# A Brief Review on the Recent Experimental Advances in Thermal Rectification at the Nanoscale
## 1 Introduction  
The same as the electrical current diode concept, thermal rectification is a phenomenon in which heat travels in one preferred direction with high thermal conductivity and in the opposite direction with low conductivity [1]. This concept has been known as the basis for thermal diodes and later thermal transistors and thermal logic circuits. A self-driven thermal computer is the final goal of this study [2]. On the other hand, thermal diodes or switches are the key components for solving complicated thermal management problems, especially as the size of the device decreases to nanometers [3]. Historically, the first experimental observation of thermal rectification was made by [PERSON] in 1936 [4]. After that, a number of studies were carried out for bulk thermal rectifiers and several theoretical models have been proposed to understand the mechanisms. A good review can be found in [5] on this topic. The involved physical mechanisms for thermal rectification include asymmetric roughness at the contact surface, a thermal potential barrier between material contacts, different temperature dependence of thermal conductivity and so on [5]. In recent years, the research focus of thermal rectification has been changed to nanomaterials along with the greatly increased interest in micro/nanoelectronic cooling and quantum thermal systems. Moreover, as the dimension scales down, new physical mechanisms need to be revealed to understand the thermal rectification at the nanoscale. On this subject, many molecular dynamics (MD) simulations and much theoretical work have been published in the past decade. Some normallyaccepted mechanisms are addressed here. The first one is the overlap between the phonon spectra of two connecting materials or asymmetric nanostructures [6; 7]. The phonon spectra overlap can be used to explain the thermal rectification across the interface between two dissimilar materials. The calculation of vibrational density of states (vDOS) indicates that the phonon spectra overlap varies by switching the direction of the temperature gradient. For nano-devices, the local phonon spectra depend on both the temperature and size of the material. Different phonon spectra overlaps may exist for a single-material device by changing the heat flux direction [8]. The second one is the dependence of thermal conductivity on temperature and space, which is also one of the mechanisms to explain the thermal rectification in bulk materials. However, the origin of this asymmetric dependence of thermal conductivity is different between bulks and nanomaterials. For the bulk device with two dissimilar materials connecting at an interface, it is necessary to have different temperature-dependent thermal conductivities in each segment to result in thermal rectification, i.e., thermal conductivity in material A increases with increasing temperature while the thermal conductivity in material B has the opposite trend [5]. For the nanomaterials, thermal conductivity is no longer a single-valued function of temperature. It depends on many factors, such as width, defect, surface roughness, etc. [9; 10; 11; 12; 13]. For the nanomaterial with asymmetric geometric size or defects, the thermal conductivity is also a space-dependent function. In this case, thermal rectification occurs in a single nanomaterial by switching the direction of the temperature gradient. The third one is the local phonon edge scattering effect. For the nanomaterials, the mean free path of phonons could be comparable with the lateral size of the sample. Therefore, the phonon edge scattering becomes an important factor for the thermal conductivity. In an asymmetric nanomaterial with one narrow end and one wide end, the narrow end imposes a stronger edge scattering effect on the propagating phonon modes and this lateral confinement on phonons is temperature dependent due to the different phonon energy level. As a result, the thermal rectification will be triggered [14].