M\"obius molecules and fragile Mott insulators

Motivated by the concept of M\"obius aromatics in organic chemistry, we extend the recently introduced concept of fragile Mott insulators (FMI) to ring-shaped molecules with repulsive Hubbard interactions threaded by a half-quantum of magnetic flux ($hc/2e$). In this context, a FMI is the insulating ground state of a finite-size molecule that cannot be adiabatically connected to a single Slater determinant, i.e., to a band insulator, provided that time-reversal and lattice translation symmetries are preserved. Based on exact numerical diagonalization for finite Hubbard interaction strength $U$ and existing Bethe-ansatz studies of the one-dimensional Hubbard model in the large-$U$ limit, we establish a duality between Hubbard molecules with $4n$ and $4n+2$ sites, with $n$ integer. A molecule with $4n$ sites is an FMI in the absence of flux but becomes a band insulator in the presence of a half-quantum of flux, while a molecule with $4n+2$ sites is a band insulator in the absence of flux but becomes an FMI in the presence of a half-quantum of flux. Including next-nearest-neighbor-hoppings gives rise to new FMI states that belong to multidimensional irreducible representations of the molecular point group, giving rise to a rich phase diagram

Emerging chiral edge states from the confinement of a magnetic Weyl semimetal in Co3_3Sn2_2S2_2

The quantum anomalous Hall effect (QAHE) and magnetic Weyl semimetals (WSMs) are topological states induced by intrinsic magnetic moments and spin-orbit coupling. Their similarity suggests the possibility of achieving the QAHE by dimensional confinement of a magnetic WSM along one direction. In this study, we investigate the emergence of the QAHE in the two-dimensional (2D) limit of magnetic WSMs due to finite size effects in thin films and step-edges. We demonstrate the feasibility of this approach with effective models and real materials. To this end, we have chosen the layered magnetic WSM Co$_3$Sn$_2$S$_2$, which features a large anomalous Hall conductivity and anomalous Hall angle in its 3D bulk, as our material candidate. In the 2D limit of Co$_3$Sn$_2$S$_2$ two QAHE states exist depending on the stoichiometry of the 2D layer. One is a semimetal with a Chern number of 6, and the other is an insulator with a Chern number of 3. The latter has a band gap of 0.05 eV, which is much larger than that in magnetically doped topological insulators. Our findings naturally explain the existence of chiral states in step edges of bulk Co$_3$Sn$_2$S$_2$ which habe been reported in a recent experiment at $T = 4K$ and present a realistic avenue to realize QAH states in thin films of magnetic WSMs.Comment: Revised 3rd version of the manuscrip

Towards a Topological Classification of Nonadiabaticity in Chemical Reactions

The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band theory has delivered new approaches and tools to characterize the electronic structure of materials, resulting in the discovery of new phases of matter with exotic properties. In the framework of topological band theory, the crossings between energy levels of electrons are characterized by topological invariants, which predict the presence of topological boundary states. Given the frequency of energy level crossings on the potential energy surface in molecules, the applicability of these concepts to molecular systems could be of great interest for our understanding of reaction dynamics. However, challenges arise due to differing quantum mechanical descriptions of solids and molecules. Out work aims to bridge the gap between topological band theory and molecular chemistry. We propose that the Euler Class, a topological invariant, can be used to categorize and analyse the distribution of nonadiabatic couplings on the potential energy surface. To exemplify this connection, we introduce a model system with two distinct regimes that are characterized by different values of the Euler Class, yet identical potential energy surfaces. Contrary to expectations set by the Born-Oppenheimer approximation, we propose that these two regimes don't exhibit identical dynamics, due to a qualitatively distinct distribution of nonadiabatic couplings

Prediction of a magnetic Weyl semimetal without spin-orbit coupling and strong anomalous Hall effect in the Heusler compensated ferrimagnet Ti2MnAl

We predict a magnetic Weyl semimetal in the inverse Heusler Ti2MnAl, a compensated ferrimagnet with a vanishing net magnetic moment and a Curie temperature of over 650 K. Despite the vanishing net magnetic moment, we calculate a large intrinsic anomalous Hall effect (AHE) of about 300 S/cm. It derives from the Berry curvature distribution of the Weyl points, which are only 14 meV away from the Fermi level and isolated from trivial bands. Different from antiferromagnets Mn3X (X= Ge, Sn, Ga, Ir, Rh, and Pt), where the AHE originates from the non-collinear magnetic structure, the AHE in Ti2MnAl stems directly from the Weyl points and is topologically protected. The large anomalous Hall conductivity (AHC) together with a low charge carrier concentration should give rise to a large anomalous Hall angle. In contrast to the Co-based ferromagnetic Heusler compounds, the Weyl nodes in Ti2MnAl do not derive from nodal lines due to the lack of mirror symmetries in the inverse Heusler structure. Since the magnetic structure breaks spin-rotation symmetry, the Weyl nodes are stable without SOC. Moreover, because of the large separation between Weyl points of opposite topological charge, the Fermi arcs extent up to 75% of the reciprocal lattice vectors in length. This makes Ti2MnAl an excellent candidate for the comprehensive study of magnetic Weyl semimetals. It is the first example of a material with Weyl points, large anomalous Hall effect and angle despite a vanishing net magnetic moment.Comment: 6 pages, 4 figure