# A Brief Review on the Recent Experimental Advances in Thermal Rectification at the Nanoscale
## 2 Experimental Study
### Thermal Rectification in Suspended Monolayer Graphene  
Previous work has introduced a macroscopic thermal rectifier based on graphene oxide [31]. However, progress at nanoscales is still a blank. [PERSON] et al. fabricated and measured different kinds of two-dimensional thermal rectifiers in suspended monolayer graphene [14]. This work is motivated by the rapidly increasing attention of achieving a high thermal rectification ratio in graphene materials. To date, many molecular dynamics simulations have been carried out in different asymmetric graphene structures and confirmed the significant thermal rectification effect [8; 32; 33; 34; 35; 36]. In this work, three types of graphene thermal rectifiers were designed by drilling nanopores, depositing nanoparticles at one side, or cutting graphene into a trapezoid shape. The largest rectification coefficient was measured up to 26%. Figure 5 shows the suspended graphene with asymmetric nanopores. Large-area monolayer graphene was prepared by a method previously proposed for graphene fabrication [37; 38]. Samples 1, 2, and 3 in Figure 5 were asymmetry-modified using a focused ion beam (FIB) method. At one side of graphene, 14 nanopores with a diameter of 100 nm, 6 nanopores with a diameter of 200 nm, and 3 nanopores with a diameter of 400 nm were drilled. In order to measure the direction-dependent thermal conductivity precisely, a H-type sensor method was used. The advantage of the H-type sensor method is that it is easy to change the heat flow direction by simply changing the electrical heating power of two sensors. The nano-film sensor can guarantee the high precision of thermal measurement on monolayer graphene [39]. Measurements of pristine graphene without nano-processing showed no rectification effect. The difference between the thermal conductivities of the same graphene sample in two heat flow directions was less than 2%, as shown in Figure 6. For the graphene with asymmetric nanopores, the thermal conductivity of the sample is larger in the heat flow direction from the perforated region to the unperforated region. The measured thermal rectification factor was up to 26%. The cause of this phenomenon is the asymmetric temperature/space dependence of the thermal conductivity of graphene. The thermal conductivity of pristine graphene in the unperforated region decreases as the temperature increases, while the thermal conductivity of graphene in the perforated region is almost independent of temperature due to the significantly enhanced phonon-defect scattering. It is worth mentioning that this asymmetric thermal conductivity is dominated by phonon transfer, while  
Figure 5: SEM images of graphene Samples 1, 2, and 3 before and after nanopores drilled by using a focused ion beam. Reprinted with permission from Springer Nature Publishing Group. the electron contribution is symmetrical here [40]. The average thermal conductivity of perforated graphene is only 10-20% of that of pristine graphene. Meanwhile, the thermal rectification coefficient was calculated by using a series of thermal resistance models, giving a value of 28%, which was consistent with the experimental results. In addition, [PERSON] et al. has demonstrated a thermal diode consisting of an array of differently shaped holes milled into silicon membrane under the same mechanism [41]. Sample 4 in Figure 7 is the suspended graphene with 10 amorphous carbon nanoparticles deposited at one side by using the electron beam-induced deposition (EBID) method. The diameter of nanoparticles is about 200 nm. Sample 5 in Figure 7 is the suspended graphene cut into a trapezoid shape. The asymmetric structure of the graphene sample causes a thermal rectification effect. The thermal conductivities of Samples 4 and 5 were measured by using the H-type sensor method. It was found that the thermal conductivity of Sample 4 is larger in the heat flow direction from the smooth region to the deposition region, and the measured thermal rectification coefficient is 10%.