Strong Zeeman effects in the Landau level spectrum of (In$_{\mathrm{x}}$Bi$_{\mathrm{1-x}})_{\mathrm{2}}$Se$_{\mathrm{3}}$

We investigate the surface states of (In$_{\mathrm{x}}$Bi$_{\mathrm{1-x}})_{\mathrm{2}}$Se$_{\mathrm{3\thinspace }}$by scanning tunneling spectroscopy (STS) in the range 0 $\le $ x ~3{\%}. We carefully examine the low-lying Landau levels of the topological surface states in attempt to extract the parameters of the surface-state Hamiltonian as a function of doping. Close examination of the data oblige us to index the Landau levels in a manner different to precedent on pristine Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$, and fits to the Landau level spectra yield large g-factors on the order of 40, which decrease with increasing x. The Landau levels of pristine Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ are also reexamined, yielding high g-factors roughly consistent with results obtained from magnetic oscillations, and suggesting a decrease in the surface-state Zeeman coupling with increasing In as the topological phase transition is approached.