Dirac-like Hamiltonians, linear in momentum k, describe the low-energy physics of a large set of novel materials, including graphene, topological insulators, and Weyl Fermions. We show here that the inclusion of a minimal k 2 Wilson's mass correction improves the models and allows for systematic derivations of appropriate boundary conditions for the envelope functions on finite systems. Considering only Wilson's masses allowed by symmetry, we show that the k 2 corrections are equivalent to Berry-Mondragon's discontinuous boundary conditions. This allows for simple numerical implementations of regularized Dirac models on a lattice, while properly accounting for the desired boundary condition. We apply our results on graphene nanoribbons (zigzag and armchair), and on a PbSe monolayer (topological crystalline insulator). For graphene, we find generalized Brey-Fertig boundary conditions, which correctly describes the small gap seen on ab initio data for the metallic armchair nanoribbon. On PbSe, we show how our approach can be used to find spin-orbital coupled boundary conditions. Overall, our discussions are set on a generic model that can be easily generalized for any Dirac-like Hamiltonian. arXiv:1908.00145v1 [cond-mat.mes-hall]

Adherence of metal oxides to graphene is of fundamental significance to graphene nanoelectronic and spintronic interfaces. Titanium oxide and aluminum oxide are two widely used tunnel barriers in such devices, which offer optimum interface resistance and distinct interface conditions that govern transport parameters and device performance. Here, we reveal a fundamental difference in how these metal oxides interface with graphene through electrical transport measurements and Raman and photoelectron spectroscopies, combined with ab initio electronic structure calculations of such interfaces. While both oxide layers cause surface charge transfer induced p-type doping in graphene, in sharp contrast to TiO x , the AlO x /graphene interface shows the presence of appreciable sp 3 defects. Electronic structure calculations disclose that significant p-type doping occurs due to a combination of sp 3 bonds formed between C and O atoms at the interface and possible slightly off-stoichiometric defects of the aluminum oxide layer. Furthermore, the sp 3 hybridization at the AlO x /graphene interface leads to distinct magnetic moments of unsaturated bonds, which not only explicates the widely observed low spin-lifetimes in AlO x barrier graphene spintronic devices but also suggests possibilities for new hybrid resistive switching and spin valves.

Two-dimensional (2D) topological insulators have fascinating physical properties which are promising for applications within spintronics. In order to realize spintronic devices working at room temperature, materials with a large nontrivial gap are needed. Bismuthene, a 2D layer of Bi atoms in a honeycomb structure, has recently attracted strong attention because of its record-large nontrivial gap, which is due to the strong spin−orbit coupling of Bi and the unusually strong interaction of the Bi atoms with the surface atoms of the substrate underneath. It would be a significant step forward to be able to form 2D materials with properties such as bismuthene on semiconductors such as GaAs, which has a band gap size relevant for electronics and a direct band gap for optical applications. Here, we present the successful formation of a 2D Bi honeycomb structure on GaAs, which fulfills these conditions. Bi atoms have been incorporated into a clean GaAs(111) surface, with As termination, based on Bi deposition under optimized growth conditions. Low-temperature scanning tunneling microscopy and spectroscopy (LT-STM/S) demonstrates a well-ordered large-scale honeycomb structure, consisting of Bi atoms in a √3 × √3 30°reconstruction on GaAs(111). X-ray photoelectron spectroscopy shows that the Bi atoms of the honeycomb structure only bond to the underlying As atoms. This is supported by calculations based on density functional theory that confirm the honeycomb structure with a large Bi−As binding energy and predict Biinduced electronic bands within the GaAs band gap that open up a gap of nontrivial topological nature. STS results support the existence of Bi-induced states within the GaAs band gap. The GaAs:Bi honeycomb layer found here has a similar structure as previously published bismuthene on SiC or on Ag, though with a significantly larger lattice constant and only weak Bi−Bi bonding. It can therefore be considered as an extreme case of bismuthene, which is fundamentally interesting. Furthermore, it has the same exciting electronic properties, opening a large nontrivial gap, which is the requirement for room-temperature spintronic applications, and it is directly integrated in GaAs, a direct band gap semiconductor with a large range of (opto)electronic devices.

We investigate the ballistic zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally, but also induces a transverse finite side-jump for both trivial and topological regimes. For finite ribbons of width W , we show that the Landau-Zener tunneling between bulk and edge states vanishes for large W as their electric field-induced coupling decays with W −3/2 . This is demonstrated by expanding the time-dependent Schrödinger equation in terms of Houston states. Hence we cannot picture the quantum spin Hall states as arising from the zitterbewegung bulk trajectories 'leaking' into the edge states, as proposed in Phys. Rev. B 87, 161115 (2013).

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