Emergence of topological Mott insulators in proximity of quadratic band touching points

Recently, the field of strongly correlated electrons has begun an intense search for a correlation induced topological insulating phase. An example is the quadratic band touching point which arises in a checkerboard lattice at half-filling, and in the presence of interactions gives rise to topological Mott insulators. In this work, we perform a mean-field theory computation to show that such a system shows instability to topological insulating phases even away from half-filling (chemical potential $\mu = 0$). The interaction parameters consist of on-site repulsion ($U$), nearest-neighbour repulsion ($V$), and a next-nearest-neighbour correlated hopping ($t_\text{c}$). The $t_\text{c}$ interaction originates from strong Coulomb repulsion. By tuning the values of these parameters, we obtain a desired topological phase that spans the area around $(V = 0 , \mu = 0)$, extending to regions with $(V>0,\mu=0)$ and $(V>0,\mu>0)$. This extends the realm of current experimental efforts to find these topological phases.Comment: 10 pages, 5 figure

High-order harmonic generation with twisted electrons

We present analytically and numerically the spectrum of high harmonic emission generated by twisted electrons in the presence of linearly polarized light. Ensuing transitions from electronic continuum states with orbital angular momentum to bound states give rise to circularly polarized attosecond pulses. For central collisions with twisted wave packets, continuum-bound transitions are subject to dipole selection rules. For noncentral collisions, a crossover from circularly to linearly polarized emission occurs for increasing impact parameter due to the transverse topology of twisted wave packets