Polymorph of 8 − P mmn borophene exhibits anisotropic tilted Dirac cones. In this work, we explore the consequences of the tilted Dirac cones in magnetotransport properties of a periodically modulated borophene. We evaluate modulation induced diffusive conductivity by using linear response theory in low temperature regime. The application of weak modulation (electric/magnetic or both) gives rise to the magnetic field dependent non-zero oscillatory drift velocity which causes Weiss oscillation in the longitudinal conductivity at low magnetic field. The Weiss oscillation is studied in presence of an weak spatial electric, magnetic and both modulations individually. The tilting of the Dirac cones gives rise to additional contribution to the Weiss oscillation in longitudinal conductivity. Moreover, it also enhances the frequency of the Weiss oscillation and modifies its amplitude too. Most remarkably, It is found that the presence of out-of phase both i.e., electric and magnetic modulations can cause a sizable valley polarization in diffusive conductivity. The origin of valley polarization lies in the opposite tilting of the two Dirac cones at two valleys.

We explore the transport properties of a periodically modulated α-T3 lattice in the presence of a perpendicular magnetic field. The effect of the Berry phase on electrical conductivity oscillation, socalled Weiss oscillation, caused by the modulation induced non-zero drift velocity of charge carriers is investigated. Employing linear response theory within the low temperature regime, we analyze Weiss oscillation as a function of the external magnetic field for both electrically and magnetically modulated α-T3 lattice numerically as well as analytically. The Berry phase makes this hexagonal lattice structure behave differently than other two-dimensional fermionic systems. It causes a significant valley polarization in magnetoconductivity. Most interestingly, the combined effect of both modulations breaks the particle-hole symmetry and causes a smooth transition from even (odd) to odd (even) filling fraction corresponding to the density of states peaks by means of the Berry phase.

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We present electronic and transport properties of a zigzag nanoribbon made of α − T3 lattice. Our particular focus is on the effects of the continuous evolution of the edge modes ( from flat to dispersive) on the thermoelectric transport properties. Unlike the case of graphene nanoribbon, the zigzag nanoribbon of α − T3 lattice can host a pair of dispersive (chiral) edge modes at the two valleys for specific width of the ribbon. Moreover, gap opening can also occur at the two valleys depending on the width. The slope of the chiral edge modes and the energy gap strongly depend on the relative strength of two kinds of hoping parameters present in the system. We compute corresponding transport coefficients such as conductance, thermopower, thermal conductance and the thermoelectric figure of merits by using the tight-binding Green function formalism, in order to explore the roles of the dispersive edge modes. It is found that the thermopower and thermoelectric figure of merits can be enhanced significantly by suitably controlling the edge modes. The figure of merits can be enhanced by thirty times under suitable parameter regime in comparison to the case of graphene. Finally, we reveal that the presence of line defect, close to the edge, can cause a significant impact on the edge modes as well as on electrical conductance and thermopower.

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