Optimal Features of a Quantum Flashing Electron Ratchet

Bryan T.G. Lau, Department of Chemistry, Northwestern University, Evanston, United States
Igal G. Szleifer, Department of Biomedical Engineering, Northwestern University, Evanston, United States
Mark A. Ratner, Department of Chemistry, Northwestern University, Evanston, United States
Emily A. Weiss, Department of Chemistry, Northwestern University, Evanston, United States

Directional transport of electrons through organic or nanostructured inorganic materials is hindered by many scattering and energy loss mechanisms that randomize this motion. The performance of low-to-zero bias photovoltaic, sensing, and logic devices based on these materials is therefore often limited by charge collection at electrodes. Biology has encountered an analogous problem as the system and environment have similar length scales, and any motion of molecules or proteins is quickly randomized by interaction with their surroundings^[1]. An evolved solution to moving in an overdamped environment is a ratchet. A “flashing ratchet”^[2] variant works by switching between two states of a potential surface within which the particle travels: (i) a surface that causes net asymmetric spatial movement of an ensemble of particles, and (ii) a surface that allows random, isotropic diffusion of the particles, Figure 1. We explore, via a genetic algorithm, an ab-initio quantum model of an electron ratchet for the shape and oscillation frequency of a potential that maximizes current. The optimal potential height when the ratchet is fully on is between 1 and 4.5 times the mean kinetic energy of the electron. This ratio causes the electron to move classically in the ratchet potential, and the time where tunneling is significant is under 1% of a characteristic electron drift time. We find that increasing the density of asymmetric features increases the ratchet current. The optimal frequency is very slow with respect to the characteristic electron drift time, i.e. an optimal inertial ratchet is adiabatic.

Figure 1. A periodic ratchet potential in its ON and OFF states, with a hypothetical (classical or quantum) particle distribution (red).

[1]          R. D. Astumian, Phys. Chem. Chem. Phys. 2007, 9, 5067.

[2]          P. Reimann, Phys. Rep. 2002, 361, 257.