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Anomalous transport near the Lifshitz transition at the LaAlO$_3$/SrTiO$_3$ interface

The two-dimensional electron liquid, at the (001) interface between band insulators {L}a{A}l{O}$_3$ and {S}r{T}i{O}$_3$, undergoes Lifshitz transition as the interface is doped with carriers. At a critical carrier density, two new orbitals populate at the Fermi level, with a concomitant change in the Fermi surface topology. Using dynamical mean-field theory, formulated within a realistic three-orbital model, we study the influence of the Lifshitz transition and local electron correlations on the transport properties. We look at the thermal conductivity, optical conductivity, Seebeck coefficient and angle resolved photoemission spectra and find that at a critical density, both the thermal and dc conductivities rise sharply to higher values while the Seebeck coefficient shows a cusp. The inter-orbital electron-electron interaction transfers spectral weight near the $Γ$ point towards lower energy, thereby reducing the critical density. In the presence of external magnetic field, the critical density further reduces due to exchange splitting. Beyond a sufficiently large field, multiple cusps appear in the Seebeck coefficient revealing multiple Lifshitz transitions.