Asymmetry induces long-lasting energy current transients inside molecular loop circuits

Energy transport and conversion at nanoscale have become an important topic of fundamental and applied research, in particular for conceiving ground-breaking solutions in energy-aware digital electronics and energy production. In this work, we propose a formal framework to address time-dependent energy transport inside quantum networks. The approach permits us to investigate how energy transferred to electrons by a femtosecond laser pulse is stored and released in a molecular circuit consisting of two donor-acceptor branches connected to an acceptor chain. Additionally, the two donors may be coupled, creating a loop inside the circuit. Time-resolved analysis reveals that when a difference exists between the two donor-acceptor branches, a loop current occurs and persists during relaxation, while only a small amount of current flows through the acceptor chain. A long-lasting energy flow thus emerges from the asymmetry of the molecular structure.

Figure 1

Schematic network and parameter definitions.

Figure 2

(a) Molecular network. (b) Schematic molecular loop and fork circuits. (c) Level structure of the molecular network made of two donors and three acceptors in series. The two donors interact simultaneously with a resonant femtosecond laser pulse of boxcar shape. The molecular network is in contact with two wide-band electron reservoirs.

Figure 3

Direct energy current (in arbitrary units) flowing between sites $D_1, D_2, A$, and $B$ for the loop (solid lines) and the fork (dashed lines) circuits, as a function of $D_2-A$ coupling.

Figure 4

Time-resolved energy currents $J_{D_{1}A}$ and $J_{D_{2}A}$ in the driven and relaxation regimes for four different $D_2-A$ coupling values, ${\beta }_{D_2-A}=0.042$ (purple), 0.060 (sky blue), 0.000 (yellow, fork circuit), and 0.050 eV (red, symmetric loop circuit). For convenience, the results have been divided into several graphs with different scales of time and energy current. Left and right panels represent the short and long time responses, respectively. The two insets show a smaller but nonzero energy current $J_{D_{2}A}$ for ${\beta }_{D_2-A}$ equal to zero, which is discussed in the text.

Figure 5

Schematic representation of the different terms inside the energy current flowing from $D_2$ to $A$ [see Eq. (4)].