Magnetothermoelectric Transport Properties Of Multi-terminal Graphene Nanoribbons

It is extremely important for thermoelectric effect in practical application that comes out the possibility of converting waste heat into electricity.Generally speaking,the measurement of the conductivity doesn’t include all physical properties of conductors.Comparing to electric conductance,the thermoelectric coefficients are more sensitive to the details of density of states(DOS),so the thermoelectric coefficients are more beneficial in understanding the particle-hole asymmetry and the ambipolar nature of graphene.Apart from the electric charge transport,the thermal transport has received more and more attention in recent years.There are two common thermoelectric power(TEPs),the Nernst effect which is the transverse TEP induced by a longitudinal thermal gradient in a perpendicular magnetic field and the Seebeck effect which is the thermalgradient-induced bias in a two-probe system.But in the early days,they were paid little attention to and even often neglected because of the experimental difficulties.In resent years,with the improvement of microfabrication technology and low-temperature measurement technology,the measurement on the thermoelectric properties becomes feasible.By now,the Nernst effect and seebeck effect has been extensively reported in experiment and theory.However,there are few reports on Peltier effect and Ettingshausen effect.In this paper,we study the Peltier effect in a two-terminal graphene nanoribbon and the Ettingshausen effect in a multi-terminal graphene nanoribbon.Peltier Effect describes the phenomena that the longitudinal electric field induces the longitudinal heat current in a two-probe system.Ettingshausen effect describes the phenomena that the longitudinal electric field induces the transverse heat current in the presence of magnetic field,which is the reciprocal effect of Nernst effect.With the aid of nonequilibrium Green’s function and Landauer-Büttiker formalism,the Peltier coefficient and Ettingshausen coefficient are obtained and make a copmparion with seebeck coeficient and nernst coefficient.Besides,we study the influence of various parameters on the Ettingshausen coefficient,including temperature,magnetic field,disorder,the width of nanoribbon.