The thermal gradient can be turned on or off accordingly to the presence or not of the electrical current flux through the supporting tube. The function p ( t ) determines when the current would be on or off. We choose a square wave-like function to represent p ( t ) with the form with P being the period of p ( t ). The modulo function mod was used to provide the p ( t ) periodicity. The parameters β (= 10 ps − $^{1}$), t$_{1}$ = P/ 6, and t$_{2}$ = 4 t$_{1}$ characterize p ( t ). An example of p ( t ) is depicted in Fig. 2 (B) for P = 400 ps. where FIG. S1: F ( x ) (Eq. 2) for L = 100 nm, l = 5 nm, and F$_{vdW}$ = 1 . 92 nN (top) and dT/dx (Eq. 5) (bottom). p ( t ) = s (mod( t, P )) (7) s ( τ ) ≡ 1 [1 + exp[ − β ( τ − t$_{1}$ )]] [1 + exp[ − β ( − τ + t$_{2}$ )]] , (8) 12 -75 -50 -25 0 25 50 75 x (nm) -2 -1 0 1 2 F (nN) -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 x (nm) -10 -5 0 5 10 dT/dx (K/nm)