The Thermoelectric Properties in Graphene and Graphene Nanoribbons

Thermodefect voltage in graphene nanoribbon junctions

“…For even larger chemical potentials, μ 2 > 0.7 eV, the thermodefect voltage drops substantially for all the three types of longitudinal vacancies and show damped oscillations around zero i.e., both positive and negative voltages are possible for high chemical potentials. These oscillations are associated with the degeneracy effects originated from the Fermi gas properties [11,85,86]. We note here that very high values of the chemical potential, such as >1 eV, are difficult to utilize in practice [37] and values larger than 2.5 eV even falls outside the validity of the tight-binding model [68].…”

“…In the linear regime the net current through a GNR attached to two reservoirs characterized by a temperature and chemical potential difference is given by [11]…”

“…To examine the Seebeck coefficients, as well as other thermoelectric transport coefficients, we employ the Landauer formalism within the linear response regime. This formalism is described in terms of the transport integrals which read [11,74] (5) with α being the energy moment index, ε the energy, T (ε) the transmission function, and…”

“…research [1]. Following the footsteps of the pioneering works by Hicks and Dresselhaus [2,3], subsequent efforts have established that quantum confinement can also be used to enhance the thermoelectric properties [4][5][6][7][8][9][10][11][12][13][14][15]. The contributions of nanoscale effects can be isolated and analyzed quite easily when all the components of the junctions are made of only a single material, having the same dominant charge carriers but different size or shape.…”

“…Since then various single-material unipolar thermoelectric junctions formed by the combination of nanomacro [18][19][20][21][22][23] or nano-micro components have been studied [24][25][26][27][28], considering both classical and quantum size effects [16,17,[29][30][31][32][33]. In particular, thermoelectric properties of quantum wells and nanowires using graphene-based materials have become a hot topic in material science in recent years [11,13,15,16,[34][35][36][37][38][39][40][41][42][43]. In these, as well as other nano-scale systems, thermoelectric devices are made by connecting many single junctions to each other such that small nano-scale effects of many single junctions are added up to generate a usable macroscopic voltage.…”