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Nernst and Seebeck effects in a graphene nanoribbon

机译：石墨烯纳米带中的能斯特和塞贝克效应

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摘要

The thermoelectric power, including the Nernst and Seebeck effects, in graphene nanoribbon is studied. By using the nonequilibrium Green's function combining with the tight-binding Hamiltonian, the Nernst and Seebeck coefficients are obtained. Due to the electron-hole symmetry, the Nemst 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 nth (excluding n = 0) peak is [In 2/|n|] for the Nernst effect and is [In 2] for the Seebeck effect. For the zeroth peak, it is abnormal with height [2 In 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 extends to the whole energy region.
机译：研究了石墨烯纳米带中的热能功率，包括能斯特效应和塞贝克效应。通过将非平衡格林函数与紧束缚哈密顿量相结合，可以得到能斯特和塞贝克系数。由于电子空穴的对称性，与磁场无关，Nemst系数是费米能量的偶函数，而塞贝克系数是奇函数。在强磁场的存在下，能斯特和塞贝克系数几乎与纳米带的手性和宽度无关，当费米能量超过朗道能级时，它们会显示出峰值。对于能斯特效应，第n个峰的高度（不包括n = 0）为[In 2 / | n |]，对于塞贝克效应，其峰高为[In 2 / n]。对于第零个峰，对于能斯特效应，其高度为[2 In 2]是异常的，对于塞贝克效应，该峰将消失。但是，当磁场关闭时，不存在能斯特效应，仅存在塞贝克效应。在这种情况下，塞贝克系数在很大程度上取决于纳米带的手性。对于具有锯齿形边缘的纳米带，这些峰是等距的，但对于扶手椅形边缘，这些峰是不规则分布的。特别地，对于绝缘扶手椅带，在狄拉克点附近的塞贝克系数可能非常大。当磁场从零变化到较大值时，不同手性带的塞贝克系数之间的差异逐渐消失，能斯特系数的非零值首先出现在狄拉克点附近，然后逐渐扩展到整个能量区域。

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