arXiv subjects

Niclas Heinsdorf

Publications and source records attributed to Niclas Heinsdorf.

23 records · Page 2Linked to original sources

arXiv2023

Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams

We derive two fundamental laws of chiral band crossings: (i) a local constraint relating the Chern number to phase jumps of rotation eigenvalues; and (ii) a global constraint determining the number of chiral crossings on rotation axes. Together with the fermion doubling theorem, these laws describe all conditions that a network of chiral band crossing must satisfy. We apply the fundamental laws to prove the existence of enforced double Weyl points, nodal planes, and generic Weyl points, among others. In addition, we show that chiral space-group symmetries cannot stabilize nodal lines with finite Chern numbers. Combining the local constraint with explicit low-energy models, we determine the generic topological phase diagrams of all multi-fold crossings. Remarkably, we find a four-fold crossing with Chern number 5, which exceeds the previously conceived maximum Chern number of 4. We identify BaAsPt as a suitable material with this four-fold crossing exhibiting Chern number 5 near the Fermi energy.

cond-mat.mtrl-sci↗

arXiv2021

A semimetallic square-octagon (fes) two-dimensional polymer with high mobility

The electronic properties of $π$-conjugated two-dimensional (2D) polymers near the Fermi level are determined by structural topology and chemical composition. Thus, tight-binding (TB) calculations of the corresponding fundamental network can be used to explore the parameter space to find configurations with intriguing properties before designing the the atomistic 2D polymer network. The vertex-transitive \textbf{fes} lattice, which is also called square-octagon lattice, is rich in interesting topological features including Dirac points and flat bands. Herein, we study its electronic and topological properties within the TB framework using representative parameters for chemical systems. Secondly, we demonstrate that the rational implementation of band structure features obtained from TB calculations into 2D polymers is feasible with a family of 2D polymers possessing \textbf{fes} structure. A one-to-one band structure correspondence between fundamental network and 2D polymers is found. Moreover, changing the relative length of linkers connecting the triangulene units in the 2D polymers reflect tuning of hopping parameters in the TB model. These perturbations allow to open sizeable local band gaps at various positions in the Brillouin zone. From analysis of Berry curvature flux, none of the polymers exhibits a large topologically non-trivial band gap. However, we find a particular configuration of semimetallic characteristics with separate electron and hole pockets, which possess very low effective masses both for electrons (as small as $m^*_\mathrm{e} = 0.05$) and holes (as small as $m^*_\mathrm{h} = 0.01$).

cond-mat.mtrl-sci↗

arXiv2021

Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in the space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire Brillouin zone. This results in a simpler connectivity of the Fermi arcs and more pronounced topological responses than in materials with four or more Weyl points. In addition, we show that the symmetries of the space groups 56, 61, and 62 enforce nontrivial weak $\mathbb{Z}_2$ topology in materials with strong spin-orbit coupling, leading to helical surface states. With these classification results in hand, we perform extensive database searches for orthorhombic materials crystallizing in the relevant space groups. We find that Sr$_2$Bi$_3$ and Ir$_2$Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial $\mathbb{Z}_2$ invariant, CuIrB possesses nodal chains near the Fermi energy, Pd$_7$Se$_4$ and Ag$_2$Se exhibit fourfold double Weyl points, the latter one even in the absence of spin-orbit coupling, whereas the fourfold degeneracies in AuTlSb are made up from intersecting nodal lines. For each of these examples we compute the ab-initio band structures, discuss their topologies, and for some cases also calculate the surface states.

cond-mat.mtrl-sci↗

arXiv2021

Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within band theory. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological phases which are not adiabatically connected to any band insulator. In this work we address the many facettes of this question by considering the specific example of a Hubbard diamond chain. This model features a Mott insulator, a trivial insulating phase and an obstructed atomic limit phase. Here we discuss the nature of the Mott insulator and determine the phase diagram and topology of the interacting model with infinite density matrix renormalization group calculations, variational Monte Carlo simulations and with many-body topological invariants. We then proceed by considering a generalization of the TQC formalism to Green's functions combined with the concept of topological Hamiltonian to identify the topological nature of the phases, using cluster perturbation theory to calculate the Green's functions. The results are benchmarked with the above determined phase diagram and we discuss the applicability and limitations of the approach and its possible extensions.

cond-mat.str-el↗

arXiv2020

Anisotropic superconductivity and Fermi surface reconstruction in the spin-vortex antiferromagnetic superconductor CaK(Fe$_{0.95}$Ni$_{0.05}$)$_4$As$_4$

High critical temperature superconductivity often occurs in systems where an antiferromagnetic order is brought near $T=0K$ by slightly modifying pressure or doping. CaKFe$_4$As$_4$ is a superconducting, stoichiometric iron pnictide compound showing optimal superconducting critical temperature with $T_c$ as large as $38$ K. Doping with Ni induces a decrease in $T_c$ and the onset of spin-vortex antiferromagnetic order, which consists of spins pointing inwards to or outwards from alternating As sites on the diagonals of the in-plane square Fe lattice. Here we study the band structure of CaK(Fe$_{0.95}$Ni$_{0.05}$)$_4$As$_4$ (T$_c$ = 10 K, T$_N$ = 50 K) using quasiparticle interference with a Scanning Tunneling Microscope (STM) and show that the spin-vortex order induces a Fermi surface reconstruction and a fourfold superconducting gap anisotropy.

cond-mat.supr-con↗