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The transition from topologically nontrivial to a trivial state is studied by first-principles calculations on bulk zinc-blende type (Hg$_{1-x}$Zn$_x$)(Te$_{1-x}$S$_x$) disordered alloy series. The random chemical disorder was treated by means of the Coherent Potential Approximation. We found that although the phase transition occurs at the strongest disorder regime (${xapprox 0.5}$), it is still manifested by well-defined Bloch states forming a clear Dirac cone at the Fermi energy of the bulk disordered material. The computed residual resistivity tensor confirm the topologically-nontrivial state of the HgTe-rich (${x<0.5}$), and the trivial state of the ZnS-rich alloy series (${x>0.5}$) by exhibiting the quantized behavior of the off-diagonal spin-projected component, independently on the concentration $x$.
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We study the magnetic proximity effect on a two-dimensional topological insulator in a CrI$_3$/SnI$_3$/CrI$_3$ trilayer structure. From first-principles calculations, the BiI$_3$-type SnI$_3$ monolayer without spin-orbit coupling has Dirac cones at the corners of the hexagonal Brillouin zone. With spin-orbit coupling turned on, it becomes a topological insulator, as revealed by a non-vanishing $Z_2$ invariant and an effective model from symmetry considerations. Without spin-orbit coupling, the Dirac points are protected if the CrI$_3$ layers are stacked ferromagnetically, and are gapped if the CrI$_3$ layers are stacked antiferromagnetically, which can be explained by the irreducible representations of the magnetic space groups $C_{3i}^1$ and $C_{3i}^1(C_3^1)$, corresponding to ferromagnetic and antiferromagnetic stacking, respectively. By analyzing the effective model including the perturbations, we find that the competition between the magnetic proximity effect and spin-orbit coupling leads to a topological phase transition between a trivial insulator and a topological insulator.
The interplay between various symmetries and electronic bands topology is one of the core issues for topological quantum materials. Spontaneous magnetism, which leads to the breaking of time-reversal symmetry, has been proven to be a powerful approach to trigger various exotic topological phases. In this work, utilizing the combination of angle-resolved photoemission spectroscopy, magneto-optical Kerr effect microscopy and first-principles calculations, we present the direct evidence on the realization of the long-sought spontaneous time-reversal symmetry breaking induced topological phase transition in soft ferromagnetic EuB$_6$. We successfully disentangle the bulk band structure from complicated surface states, and reveal the hallmark band inversion occurring between two opposite-parity bulk bands below the phase transition temperature. Besides, our magneto-optical Kerr effect microscopy result confirms the simultaneous formation of magnetic domains in EuB$_6$, implying the intimate link between the topological phase transition and broken time-reversal symmetry therein. Our results demonstrate that EuB$_6$ provides a potential platform to study the interplay between the topological phases and tunable magnetic orders.
MXenes, a family of two-dimensional transition metal carbides and nitrides, have various tunable physical and chemical properties. Their diverse prospective applications in electronics and energy storage devices have triggered great interests in science and technology. MXenes can be functionalized by different surface terminations. Some O and F functionalized MXenes monolayers have been predicted to be topological insulators (TIs). However, the reported OH functionalized MXenes TIs are very few and their electronic structures need to be investigated in more detail. It has been revealed that the work functions of MXenes are reduced significantly by OH termination and the image potential (IP) states move close to the Fermi level. The wave functions of these IP states are spatially extensive outside the surfaces. By stacking the OH-functionalized MXenes, the energies of the IP states can be modulated by the interlayer distances of multilayers, because the overlap and hybridization of the wave functions between the neighboring layers are significant. Therefore, these stacking layers are interacted and coupled with IP states. Here, based on first-principles calculations, we demonstrate that the stacking of two-dimensional topologically trivial OH-functionalized MXenes, such as V$_2$HfC$_2$(OH)$_2$, possibly gives rise to the topologically nontrivial energy bands. In other words, the topological properties of V$_2$HfC$_2$(OH)$_2$ multilayers can be modulated by its interlayer distance. An energy band inversion involving IP states is proposed. We expect that these results can advance the future application of MXenes or other low work function multilayer materials as controllable TI devices.
In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Here we show an example of the opposite. We consider a spin chain with two competing interactions, set on a ring with an odd number of sites. When only the dominant interaction is antiferromagnetic, and thus induces topological frustration, the standard antiferromagnetic order (expressed by the magnetization) is destroyed. When also the second interaction turns from ferro to antiferro, an antiferromagnetic order characterized by a site-dependent magnetization which varies in space with an incommensurate pattern, emerges. This modulation results from a ground state degeneracy, which allows to break the translational invariance. The transition between the two cases is signaled by a discontinuity in the first derivative of the ground state energy and represents a quantum phase transition induced by a special choice of boundary conditions.
Recent progress in understanding the electronic band topology and emergent topological properties encourage us to reconsider the band structure of well-known materials including elemental substances. Controlling such a band topology by external field is of particular interest from both fundamental and technological view point. Here we report the pressure-induced topological phase transition from a semiconductor to a Weyl semimetal in elemental tellurium probed by transport measurements. Pressure variation of the periods of Shubnikov-de Haas oscillations, as well as oscillations phases, shows an anomaly around the pressure theoretically predicted for topological phase transition. This behavior can be well understood by the pressure-induced band deformation and resultant band crossing effect. Moreover, effective cyclotron mass is reduced toward the critical pressure, potentially reflecting the emergence of massless linear dispersion. The present result paves the way for studying the electronic band topology in well-known compounds and topological phase transition by the external field.
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