Reversal of Thermoelectric Current in Tubular Nanowires

Abstract

We calculate the charge current generated by a temperature bias between the two ends of a tubular nanowire. We show that in the presence of a transversal magnetic field the current can change sign, i.e., electrons can either flow from the hot to the cold reservoir, or in the opposite direction, when the temperature bias increases. This behavior occurs when the magnetic field is sufficiently strong, such that Landau and snaking states are created, and the energy dispersion is nonmonotonic with respect to the longitudinal wave vector. The sign reversal can survive in the presence of impurities. We predict this result for core/shell nanowires, for uniform nanowires with surface states due to the Fermi level pinning, and for topological insulator nanowires. PACS numbers: 73.23.b, 73.50.Lw, 73.63.Nm, 73.50.Fqi A temperature gradient across a conducing material induces an energy gradient, which in turn results in particle transport. In an open circuit, where no net current flows, a voltage is then generated when two ends of a sample are maintained at different temperatures -this is the Seebeck effect and the linear voltage response is known as thermopower. The hotter particles have larger average kinetic energy, and the net particle flow is therefore generally from the hot to the cold side. The thermopower and thermoelectric current can be positive or negative, depending on the type of charge carriers, i.e., electrons or holes.In comparison to this macroscopic case, the thermopower at the nanoscale has special characteristics. For example, if the energy separation between the quantum states of the system is larger than the thermal energy the thermopower may alternate between positive and negative values, depending on the position of the Fermi level relatively to a resonant energy, which can be controlled with a gate voltage. These oscillations were predicted a long time ago [1], and subsequently experimentally observed in quantum dots [2][3][4], and in molecules [5]. A sign change in the thermopower can also be obtained by increasing the temperature gradient and thus the population of the resonant level [6][7][8][9]. In these examples the charge carriers are electrons and the sign change of the thermopower means that they travel from the cold side to the hot side, which may appear counterintuitive. Other nonlinear effects can occur if the characteristic relaxation length of electrons and or phonons exceeds the sample size [10], because the energy of electrons and/or phonons is no longer controlled by the temperature of the bath, but by the generated electric bias, including Coulomb interactions [11,12].Observing such negative thermopower at the nanoscale is difficult for at least two reasons: the currents tend to be small and it is hard to maintain a constant temperature difference across such short distances. Here we argue that a generic class of tubular nanowires, to be defined in more detail below, are ideal systems for both realizing and observing negative thermopower. Semiconductor nanowires are versatile syst...

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“…For topological insulator nanowires one can expect reversed, or anomalous, currents measured in tens of nanoamperes [ 11 ], well within experimental reach. Also, since the transport is over long systems, it is much simpler to maintain a large temperature difference of tens of kelvins, compared to the case of quantum dots.…”

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