Theoretical Study On Phonon Hydrodynamics In Two-dimensional Materials

The understanding of heat transport phenomenon has a long history,dating back to the first utilization of fire in human history.Heat conduction,convection,radiation are three main mechanisms of heat transfer.Fourier’s law is the most intuitive understanding of the thermal conductivity of materials.It tells us that the magnitude of the heat flux is proportional to the temperature gradient,but with opposite direction.The proportionality factor between the heat flux density and the temperature gradient is the thermal conductivity,an intrinsic property of the material.However,recent studies on heat transport in systems with micro-or nano-scale have found that new phenomena emerge for which the classical Fourier heat conduction law could be broken.These new phenomena are collectively referred to as non-Fourier heat conduction phenomena,which includes size-dependent thermal conductivity of low-dimensional materials,ballistic and hydrodynamic phonon transport,etc.These non-Fourier heat conduction phenomena also provide new possibilities for designing and fabricating novel phononic devices and optimizing the thermal transport properties of materials.Phonons in hydrodynamic regime exhibit collective macroscopic drift motion,which causes interesting hydrodynamic transport phenomena.The Poiseuille flow and the second sound of phonons are two typical representatives.Despite the interesting features of hydrodynamic phonon transport,the temperature range in which it is observed is so low and narrow for bulk materials that studies are scarce.These extremely stringent temperature conditions are caused by the dissipation of lattice momentum due to frequent scattering of phonons from impurities,defects,electrons,and other phonons.Hydrodynamic phonon transport can occur only if these scattering processes are much weaker than the momentum-conserving scattering among phonons.Recent studies on heat transport at micron/nanometer scale found that,unlike three-dimensional materials,two-dimensional materials may exhibit hydrodynamic transport behavior in a wider temperature range,and thus have received extensive attention.In this thesis,starting from the Peierls-Boltzmann phonon transport equation within the Callaway approximation and combining the unique phonon dispersion relation of two-dimensional materials,we study the hydrodynamic phonon transport in two-dimensional materials both theoretically and numerically.The main results of this thesis are as follows:(1)We have developed a unified theory describing the propagation of different types of second sound in two-dimensional materials.Previously studied drifting and driftless second sound are two limiting cases of the theory,corresponding to the drift and diffusive part of the energy flux,respectively.We find that out-of-plane acoustic phonons(ZA phonons)with ideal quadratic dispersion do not support drifting second sound in the thermodynamic limit,and severely reduce its group velocity for finite size sample.However,the driftless mode is less affected.This is understood as a result of infinite effective mass density of the flexural phonons.This is because phonons,as quasi-particles in solids,do not have particle number conservation.In the long wave length limit,the quadratic flexural phonons have a constant density of states,but their average occupation number is divergent.This is a common feature of bosonic quasi-particles with quadratic dispersion but without number conservation.Our results explain the physical mechanism of the divergent macroscopic physical quantities encountered when dealing with quadratic phonon dispersion in the traditional kinetic theory treatment of phonon hydrodynamics.Moreover,we obtain dispersion relations of the associated second sound from a set of linearized hydrodynamic equations.A clear transition from low frequency,slow drifting mode to high frequency,fast driftless mode is observed.Finally,we study the effect of tensile strain on the second sound velocity.The velocities of drifting and driftless mode increase with tensile strain due to the linearization of the flexural phonon dispersion.Our results clarify several puzzles encountered in previous theoretical work and lay a theoretical foundation for numerical and experimental study of second sound propagation in two-dimensional materials.(2)We have studied the heat current vortices in two-dimensional materials due to the viscosity of phonon gas.As a result of vortices formation in hydrodynamic phonon transport,there appears the spatial separation of temperature gradient and heat flow.Even negative non-local thermal resistance can be observed,which is characteristic feature of the viscous flow.Vortices are common in classical fluids but have not yet been considered in phonon transport before,as far as we know.Therefore,our results illustrate the universal transport behaviors in the hydrodynamic regime,independent of the type of quasi-particles and their microscopic interactions.Our study provides ideas for the experimental observation of hydrodynamic phonon transport in two-dimensional materials,which has remained illusive up to now.