Signatures of Bloch-band geometry on excitons: non-hydrogenic spectra in transition metal dichalcogenides

The geometry of electronic bands in a solid can drastically alter single-particle charge and spin transport. We show here that collective optical excitations arising from Coulomb interactions also exhibit unique signatures of Berry curvature and quantum geometric tensor. A non-zero Berry curvature mixes and lifts the degeneracy of $l \neq 0$ states, leading to a time-reversal-symmetric analog of the orbital Zeeman effect. The quantum geometric tensor, on the other hand, leads to $l$-dependent shifts of exciton states that is analogous to the Lamb shift. Our results provide an explanation of the non-hydrogenic exciton spectrum recently calculated for transition metal dichalcogenides. Numerically, we find a Berry curvature induced splitting of $\sim 10$ meV between the $2p_x \pm i2p_y$ states of WSe$_2$.Comment: 5 pages, 2 figure

On the Production of Flux Vortices and Magnetic Monopoles in Phase Transitions

We examine the basic assumptions underlying a scenario due to Kibble that is widely used to estimate the production of topological defects. We argue that one of the crucial assumptions, namely the geodesic rule, although completely valid for global defects, becomes ill defined for the case of gauged defects. We address the issues involved in formulating a suitable geodesic rule for this case and argue that the dynamics plays an important role in the production of gauge defects.Comment: 9 pages, in LATEX, UMN-TH-1028/92, TPI-MINN-92/20-