Are better conductors more rigid?

The variation of the bending stiffness of various materials is studied from the point of view of the electronic band characteristics. As far as the electronically generated bending stiffness κ_e (which we refer to as electro-stiffness) is concerned, the relevant factors are the orbital overlap t, the gap width u between the valence band and the conduction band, and the electron filling fraction γ. A perturbative calculation leads to the approximate expression κ_e ∼ t²/√ u ² + t². This shows that materials with a large overlap and narrow band gap should be stiffer. The electro-stiffness also depends on the electron filling-fraction. We find that κ_e(γ) ≤ κ_e(1/2). These kinds of behavior are confirmed by numerical calculations. In addition, we study the variation in the projected length of flexible molecules under a voltage bias. The nonlinear variation of the bending rigidity is shown to give rise to a length contraction or dilation, depending on the voltage bias.