*2.1.3 Disconnection mechanism*

The disconnection mechanism means that resistance change is caused by disconnection process between adjacent nanoflakes. It consists of three situations under different strains or pressures, which are contact area change, tunneling effect, and crack propagation.

When the applied strain or pressure is small, contact area changes between adjacent nanoflakes dominants. The electrons mainly pass through overlapped nanoflakes within the percolation conductive network. When the applied strain or pressure increases and fully pull some adjacent nanoflakes apart, the electrons still can pass through them because the distance between them is small enough. This phenomenon is called tunneling effect, and the distance is called tunneling distance. The tunneling resistance between two adjacent nanoflakes can be approximately estimated by Simmons's theory [14]:

$$R\_{\text{tumel}} = \frac{h^2 d}{A e^2 \sqrt{2m\lambda}} \exp\left(\frac{4\pi d}{h} \sqrt{2m\lambda}\right) \tag{2}$$

where A, e, h, d, m, λ represent the cross-sectional area of the tunneling junction, single electron charge, Plank's constant, the distance between adjacent nanoflakes, the mass of electron and the height of energy barrier for insulators, respectively. It can be found that the distance between adjacent nanoflakes dominates the tunneling resistance. When there is no electron pass through by tunneling, the distance is defined as cut-off tunneling distance. The cut-off distance is usually several nanometers. When the applied strain or pressure is large enough, crack is formed, leading to rapidly increasing of resistance. Strain or pressure leads opening and enlargement of cracks, critically limiting the electrical conduction due to the separation of several crack edges.
