Nernst and Seebeck effects in a graphene nanoribbon

Abstract

The thermoelectric power, including the Nernst and Seebeck effects, in graphene nanoribbon is studied. By using the non-equilibrium Green function combining with the tight-binding Hamiltonian, the Nernst and Seebeck coefficients are obtained. Due to the electron-hole symmetry, the Nernst coefficient is an even function of the Fermi energy while the Seebeck coefficient is an odd function regardless of the magnetic field. In the presence of a strong magnetic field, the Nernst and Seebeck coefficients are almost independent of the chirality and width of the nanoribbon, and they show peaks when the Fermi energy crosses the Landau levels. The height of n-th (excluding n = 0) peak is [ln 2/|n|] for the Nernst effect and is ln 2/n for the Seebeck effect. For the zeroth peak, it is abnormal with height [2 ln 2] for the Nernst effect and the peak disappears for the Seebeck effect. When the magnetic field is turned off, however, the Nernst effect is absent and only Seebeck effect exists. In this case, the Seebeck coefficient strongly depends on the chirality of the nanoribbon. The peaks are equidistant for the nanoribbons with zigzag edge but are irregularly distributed for the armchair edge. In particular, for the insulating armchair ribbon, the Seebeck coefficient can be very large near the Dirac point. When the magnetic field varies from zero to large values, the differences among the Seebeck coefficients for different chiral ribbons gradually vanish and the nonzero value of Nernst coefficient appears first near the Dirac point then gradually extents to the whole energy region.

A review of carrier thermoelectric-transport theory in organic semiconductors

“…For this favorable technology, the most intrinsic parameter is the Seebeck effect which plays an indispensable role in converting temperature differences directly into electrical voltages [7][8][9]. Although the thermoelectric Seebeck effect was firstly discovered by Thomas Johann Seebeck in 1821 [10], the basic principle for harvesting electricity from a temperature gradient was utilized and developed as the contemporary technology in inorganic semiconductors until the late 1950's [11,12].…”

Enhanced thermoelectric properties in hybrid graphene/boron nitride nanoribbons

“…[10][11][12][13][14][15][16][17][18] Because of the quantum confinement effect, graphene and h-BN exhibit very high electrical conductance and Seebeck coefficient. [19][20][21] However, both pristine graphene and pristine h-BN are poor thermoelectric materials because their thermal conductance is also very high. [22][23][24][25] Recently, a novel nanomaterial compounded of graphene and h-BN has been synthesized by the thermal catalytic chemical vapor deposition method.…”

Thermoelectric Power in Graphene

“…As shown in section 3.3.3, with regard to the diffusion TEP, the geometry and edge roughness can greatly influence the TE properties of GNRs [7,65,[88][89][90]109]. A dramatic reduction in phonon transport in ZGNR [7] indicates small value for Λ.…”

“…Divari and Kliros [87] have studied TEP of ballistic wide graphene ribbons with aspect ratio (W/L ≥ 3) using linear response theory and the Landauer formalism. Xing et al [88] have studied TEP of GNRs in zero and non-zero magnetic field using non-equilibrium Green's function technique and shown that TEP depends on the chirality of the GNR. The TE properties have also been investigated by solving the electron and phonon transport equations in the nonequilibrium Green's function formalism [7,[89][90][91].…”