Formation of Tropylium carbocation I've read that Tropylium carbocation is formed by the ring expansion of benzyl carbocation. But in benzyl carbocation, the $\ce{C}$ atoms in the benzene ring are $sp^2$ hybridized i.e. $120^\circ$  is the required angle for stability. And in the benzene ring of the benzyl carbocation, the angle is already 120 degrees. Therefore benzyl ring need not expand for stability. Therefore why does benzyl rearrange to give tropylium?
More stable products are lower in energy.  At first glance the bonding arrangements might seem equivalent in both cases in terms of number of $\ce{C-C}$ and $\ce{C-H}$ bonds from $\ce{sp^2}$ carbons, which would result in no net change.  However, the change in molecular structure leads to a change in the molecular orbitals and the resulting energies of the molecule for the aromatic/resonance component to the energy. Using the Frost diagram technique we want to compare the orbital energies, nicely pictured here:



The key point to notice is the filled orbitals for seven member ring are slightly lower in energy than the filled orbitals for the six-member ring.  This means there is an increase in resonance stabilization energy for making a fully aromatic system rather than just a cation in resonance with benzene ring.