Two-dimensional (2D) honeycomb lattices beyond graphene promise new physical properties such as quantum spin Hall effect. While there have been claims of growth of such lattices (silicene, germanene, stanene), their existence needs further support and their preparation and characterization remain a difficult challenge. Our findings suggest that two distinct phases associated with germanene, the analog of graphene made of germanium (Ge) instead of carbon, can be grown on Ag(111) as observed by scanning tunneling microscopy, low-energy electron diffraction, and angle-resolved photoemission spectroscopy. One such germanene exhibits an atom-resolved alternatively buckled full honeycomb lattice, which is tensile strained and partially commensurate with the substrate to form a striped phase (SP). The other, a quasifreestanding phase (QP), is also consistent with a honeycomb lattice with a lattice constant incommensurate with the substrate but very close to the theoretical value for freestanding germanene. The SP, with a lower atomic density, can be driven into the QP and coexist with the QP by additional Ge deposition. Band mapping and first-principles calculations with proposed SP and QP models reveal an interface state exists only in the SP but the characteristic σ band of freestanding germanene emerges only in the QP—this leads to an important conclusion that adlayer-substrate commensurability plays a key role to affect the electronic structure of germanene. The evolution of the dual germanene phases manifests the competitive formation of Ge-Ge covalent and Ge-Ag interfacial bonds.

The search for a superconductor with non-$s$-wave pairing is important not only for understanding unconventional mechanisms of superconductivity but also for finding new types of quasiparticles such as Majorana bound states. Materials with both topological band structure and superconductivity are promising candidates as $p+ip$ superconducting states can be generated through pairing the spin-polarized topological surface states. In this work, the electronic and phonon properties of the superconductor molybdenum carbide (MoC) are studied with first-principles methods. Our calculations show that nontrivial band topology and $s$-wave Bardeen–Cooper–Schrieffer superconductivity coexist in two structural phases of MoC, namely the cubic $\alpha$ and hexagonal $\gamma$ phases. The $\alpha$ phase is a strong topological insulator and the $\gamma$ phase is a topological nodal-line semimetal with drumhead surface states. In addition, hole doping can stabilize the crystal structure of the $\alpha$ phase and elevate the transition temperature in the $\gamma$ phase. Therefore, MoC in different structural forms can be a practical material platform for studying topological superconductivity.

The interplay of BCS superconductivity and nontrivial band topology is expected to give rise to opportunities for creating topological superconductors, achieved through pairing spin-filtered boundary modes via superconducting proximity effects. The thus-engineered topological superconductivity can, for example, facilitate the search for Majorana fermion quasiparticles in condensed matter systems. Here we report a first-principles study of $\mathrm{M}{\mathrm{g}}_2\mathrm{Pb}$ and predict that it should be a superconducting topological material. The band topology of $\mathrm{M}{\mathrm{g}}_2\mathrm{Pb}$ is identical to that of the archetypal quantum spin Hall insulator HgTe, while isostructural and isoelectronic $\mathrm{M}{\mathrm{g}}_2\mathrm{Sn}$ is topologically trivial; a trivial-to-topological transition is predicted for $\mathrm{M}{\mathrm{g}}_2\mathrm{S}{\mathrm{n}}_{1-x}\mathrm{P}{\mathrm{b}}_x$ for $x\approx 0.77$. We propose that $\mathrm{M}{\mathrm{g}}_2\mathrm{Pb}–\mathrm{M}{\mathrm{g}}_2\mathrm{Sn}$ quantum wells should generate robust spin-filtered edge currents in analogy to HgTe/CdTe quantum wells. In addition, our calculations predict that $\mathrm{M}{\mathrm{g}}_2\mathrm{Pb}$ should become superconducting upon electron doping. Therefore, $\mathrm{M}{\mathrm{g}}_2\mathrm{Pb}$ is expected to provide a practical material platform for studying emergent phenomena arising from the interplay of superconductivity and band topology.

Films of $\mathrm{Pb}\left(111\right)$ with thickness ranging from 1 to 16 monolayers (ML) were grown on $\mathrm{Ge}\left(111\right)$ and examined by angle-resolved photoemission spectroscopy. The measured thickness dependences of the work function and surface energy from the same set of samples were both well described by damped sinusoidal oscillatory functions with the same period, but the oscillation phases differ by $1/4$ period between the two quantities, as judged by the node positions. This difference agrees with the prediction of a generic quantum-well model. The varied node positions of damped oscillations of the work function and surface energy were examined in terms of the details of Pb subband dispersions, indicating the different roles of the density of states at the Fermi level to both thin-film properties. The surface dipoles of Pb films were found to have no relevant effects on the phase shift of thickness-dependent work functions except for the amplitudes of oscillations. The total boundary phase shifts of the quantum well states, extracted from the energy positions of the quantum-well states for both $\mathrm{Pb}/\mathrm{Ge}\left(111\right)$ and freestanding Pb films, are compared and related to the thickness-dependent work function and surface energy.

Transition metal oxides are well known for their complex magnetic and electrical properties. When brought together in heterostructure geometries, they show particular promise for spintronics and colossal magnetoresistance applications. In this article, we propose a carrier-driven coupling mechanism in heterostructures composed of itinerant ferromagnetic materials. The coupling is mediated by charge carriers that strive to maximally delocalize through the heterostructure to gain kinetic energy. In doing so, they force a ferromagnetic or antiferromagnetic coupling between the constituent layers. To illustrate this, we focus on heterostructures composed of ${\mathrm{SrRuO}}_3$ and ${\mathrm{La}}_{1-x}{\mathrm{A}}_x{\mathrm{MnO}}_3$ (A = Ca/Sr). Using the minority-carrier nature of ${\mathrm{SrRuO}}_3$, we provide a simple explanation for antiferromagnetic alignment that is known to occur in multilayers. We present a phenomenological Kondo-lattice model which reproduces the known magnetization properties of multilayers. In addition, we discuss a quantum well model for heterostructures and argue that the spin-dependent density of states determines the nature of the coupling. As a smoking gun signature, we propose that bilayers with the same constituents will oscillate between ferromagnetic and antiferromagnetic coupling upon tuning the relative thicknesses of the layers. We present ab initio results that support this prediction.