Graphene bond-dimerization model
--------------------------------
Assumption: one nearest-neighbor bond inside each unit cell is strengthened from t to t + delta_t,
while the other two nearest-neighbor bonds remain equal to t.

t = 1.000000
delta_t = 0.300000
strong dimer bond = 1.300000

Primitive reciprocal vectors:
b1 = (3.627599, 2.094395)
b2 = (-3.627599, 2.094395)

Hamiltonian:
H(k) = [[0, -g(k)],
        [-g*(k), 0]]

g(k) = (t + delta_t) exp(i k.d1) + t exp(i k.d2) + t exp(i k.d3)
Band energies: E_pm(k) = pm |g(k)|

Gap conclusion:
This minimal bond-dimerization does not open a gap for the current parameters.
The Dirac points shift in k-space and the cone becomes anisotropic.
For positive hoppings, a true gap appears only when t + delta_t > 2 t,
which is equivalent to delta_t > t.
In that regime, Eg = 2 * (delta_t - t).

Numerical minimum gap from the reciprocal-space grid = 0.049924
Analytical gap formula value = 0.000000