Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices.

Materials with properties designed on-demand arise in a synergy between theoretical and experimental approaches. Here, we explore a set of Archimedean lattices, providing a guide to their electronic properties and topological phases. Within these lattices, a rich electronic structure emerges forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points with linear and flat dispersions. Employing a tight-binding model with spin-orbit coupling, we characterize quantum spin Hall (QSH) phases in all Archimedean lattices. Our discussions are validated within density functional theory calculations, where we show the characteristic bands of the studied lattices arising in 2D carbon allotropes.

Quantum anomalous Hall effect in metal-bis(dithiolene), magnetic properties, doping and interfacing graphene.

The realization of the Quantum anomalous Hall effect (QAHE) in two dimensional (2D) metal organic frameworks (MOFs), (MC4S4)3 with M = Mn, Fe, Co, Ru and Rh, has been investigated based on a combination of first-principles calculations and tight binding models. Our analysis of the magnetic anisotropy energy (MAE) reveals that the out-of-plane (in-plane) magnetization is favored for M = Mn, Fe, and Ru (Co, and Rh). Therefore, we predict that the structural symmetry of (MC4S4)3 yields the QAHE only for M = Mn, Fe and Ru. Such a quantum anomalous Hall phase has been confirmed through the calculation of the Chern number, and examining the formation of topologically protected (metallic) edge states. Furthermore, we show that viable electron (n-type) doping of the MOFs can be used to place the Fermi level within the non-trivial energy gap; where we find that in (RuC4S4)3, in addition to the up-shift of the Fermi level, the MAE energy increases by 40%. Finally, we show that in MOF/graphene (vdW) interfaces, the Fermi level tuning can be done with an external electric field, which controls the charge transfer at the MOF/graphene interface, giving rise to switchable topologically protected edge currents in the MOFs.

Suppressed topological phase transitions due to nonsymmorphism in SnTe stacking.

We combine first principles calculations with a group theory analysis to investigate topological phase transitions in the stacking of SnTe monolayers. We show that distinct finite stacking yields different symmetry-imposed degeneracy, which dictates the hybridization properties of opposite surface states. For SnTe aligned along the [001] direction, an (even) odd number of monolayers yields a (non)symmorphic space group. For the symmorphic case, the hybridization of surface states lead to band inversions and topological phase transitions as the sample height is reduced. In contrast, for a nonsymmorphic stacking, an extra degeneracy is guaranteed by symmetry, thus avoiding the hybridization and topological phase transitions, even in the limit of a few monolayers. Our group theory analysis provide a clear picture for this phenomenology and matches well the first principles calculations.

Conductance and Kondo Interference beyond Proportional Coupling.

The transport properties of nanostructured systems are deeply affected by the geometry of the effective connections to metallic leads. In this work we derive a conductance expression for a class of interacting systems whose connectivity geometries do not meet the Meir-Wingreen proportional coupling condition. As an interesting application, we consider a quantum dot connected coherently to tunable electronic cavity modes. The structure is shown to exhibit a well-defined Kondo effect over a wide range of coupling strengths between the two subsystems. In agreement with recent experimental results, the calculated conductance curves exhibit strong modulations and asymmetric behavior as different cavity modes are swept through the Fermi level. These conductance modulations occur, however, while maintaining robust Kondo singlet correlations of the dot with the electronic reservoir, a direct consequence of the lopsided nature of the device.

Magnetically defined qubits on 3D topological insulators.

We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect (QAHE). Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits.

Many-body effects on the rho(xx) ringlike structures in two-subband wells.

The longitudinal resistivity rho(xx) of two-dimensional electron gases formed in wells with two subbands displays ringlike structures when plotted in a density-magnetic-field diagram, due to the crossings of spin-split Landau levels (LLs) from distinct subbands. Using spin density functional theory and linear response, we investigate the shape and spin polarization of these structures as a function of temperature and magnetic-field tilt angle. We find that (i) some of the rings "break" at sufficiently low temperatures due to a quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of spin polarization (approximately 50%) within, consistent with the NMR data of Zhang et al. [Phys. Rev. Lett. 98, 246802 (2007)], and (ii) for increasing tilting angles the interplay between the anticrossings due to inter-LL couplings and the exchange-correlation effects leads to a collapse of the rings at some critical angle theta(c), in agreement with the data of Guo et al. [Phys. Rev. B 78, 233305 (2008)].