electrons with a density much smaller than one electron per metal atom. Two-dimensional electron systems of this type can be described perturbatively using a GW approximation which predicts that Coulomb interactions enhance quasiparticle effective masses more strongly than in simple two-dimensional electron gases, and that they reshape the Fermi surface, reducing its anisotropy.

In the second part of this thesis I describe a variational theory of multi-band two-dimensional electron gases that captures the interplay between electrostatic confining potentials, orbital-dependent interlayer electronic hopping and electron-electron interactions, and apply it to the d-band two-dimensional electron gases that form near perovskite oxide surfaces and heterojunctions. These multi-band two-dimensional electron gases are prone to the formation of Coulomb-interaction-driven orbitally-ordered nematic ground-states. I find that as the electron density is lowered and interaction effects strengthen, spontaneous orbital order occurs first, followed by spin order. I compare my results with known properties of single-component two-dimensional electron gas systems and comment on closely related physics in semiconductor quantum wells and van der Waals heterostructures.



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