  Haldane model is a celebrated tight binding toy model in a 2D honeycomb
lattice that exhibits quantized Hall conductance in the absence of an external
magnetic field. In our work, we deform the bands of the Haldane model smoothly
by varying one of its three nearest neighbour hopping amplitudes ($t_1$), while
keeping the other two ($t$) fixed. This breaks the $C_3$ symmetry of the
Hamiltonian, while the $M_x*T$ symmetry is preserved. The symmetry breaking
causes the Dirac cones to shift from the K and the K' points in the Brillouin
zone (BZ) to an intermediate M point. This is evident from the Berry curvature
plots which show a similar shift in the corresponding values as a function of
$\frac{t_1}{t}$. We observe two different topological phases, one being a
topological insulator (TI) phase and the other is a higher order topological
insulator (HOTI). The Chern number ($C$) remains perfectly quantized at a value
of $C=1$ for the TI phase and goes to zero in the HOTI phase. Furthermore the
evolution of the Wannier charge center (WCC) as the band is deformed shows a
jump in the TI phase indicating a non-trivial bulk. We also study the HOTI
phase and diagonalize the real space Hamiltonian on a rhombic supercell to show
the presence of in-gap zero energy corner modes. The polarization of the
system, namely $p_x$ and $p_y$, are evaluated, along the $x$ and the $y$
directions respectively. We see that both $p_x$ and $p_y$ are quantized in the
HOTI phase owing to the presence of the inversion symmetry of the system.
