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Register a new userTemperature-induced topological phase transitions: promoted vs. suppressed non-trivial topology
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We determine the topological phase diagram of BiTl(S$_{1-delta}$Se$_{delta}$)$_2$ as a function of doping and temperature from first-principles calculations. Due to electrontextendash phonon interaction, the bands are renormalized at finite temperature, allowing for a transition between the trivial ($Z_2=0$) and non-trivial ($Z_2=1$) topological phase. We find two distinct regions of the phase diagram with non-trivial topology. In BiTlS$_2$, the phonons promote the crystal to the topological phase at high temperature, while in BiTlSe$_2$, the topological phase exists only at low temperature. This behaviour is explained by the symmetry of the phonon coupling potential, whereby the even phonon modes (whose potential is even under inversion) promote the topological phase and the odd phonon modes promote the trivial phase.
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In the quest for topological insulators with large band gaps, heterostructures with Rashba spin-orbit interactions come into play. Transition metal oxides with heavy ions are especially interesting in this respect. We discuss the design principles for stacking oxide Rashba layers. Assuming a single layer with a two-dimensional electron gas (2DEG) on both interfaces as a building block, a two-dimensional topological insulating phase is present when negative coupling between the 2DEGs exists. When stacking multiple building blocks, a two-dimensional or three-dimensional topological insulator is artificially created, depending on the intra- and interlayer coupling strengths and the number of building blocks. We show that the three-dimensional topological insulator is protected by reflection symmetry, and can therefore be classified as a topological crystalline insulator. In order to isolate the topological states from bulk states, the intralayer coupling term needs to be quadratic in momentum. It is described how such a quadratic coupling could potentially be realized by taking buckling within the layers into account. The buckling, thereby, brings the idea of stacked Rashba system very close to the alternative approach of realizing the buckled honeycomb lattice in [111]-oriented perovskite oxides.
The anomalous Hall, Nernst and thermal Hall coefficients of Fe$_{3-x}$GeTe$_2$ display several features upon cooling, like a reversal in the Nernst signal below $T = 50$ K pointing to a topological transition (TT) associated to the development of magnetic spin textures. Since the anomalous transport variables are related to the Berry curvature, a possible TT might imply deviations from the Wiedemann-Franz (WF) law. However, the anomalous Hall and thermal Hall coefficients of Fe$_{3-x}$GeTe$_2$ are found, within our experimental accuracy, to satisfy the WF law for magnetic-fields $mu_0H$ applied along its inter-layer direction. Surprisingly, large anomalous transport coefficients are also observed for $mu_0H$ applied along the planar emph{a}-axis as well as along the gradient of the chemical potential, a configuration that should not lead to their observation due to the absence of Lorentz force. However, as $mu_0H$ $|$ emph{a}-axis is increased, magnetization and neutron scattering indicate just the progressive canting of the magnetic moments towards the planes followed by their saturation. These anomalous planar quantities are found to not scale with the component of the planar magnetization ($M_{|}$), showing instead a sharp decrease beyond $sim mu_0 H_{|} = $ 4 T which is the field required to align the magnetic moments along $mu_0 H_{|}$. We argue that locally chiral spin structures, such as skyrmions, and possibly skyrmion tubes, lead to a field dependent spin-chirality and hence to a novel type of topological anomalous transport. Locally chiral spin-structures are captured by our Monte-Carlo simulations incorporating small Dzyaloshinskii-Moriya and biquadratic exchange interactions.
Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the presence of disassortative degree correlations. We show it both analytically and numerically, providing also a microscopic interpretation of inverse transitions in terms of freezing of sparse subgraphs and coupling renormalization.
Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics can be tested. Here, we generalize this system to non-Abelian quantum electrodynamics, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly-interacting induced. Moreover, such phase transitions can be controlled and characterized in optical lattice experiments.
The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators, here we investigate topological phase transitions to/from quantum spin Hall (QSH) insulators driven by non-Hermiticity. We show that a trivial to QSH insulator phase transition can be induced by solely varying non-Hermitian terms, and there exists exceptional edge arcs in QSH phases. We establish two topological invariants for characterizing the non-Hermitian phase transitions: i) with time-reversal symmetry, the biorthogonal $mathbb{Z}_2$ invariant based on non-Hermitian Wilson loops, and ii) without time-reversal symmetry, a biorthogonal spin Chern number through biorthogonal decompositions of the Bloch bundle of the occupied bands. These topological invariants can be applied to a wide class of non-Hermitian topological phases beyond Chern classes, and provides a powerful tool for exploring novel non-Hermitian topological matter and their device applications.
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