Local-noise spectroscopy for nonequilibrium systems

We introduce the notion, and develop the theory of, local-noise spectroscopy (LNS)—a tool to study the properties of systems far from equilibrium by means of flux density correlations. As a test bed, we apply it to biased molecular junctions. This tool naturally extends those based on local fluxes, while providing complementary information on the system. As examples of the rich phenomenology that one can study with this approach, we show that LNS can be used to yield information on microscopic properties of bias-induced light emission in junctions, provide local resolution of intrasystem interactions, and employed as a nanothermometry tool. Although LNS may, at the moment, be difficult to realize experimentally, it can nonetheless be used as a powerful theoretical tool to infer a wide range of physical properties on a variety of systems of present interest.

Figure 1

Molecular junctions used to illustrate the local-noise spectroscopy: (a) parabenzenedithiol (PBDT), (a) metabenzenedithiol (MBDT), and (b) 2,11-dithi(3,3)paracyclophane molecular structures. The yellow circles represent the sulfur atoms that attach to two macroscopic electrodes.

Figure 2

Electroluminescence profile in a MBDT molecular junction [Fig. 1] at $V_{sd}=3$ V. The profile is plotted parallel to the molecule at 1.5 Å above the molecular plane. The horizontal axis ($X$) is the direction of tunneling in the junction. The localized surface plasmon-polariton vector is assumed to be directed along $X$. The light emission profiles are shown for the outgoing photons of frequencies (a) $\omega =2$ eV and (b) 3 eV.

Figure 3

Local noise cross-correlation $S({\vec{r}}_1,{\vec{r}}_2;\omega )=\sqrt{{\sum }_{i=\{x,y,z\}}{S}_{ii}^2({\vec{r}}_1,{\vec{r}}_2;\omega )}$ in a 2,11-dithi(3,3)paracylophane molecular junction [Fig. 1] at $V_{sd}=1$ V. The horizontal axis ($X$) is the direction of tunneling in the junction. The profile is plotted parallel to the molecular planes with $Z$ projections of ${\vec{r}}_1$ and ${\vec{r}}_2$ taken 1.5 Å on outer sides of molecular planes. We show (a) the cross-correlation map in the $XY$ plane at $\omega =3.5$ eV and (b) the cross-correlation at the points corresponding to positions of carbon atoms of the benzene rings vs frequency $\omega$.

Figure 4

Local noise thermometry in a PBDT molecular junction [Fig. 1] at a bias $V_{sd}=1$ V. The temperature distribution, Eq. (11), is plotted parallel to the molecule at 1.5 Å above the molecular plane. The horizontal axis ($X$) is the direction of tunneling in the junction. The temperature estimates are shown from a noninvasive probe oriented (a) perpendicular to the junction tunneling direction, (b) parallel to the junction tunneling direction and perpendicular to the molecular plane, (c) parallel to the molecular plane, and (d) perpendicular to the local current. The vertical (color) bar shows the temperature scale in K.