In this paper, the effect of the direction of a magnetic field has been studied in leads (electrodes with limited width) on thermoelectric properties of Al$_{12}$N$_{12}$ cage with and without considering inelastic electron–phonon interactions. Results showed that the biggest (smallest) value of total conductivity is observed in the case of the maximum value of elastic conductivity (G$^M$$_{σ,σ'}$ ) with respect to the direction of the magnetic field for antiparallel (↑↓ or ↓↑), parallel configurations (↓↓ or ↑↑) for the left (σ =↑↓) and the right (σ' =↑↓) lead spins, i.e.,G$^M$$_{ ↓,↑}$ (G$^M$$_{ ↓,↑}$). The maximum number of conduction heights was seen for σ =↓ and σ ' =↑. With respect to the direction of magnetic field in the leads, the maximum value of electronic thermal conductance (K$^{max}$$_ {e,σσ'}$ ) can be arranged in the following order: K$^{max}$$_ {e↓↑}$ > K$^{max}$${_ e↓↓}$ >K$^{max}$$_ {e,↑↓}$ > K$^{max}$$_ {e,↑↑}$. The direction of the magnetic field in the leads affects the numbers, height and width peaks and valleys of the first derivative of thermopower (TP). We observe the highest (deepest) peak (valley) when σ =↑ and σ' =↓ (σ =↑ and σ' =↑). Also, the effect of temperature on current and tunnel magnetoresistance (TMR) was considered in this paper.

Currently, one of the major challenges facing today’s societies is the high-energy consumption of fuel and reduced fuel reserves. Employing wasted heat to produce electricity has attracted the attention of many researchers. This paper investigates the thermoelectric properties of defective boron nitride (BN) nanosheet. For this purpose, the influence of the position of the single-vacancy defect on the thermoelectric characteristics is evaluated. The investigations are performed at three arbitrary temperatures, 200, 300 and 600 K. Results show thatthe figure-of-merit (ZT) value of the BN nanosheet without defect is much better than that of the single-vacancy defect in the BN nanosheet. Because the defect occurs naturally during synthesis, the study shows that the ZT value at all three temperatures with boron atoms removed from the left and the right positions and also the nitrogen atoms removed from the right BN nanosheets is larger than other defective structures. The resonant tunnelling of electrons causes fluctuations in electronic conductance and also significantly increases the Seebeck coefficient. Studies show that the Seebeck coefficient in the structure without defects is larger than in other structures. Due to the increasing need for energy in the world, the conversion of thermal energy into electricity can be a good solution to prevent thedepletion of natural reserves. Therefore, it seems that the results and properties obtained from BN nanostructures can help in designing the nanoelectronic and cooling systems.