We consider the thermoelectric properties of a double-quantum-dot molecule coupled in parallel to metal electrodes with a magnetic flux threading the ring. By means of the Sommerfeld expansion we obtain analytical expressions for the electric and thermal conductances, thermopower and figure of merit for arbitrary values of the magnetic flux. We neglect electronic correlations. The Fano antiresonances in transmission demand that terms usually discarded in the Sommerfeld expansion are taken into account. We also explore the behavior of the Lorenz ratio L = κ/σT, where κ and σ are the thermal and electrical conductances and T the absolute temperature, and we discuss the reasons why the Wiedemann-Franz law fails in presence of Fano antiresonances.

We explore proximity-induced ferromagnetism on transition metal dichalcogenides (TMDs), focusing on molybdenum ditelluride ribbons with zigzag edges, deposited on ferromagnetic europium oxide (EuO). A tight-binding model incorporates exchange and Rashba fields induced by proximity to EuO or similar substrates. For in-gap Fermi levels, electronic modes in the nanoribbon are localized along the edges, acting as one-dimensional (1D) conducting channels with tunable spin-polarized currents. TMDs on magnetic substrates can become very useful in spintronics, providing versatile platforms to study the proximity effects and electronic interactions in complex 1D systems.

The growth and exfoliation of two-dimensional (2D) materials have led to the creation of edges and novel interfacial states at the juncture between crystals with different composition or phases. These hybrid heterostructures (HSs) can be built as vertical van der Waals stacks , resulting in a 2D interface, or as stitched adjacent monolayer crystals, resulting in one-dimensional (1D) interfaces. Although most attention has been focused on vertical HSs, increasing theoretical and experimental interest in 1D interfaces is evident. In-plane interfacial states between different 2D materials inherit properties from both crystals, giving rise to robust states with unique 1D non-parabolic dispersion and strong spin–orbit effects. With such unique characteristics, these states provide an exciting platform for realizing 1D physics. Here, we review and discuss advances in 1D heterojunctions, with emphasis on theoretical approaches for describing those between semiconducting transition metal dichalcogenides MX ₂ (with M = Mo, W and X = S, Se, Te), and how the interfacial states can be characterized and utilized. We also address how the interfaces depend on edge geometries (such as zigzag and armchair) or strain, as lattice parameters differ across the interface, and how these features affect excitonic/optical response. This review is intended to serve as a resource for promoting theoretical and experimental studies in this rapidly evolving field.

We study features of thermoelectric transport through a one-dimensional topological system model hosting Majorana bound states (MBSs) at its ends. We describe the behavior of the Seebeck coefficient and the $ZT$ figure of merit for two configurations between the MBS and normal current leads. We find an important violation of the Wiedemann-Franz law in one of these geometries, leading to sizable values of the thermoelectric efficiency over a narrow window in chemical potential away from neutrality. These findings could lead to interesting thermoelectric-based MBS detection devices, via measurements of the Seebeck coefficient and figure of merit.