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Causal Green’s Function for Modeling of Phonon Transport: Application to New Two-Dimensional Materials for Thermal Management and Energy Applications


Material Measurement Laboratory, Applied Chemicals and Materials Division

RO# Location
50.64.72.B8160 Boulder, CO

Please note: This Agency only participates in the February and August reviews.


Name E-mail Phone
Tewary, Vinod K. 303.497.5753


Efficient thermoelectric devices and thermal management systems consist of complex nanostructures. Thermal properties of materials are largely determined by low-frequency phonons and their interactions, and phonon confinement effects. Therefore, it is important to understand phonon propagation in nanomaterial systems at multiple length and temporal scales for which we need a robust mathematical model.

Modeling low frequency phonons requires an accurate knowledge of the temporal behavior of a many-body system over an extended time range (up to nano or even microseconds). Modeling atomistic processes over such an extended time range is a formidable task for conventional molecular dynamics. We have developed a mathematical technique for simulation of phonon transport in nanomaterials based on the use of causal Green’s functions (CGF). This technique, which may be a breakthrough in the field of atomistic modeling, seems to be ideally suited for modeling of low frequency phonons and thermal processes in nanomaterials. In this technique, we expand the Hamiltonian or the potential energy up to second order terms in atomic displacements. The power of the CGF technique arises from the fact that the corresponding temporal equations can be solved exactly even for quadratic terms. This is in contrast to the conventional molecular dynamics based in which only the first order terms. This improves the convergence of our technique by several orders of magnitude. Further, the technique is especially suitable for representing phonons because it is the second order terms that define the phononic characteristics of the system. This model can be extended to include electromagnetic effects such as plasmon phonon coupling that may be important for electronic nanomaterials.

We propose to apply the CGF technique for multiscale modeling of thermal processes in the new two-dimensional materials such as silicene, germanene, molybdenum disulphide, and graphene with antidots and other discontinuities. All these materials are of strong topical interest because of their potential application to the design of efficient thermal management and energy conversion devices.


Causal Green’s function; Graphene; Molybdenum Disulphide; Multiscale modeling; Nanomaterials; Phonons; Silicene and germanene; Thermal management and energy conversion; Two-dimensional materials;


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Level:  Open to Postdoctoral applicants
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