Laserlike Vibrational Instability in Rectifying Molecular Conductors

We study the damping of molecular vibrations due to electron-hole pair excitations in donor-acceptor (D-A) type molecular rectifiers. At finite voltage additional nonequilibrium electron-hole pair excitations involving both electrodes become possible, and contribute to the stimulated emission and absorption of phonons. We point out a generic mechanism for D-A molecules, where the stimulated emission can dominate beyond a certain voltage due to the inverted position of the D and A quantum resonances. This leads to current-driven amplification (negative damping) of the phonons similar to laser action. We investigate the effect in realistic molecular rectifier structures using first-principles calculations.

Figure 1

(a) Simple two-level model for the donor-acceptor (DA) system. (b)–(d) D- and A-DOS and filling (gray) at $T=0$. The D (A) levels follow the chemical potential ${\mu }_L({\mu }_R)$ of the closest $L(R)$ electrode. (b) For zero voltage $eV\equiv {\mu }_L-{\mu }_R=0$ only absorption processes around ${\mu }_L={\mu }_R\equiv {\mu }_0$ are possible. Similar excitations from the right electrode are not shown. (c) Absorption dominates for a voltage where ${\epsilon }_{\mathrm{A}}-{\epsilon }_{\mathrm{D}}\approx \hslash \Omega$ and ${\gamma }^{\mathrm{eh}}$ is maximal. (d) Population inversion for larger voltage when ${\epsilon }_{\mathrm{D}}-{\epsilon }_{\mathrm{A}}\approx \hslash \Omega$: emission dominates and ${\gamma }^{\mathrm{eh}}<0$. (e) Contours of ${\gamma }^{\mathrm{eh}}(V)$ for varying $t$ (dark is negative), ${\epsilon }_0=0.35\mathrm{eV}$, ${\Gamma }_1=0.3\mathrm{eV}$, ${\Gamma }_2=0.1\mathrm{eV}$, $m=0.005\mathrm{eV}$, $\hslash \Omega =20\mathrm{meV}$, ${\mu }_0=-0.2\mathrm{eV}$. (f) ${\gamma }^{\mathrm{eh}}(V)$ for $t=0.05\mathrm{eV}$ showing the generic behavior (maximum followed by negative values).

Figure 2

(a) Molecular STM junction: S atom adsorbed on the left adatom (”tip”), the right (”sample”) adatom has adsorbed an ${\mathrm{NH}}_2$ molecule. (b) Positions of the D ($3p_x$, $3p_y$ of S) and A levels ($2p_z$ of N) as a function of bias. The dashed lines indicate ${\mu }_L$, ${\mu }_R$. Inset: Left and right DOS for 1 V bias. (c) Electron-hole damping (${\gamma }^{\mathrm{eh}}$) as a function of bias for unstable phonon modes (inset) showing ${\gamma }^{\mathrm{eh}}<0$ at high bias.

Figure 3

(a),(b) The A (LUMO) and D (HOMO) states at 0.3 V (${\mu }_L=0.15\mathrm{V}$, ${\mu }_R=-0.15\mathrm{V}$ shown as vertical lines). (c) The position of D and A levels (DOS peaks) as a function of bias. (d) The ${\mathrm{A}}_L$, ${\mathrm{A}}_R$ at 0.3 V. The dashed lines include only contribution from the single D or A orbitals, while the solid lines include all contributions.

Figure 4

Correlation between the interelectrode damping rate ${\gamma }_{LR}^{\mathrm{eh}}$ (including only $LR$ terms in $\mathcal{A}$, $\mathcal{B}$), and phonon-coupling matrix element between the D and A states. Each dot represents one phonon mode. The larger dot has smaller mode frequency, and the darker one has smaller ${\gamma }_{LL}^{\mathrm{eh}}+{\gamma }_{RR}^{\mathrm{eh}}$. Modes displaying ${\gamma }^{\mathrm{eh}}<0$ for $V<0.4\mathrm{V}$ are marked with cross line or frequency. Insets: The 63 meV mode, and bias dependence of its damping rate.