Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions

Advances in the fabrication and characterization of nanoscale systems now allow for a better understanding of one of the most basic issues in science and technology: the flow of heat at the microscopic level. In this Colloquium recent advances are surveyed and an understanding of physical mechanisms of energy transport in nanostructures is presented, focusing mainly on molecular junctions and atomic wires. Basic issues are examined such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between heat current density and temperature gradient—known as Fourier’s law. Both theoretical and experimental progress are critically reported in each of these issues and future research opportunities in the field are discussed.

Figure 1

Schematic representation of the different systems we consider in this Colloquium, ranging from metallic point contacts to molecular junctions.

Figure 2

(a) A schematic representation for a simple setup to measure the thermal conductance. (b) An actual device to measure the thermal conductance of boron nitrade nanotubes. From 30.

Figure 3

Thermal conductance of a quasi-1D wire with surface roughness, exhibiting inhomogeneous thermal conductance. Points correspond to experimental data of 198, and the solid line is the theoretical curve. From 191.

Figure 4

Local temperature as a function of bias, calculated from a scattering theory approach, for a benzene-dithiol molecular junction (dashed line) and a gold-atom point contact (solid line). From 36.

Figure 5

A schematic representation of the mechanism of ionic heating in nanoscale junctions. The electric current dissipates a fraction $\alpha V^2/R$ of its power in the junction, depending on the strength of the electron-phonon interaction. This power is then dissipated to the phonons in the electrodes in the form of a heat current. The balance between the power flowing into the junction and the heat current $I_Q$ flowing out of the junction determines the ionic temperature of the junction.

Figure 6

Scanning thermal microscopy (SThM) of a 10 nm diameter multiwall carbon nanotube. (a) Full thermal image. (b) A cut along the nanotube. (c) A cut across the nanotube. From 25.

Figure 7

Effective temperature of a molecular junction, for three different types of molecules $n$-alkanedithiol, with $n=6$ (squares), $n=8$ (circles), and $n=10$ (triangles). The solid lines are theoretical estimates from Eq. (15). From 95.

Figure 8

Effective temperature of a molecular junction measured using Raman scattering. The different points correspond to different modes, and while the temperature is slightly different, the overall voltage dependence shows roughly similar features. Note also the apparent decrease in the local temperature with bias, which is in line with the results of 95. From 98.

Figure 9

Upper panel: Schematic representation of thermopower experiments on molecular junctions. (a)–(c) Distribution of thermovoltages obtained at different temperature gradients. Note the widening of the distributions and their nontrivial structure. (d) The most-probable thermovoltage obtained from (a)–(c) as a function of the temperature gradient. The derivative of the linear fit of this curve yields the thermopower $S$. (e) $S$ of various molecules, in terms of the molecule’s length. Adapted from 179.

Figure 10

Transmission (solid line) and normalized thermopower (dashed line) as a function of the position of the Fermi energy with respect to the HOMO-LUMO gap, based on the Landauer formula, Eq. (24), with approximation Eq. (25).

Figure 11

Upper panel: Schematic representation of the model molecular junction composed of two quasi-two-dimensional leads connected with a molecular wire. The leads are coupled to external heat baths, each at its own temperature. (a) Electron charge imbalance as a function of the ratio between the couplings $g_{R(L)}$ between the wire and the right (left) lead. A strong dependence can be observed and even a change of sign. (b) Distribution of charge imbalance, when the couplings between the wire and the leads are drawn from a Gaussian distribution, with an average $g=0.1$ and width $\Delta g=0.001$, 0.01, and 0.1 in units of the hopping parameter (see text). From 63.