Colloquium: Phononic thermal properties of two-dimensional materials

Following the emergence of many novel two-dimensional (2D) materials beyond graphene, interest has grown in exploring implications for fundamental physics and practical applications ranging from electronics, photonics, and phononics to thermal management and energy storage. In this Colloquium, a summary and comparison are given of the phonon properties, such as phonon dispersion and relaxation time, of pristine 2D materials with single-layer graphene to understand the role of crystal structure and dimension on thermal conductivity. A comparison is made of the phonon properties, contrasting idealized 2D crystals, realistic 2D crystals, and 3D crystals, and synthesizing this to develop a physical picture of how the sample size of 2D materials affects their thermal conductivity. The effects of geometry such as the number of layers and the nanoribbon width, together with the presence of defects, mechanical strain, and substrate interactions on the thermal properties of 2D materials are discussed. Intercalation affects both the group velocities and phonon relaxation times of layered crystals and thus tunes the thermal conductivity along both the through-plane and basal-plane directions. This Colloquium concludes with a discussion of the challenges in theoretical and experimental studies of thermal transport in 2D materials. The rich and special phonon physics in 2D materials make them promising candidates for exploring novel phenomena such as topological phonon effects and applications such as phononic quantum devices.

Figure 1

Thermal conductivities of some typical single-layer 2D materials. (a) Graphene; (b) boron nitride, silicene, stanene, and blue phosphorene, which are of hexagonal crystal structures; (c) a few transition metal dichalcogenides; and (d) a few 2D crystals with puckered structures. The lines in (d) refer the thermal conductivity along the zigzag direction, while the lines with marks are along the armchair direction.

Figure 2

Comparison of thermal conductivities of some 2D materials calculated from the Slack equation ($x$ axis) and from the first-principles-based PBTE ($y$ axis).

Figure 3

Thermal conductivity of some typical single-layer 2D materials at room temperature. The data are sorted by descending thermal conductivity values. Inset: The atomic structures of boron nitride, silicene, ${\mathrm{MoS}}_2$, and ${\mathrm{ZrS}}_2$ as examples of 2D materials with different crystal structures.

Figure 4

(a) Scanning electron microscopy image of the microbridge measurement device, which consists of two $\mathrm{Pt}/{\mathrm{SiN}}_x$ membranes. The red and blue Pt coils are the heater and temperature sensors, which are thermally connected by suspended graphene (the gray sheet in the middle). Scale bar: 5 mm. (b) ${\mathrm{SiN}}_x$ membrane-based heater structures optimized for length-dependent studies. Scale bar: 20 mm. From [257]. (c) Thermal conductivity of graphene as a function of sample size. (d) Thermal conductivity of some 2D materials as a function of the sample size.

Figure 5

(a) Schematic representation of phonon annihilation processes using the phonon dispersion curves of single-layer graphene as an example. Solid red arrows: the annihilation of a phonon mode generating a third phonon on the same branch as the second one; dashed blue arrows: the annihilation of a phonon mode generating a third phonon on a different branch from the second one. (b) Phonon decay processes. The solid circles are the phonon modes taking part in the scatterings. The solid circles pointed by arrows are the final states after scattering, while others are the initial states before scattering.

Figure 6

Scattering rates for the ZA phonon modes along the $\mathrm{\Gamma }\text{−}K$ direction in (a) unstrained graphene and (b) graphene under 0.5% tensile strain at 300 K. Inset: Contributions to the total rates $\mathrm{ZA}+\mathrm{ZA}\to \mathrm{TA}$ (LA) (open circles) and $\mathrm{ZA}+\mathrm{ZO}\to \mathrm{LA}$ (TA) or $\mathrm{ZA}+\mathrm{LA}(\mathrm{TA})\to \mathrm{ZO}$ (solid circles). Adapted from [12].

Figure 7

Thickness-dependent thermal conductivity of (a) graphene, (b) ${\mathrm{MoS}}_2$, (c) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and (d) black phosphorus. The data in (d) come from (1)  [118], (2)  [150], (3)  [91], (4)  [287], (5) [219], (6) [288], (7) [90], and (8) [197]. The layer coordinates for some data in (a) and (d) have been offset slightly for clarity.

Figure 8

(a) Thermal conductivity of some 2D materials as a function of tensile strain. (b) Phonon dispersion of silicene under different tensile strain. From [254].

Figure 9

(a) Measured thermal conductivity of supported graphene (on ${\mathrm{SiO}}_2$) together with the highest reported values of pyrolytic graphite (PG). G1, G2, and G3 refer to the three graphene samples. From [209]. (b) Measured room-temperature thermal conductivity of supported graphene (on ${\mathrm{SiN}}_x$) as a function of the number of atomic layers (red star) with the best-fit curve (red line). Inset: Temperature dependence of thermal conductivity around 300 K. From [237].

Figure 10

Thermal conductivity of supported or encased few-layer graphene at room temperature as a function of sample thickness.

Figure 11

(a) Basal-plane thermal conductivity and (b) thermal conductivity along the $c$ axis as a function of lithium composition. The experimental data are taken from [208]. (c), (d) Comparison of phonon dispersion in the basal plane of pristine graphite and ${\mathrm{LiC}}_6$. (e), (f) Comparison of phonon dispersion along the $c$ axis of pristine graphite and ${\mathrm{LiC}}_6$. Adapted from [193].

Figure 12

(a) High angle annular dark field scanning transmission electron microscopy image of ${\mathrm{TiS}}_2[{(\mathrm{HA})}_x{({\mathrm{H}}_2\mathrm{O})}_y{(\mathrm{DMSO})}_z]$ along with the schematic atomic structure. (b) Measured in-plane thermal conductivity. Adapted from [229].