I am having trouble understanding what causes metallic behaviour in context of Nearly free electron model. Is it because
1) In 2d material with fermi level equation is $k_F=\frac{√2πz}{a}$. If for a certain valency the fermi level (circle) doesn't touch the Brillouin zone there is no band gap, thus electrons can move freely between bands.
2) Is it because in 2D material (for example) we can have two different reciprocal lattice length, thus two different band gaps depending on the direction. And if the second band starts at B below the top of the first band at A. Two electrons per primitive cell would fill exactly one band. But some states in the 2nd band at B lie lower in energy than some 1st band states at A. The fermi energy will straddle both first and second bands. We get partially full first and second bands.
Or is it a combination of this