Two-dimensional topological insulators show great promise for spintronic applications. Much attention has been placed on single atomic or molecular layers, such as bismuthene. The selections of such materials are, however, limited. To broaden the base of candidate materials with desirable properties for applications, we report herein an exploration of the physics of double layers of bismuthene and antimonene. The electronic structure of a film depends on the number of layers, and it can be modified by epitaxial strain, by changing the effective spin-orbit coupling strength, and by the manner in which the layers are geometrically stacked. First-principles calculations for the double layers reveal a number of phases, including topological insulators, topological semimetals, Dirac semimetals, trivial semimetals, and trivial insulators. Their phase boundaries and the stability of the phases are investigated. The results illustrate a rich pattern of phases that can be realized by tuning lattice strain and effective spin-orbit coupling.

Two-dimensional topological materials, in the form of ultrathin films grown on substrates, are outstanding candidates for spintronic applications. Their electronic structures including the topological class can be tuned or altered by strain and isoelectronic substitutional alloying. First-principles calculations show that the topological order of a monolayer Bi, bismuthene, is unusually robust against strain and changes in spin-orbit coupling strength. The phase diagram shows a large area in which the system is a topological insulator; phase boundaries for transforming into other phases, trivial or not, are mapped out.

The transformations of the topological phase and the edge modes of a double-bilayer bismuthene were investigated with first-principles calculations and Green’s function as the inter-bilayer spacing increased from 0 Å to 10 Å. At a critical spacing of 2 Å, a topological phase transition from a topological insulator to a band insulator resulting from a band inversion between the highest valence band and the second lowest conduction band, was observed, and this was understood based on the particular orbital characters of the band inversion involved states. The edge modes of double-bilayer bismuthene survived the phase transition. When d was 2 Å < d < 4 Å, the interaction between the edge modes of two separated bismuthene bilayers induced an anti-crossing gap and resulted in a trivial band connection. At and beyond 4 Å, the two bilayers behavior decoupled entirely. The results demonstrate the transformability of the topological phase and the edge modes with the inter-bilayer spacing in double-bilayer bismuthene, which may be useful for spintronic applications.

We present a generic mechanism that explains why many Kondo materials show magnetic ordering along directions that are not favoured by the crystal-field anisotropy. Using a renormalization-group (RG) analysis of single impurity Kondo models with single-ion anisotropy, we demonstrate that strong fluctuations above the Kondo temperature drive a moment re-orientation over a wide range of parameters. In tetragonal systems this can happen for both easy-plane or easy axis anisotropy. The characteristic crossing of magnetic susceptibilities is not an artefact of the RG treatment but can be reproduced in brute-force perturbation theory. Finally, we demonstrate that anisotropic fluctuations on the single-ion level and the fluctuation-induced anisotropy of RKKY interactions cooperate to drive magnetic hard-direction ordering.

We investigate the stability of the Néel quantum critical point of two-dimensional quantum antiferromagnets, described by a nonlinear σ model, in the presence of a Kondo coupling to N f flavors of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using the momentum-shell renormalization group (RG), we demonstrate that the Landau damping is weakly irrelevant at the Néel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the Néel quantum critical point quasistable for N f 4 and thermodynamically stable for N f < 4. In the latter case, we identify a multicritical point which describes the transition between the Néel critical and Kondo runaway regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multicritical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.