arXiv subjects

Lukas Muechler

Publications and source records attributed to Lukas Muechler.

At least 19 recordsLinked to original sources

arXiv2026

Symmetry and Topology in Wavepacket Dynamics near Conical Intersections

Whether topology directly shapes chemical dynamics remains an open question in theoretical chemistry. The issue arises because degeneracies of adiabatic electronic states can generate nontrivial topological structure, and such degeneracies are common in polyatomic molecules. Existing work has largely emphasized static characterizations and dynamical studies of low-energy, highly symmetric models. Here we develop a symmetry-based analysis of nonadiabatic dynamics in two-state conical-intersection models that is predictive without invoking topological invariants. We show that the nodal-line structures associated with dynamics near a conical intersection are robust in highly symmetric settings, but should not in general be expected to persist once the relevant symmetry is broken.

physics.chem-ph↗

arXiv2026

Irreducible Representations as Multireference Indicators for Diradicaloid Systems

Multireference behavior in molecules often arises when a small gap between frontier orbitals results in mixing of closed and open-shell configurations. Standard multireference diagnostics of this regime usually rely on correlated wavefunctions, natural-orbital occupations, or reduced density matrices. Here, we examine a complementary, symmetry-based criterion for a model system. For a time-reversal-invariant Hamiltonian, a symmetry-preserving, closed-shell Slater determinant must transform as the trivial irreducible representation of its point group. Therefore, a nontrivial, many-electron irreducible representation excludes such a description. We compare two pathways within the same model to demonstrate this. Along the control pathway, the frontier orbitals remain separated and the ground state retains a trivial irreducible representation over the weak-to-intermediate interaction regime. Along the obstructed pathway, a high-symmetry point produces a frontier-orbital degeneracy, resulting in a singlet ground state with two-configuration character and a nontrivial irreducible representation. Exact diagonalization, a two-state effective model, and the Frobenius norm of the two-particle cumulant provide a consistent picture in this regime, demonstrating that irreducible representations can serve as a low-cost diagnostic of multireference character in diradicaloid models. While symmetry is not a quantitative measure of correlation strength, it does offer a computationally inexpensive screening tool to identify obstructions to a single-reference description.

physics.chem-ph↗

arXiv2026

Predicting Defect States: A Quick Screening Protocol for Substitutional Point Defect Engineering

Point defects in crystalline materials play a central role in determining electronic, optical, and magnetic properties. However, systematic exploration of defect configurations remains computationally expensive because large supercell calculations are required to approximate isolated defects under periodic boundary conditions. We present a unit-cell-based tight-binding protocol that enables rapid pre-screening of substitutional defects. The protocol extracts Wannier tight-binding Hamiltonians from small, fully relaxed unit cells of the host and defect-like systems, replicates the host Hamiltonian to construct a supercell model, and introduces the defect by modifying only the on-site energies at the substitution site while leaving the hopping parameters unchanged. We validate the protocol across three diverse systems: isostructural substitutional defects in transition-metal dichalcogenides (M$_\mathrm{Mo}$ MoS$_2$, M = Ce, Zr, Nb, Tc, and Ru), symmetry-breaking carbon substitutions in hexagonal boron nitride (C$_\mathrm{B}$C$_\mathrm{N}$ h-BN), and nitrogen-vacancy (NV$^-$) centers in diamond. These case studies span two-dimensional and three-dimensional hosts, simple substitutions, and substitution-vacancy complexes. In all cases, the protocol successfully captures the number of in-gap states, their degeneracies, and their shallow or deep character relative to host band edges, despite some quantitative deviations in absolute energy positions. We further identify limitations for vacancies of highly electronegative atoms and for charge-state or spin-polarization effects, both of which involve self-consistent charge redistribution not captured by the protocol.

cond-mat.mtrl-sci↗

arXiv2026

Nudged Elastic Membranes for Constructing Reduced Two-Dimensional Potential Energy Surfaces

Path optimization methods have been widely used and highly successful for the analysis of chemical reactions. Yet, they can fail to capture intrinsically multidimensional features of potential energy surfaces (PES). We introduce the nudged elastic membrane method, a framework for constructing two-dimensional reduced potential-energy surfaces in chemically relevant regions of a PES using only energies and forces without requiring more costly Hessian information. The method is demonstrated for a three-dimensional prototype model and for the triplet formaldehyde molecular system. In both cases, the resulting membrane captures one-dimensional reaction-path features as well as genuinely two-dimensional structures such as a yet unreported reported second-order saddle point in the PES of triplet formaldehyde. The method further provides direct access to structures that can serve as starting points for subsequent refinement. Our results show that the method offers a practical route to exploring multidimensional PES topography beyond the single-path picture.

cond-mat.stat-mech↗

arXiv2025

Topological Transitions in Orbital-Symmetry-Controlled Chemical Reactions

Topological band theory has transformed our understanding of crystalline materials by classifying the connectivity and crossings of electronic energy levels. Extending these concepts to molecular systems has therefore attracted significant interest. Reactions governed by orbital symmetry conservation are ideal candidates, as they classify pathways as symmetry-allowed or symmetry-forbidden depending on whether molecular orbitals cross along the reaction coordinate. However, the presence of strong electronic correlations in these reactions invalidate the framework underlying topological band theory, preventing direct generalization. Here, we introduce a formalism in terms of Green's functions to classify orbital symmetry controlled reactions even in the presence of strong electronic correlations. Focusing on prototypical 4$π$ electrocyclizations, we show that symmetry-forbidden pathways are characterized by crossings of Green's function zeros, in stark contrast to the crossings of poles as predicted by molecular-orbital theory. We introduce a topological invariant that identifies these symmetry protected crossings of both poles and zeros along a reaction coordinate and outline generalizations of our approach to reactions without any conserved spatial symmetries along the reaction path. Our work lays the groundwork for systematic application of modern topological methods to chemical reactions and can be extended to reactions involving different spin states or excited states.

cond-mat.str-el↗

arXiv2025

A Recipe for Flat Bands in Pyrochlore Materials: A Chemist's Perspective

Materials in which atoms are arranged in a pyrochlore lattice have found renewed interest, as, at least theoretically, orbitals on those lattices can form flat bands. However, real materials often do not behave according to theoretical models, which is why there has been a dearth of pyrochlore materials exhibiting flat band physics. Here we examine the conditions under which ideal 'pyrochlore bands' can exist in real materials and how to have those close to the Fermi level. We find that the simple model used in the literature does not apply to the bands at the Fermi level in real pyrochlore materials. However, surprisingly, certain oxide compounds which have oxygen orbitals inside the pyrochlore tetrahedra do exhibit near-ideal pyrochlore bands near the Fermi level. We explain this observation by a generalized tight-binding model including the oxygen orbitals. We further classify all known pyrochlore materials based on their crystal structure, band structure, and chemical characteristics and propose materials to study in future experiments.

cond-mat.mtrl-sci↗

arXiv2025

Electronic and Structural Properties of Lanthanide-Doped MoS$_2$: Impact of Ionic Size and Orbital Configuration Mismatch

Single-photon emitters (SPEs) are crucial for quantum technologies such as quantum simulation, secure quantum communication, and precision measurements. Two-dimensional transition metal dichalcogenides (TMDCs) are promising SPE candidates due to their atomically thin nature and efficient photon extraction. However, their emission wavelengths limit compatibility with existing telecommunication technologies. Lanthanide doping in TMDCs, such as \defect{MoS}{2}, offers a potential solution by introducing sharp, $f$-orbital derived emissions in the infrared range. Yet, the feasibility of introducing these dopants remains uncertain due to their large ionic radii of the lanthanides. We employ density functional theory (DFT) calculations to investigate the structural and electronic properties of lanthanide-doped \defect{MoS}{2} monolayers (Ln=Ce, Er). By evaluating formation energies with up to three adjacent S vacancies, we assess how these vacancies mitigate lattice strain caused by the size mismatch of Ce and Er with Mo. Our results show that while \defect{Ln}{Mo} destabilizes the pristine lattice, S vacancies enhance thermodynamic stability. Charge state analysis indicates that defect states introduced by \defect{Ln}{Mo} localize near the valence band and remain stable across a wide Fermi energy range. Electronic structure analysis shows that Ce$^{4+}$ and Er$^{3+}$ maintain their oxidation states upon electron doping due to additional acceptor states from host-induced dangling bonds. These states arise from an orbital filling mismatch between dopants and Mo. Consequently, \defect{Ce}{Mo} is unlikely to exhibit infrared emissions due to its empty $f$-shell, whereas \defect{Er}{Mo} is expected to emit in the infrared. These findings demonstrate the potential of lanthanide-doped TMDCs as tunable SPEs and provide design strategies for optimizing their optical and electronic properties.

cond-mat.mtrl-sci↗

arXiv2024

Topological Woodward-Hoffmann classification for cycloadditions in polycyclic aromatic azomethine ylides

The study of cycloaddition mechanisms is central to the fabrication of extended sp2 carbon nanostructures. Reaction modeling in this context has focused mostly on putative, energetically preferred, exothermic products with limited consideration for symmetry allowed or forbidden mechanistic effects. Here, we introduce a scheme for classifying symmetry-forbidden reaction coordinates in Woodward-Hoffmann correlation diagrams. Topological classifiers grant access to the study of reaction pathways and correlation diagrams in the same footing, for the purpose of elucidating mechanisms and products of polycyclic aromatic azomethine ylide (PAMY) cycloadditions with pentacene-yielding polycyclic aromatic hydrocarbons with an isoindole core in the solid-state and on surfaces as characterized by mass spectrometry and scanning tunneling microscopy, respectively. By means of a tight-binding reaction model and density functional theory (DFT) we find topologically-allowed pathways if a product is endothermic, and topologically-forbidden if a product is exothermic. Our work unveils topological classification as a crucial element for reaction modeling for nanographene engineering, and highlights its fundamental role in the design of cycloadditions in on-surface and solid-state chemical reactions, while underscoring that exothermic pathways can be topologically-forbidden.

physics.chem-ph↗

arXiv2023

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.

cond-mat.mtrl-sci↗

arXiv2022

Quantum embedding methods for correlated excited states of point defects: Case studies and challenges

A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density-functional theory (DFT) is inherently a ground state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (C$_{\text{B}}$C$_{\text{N}}$), the negatively charged nitrogen-vacancy center in diamond (NV$^-$), and an Fe impurity on the Al site in wurtzite AlN ($\text{Fe}_{\text{Al}}$). For C$_{\text{B}}$C$_{\text{N}}$ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the NV$^-$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in $\text{Fe}_{\text{Al}}$.

cond-mat.mtrl-sci↗

arXiv2022

Quasiparticle interference observation of the topologically non-trivial drumhead surface state in ZrSiTe

Drumhead surface states that link together loops of nodal lines arise in Dirac nodal-line semimetals as a consequence of the topologically non-trivial band crossings. We used low-temperature scanning tunneling microscopy and Fourier-transformed scanning tunneling spectroscopy to investigate the quasiparticle interference (QPI) properties of ZrSiTe. Our results show two scattering signals across the drumhead state resolving the energy-momentum relationship through the occupied and unoccupied energy ranges it is predicted to span. Observation of this drumhead state is in contrast to previous studies on ZrSiS and ZrSiSe, where the QPI was dominated by topologically trivial bulk bands and surface states. Furthermore, we observe a near $\mathbf{k} \rightarrow -\mathbf{k}$ scattering process across the $Γ$-point, enabled by scattering between the spin-split drumhead bands in this material.

cond-mat.mtrl-sci↗

arXiv2021

Topological surface Fermi arcs in the magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$

Very recently, the half-metallic compound Co$_3$Sn$_2$S$_2$ was predicted to be a magnetic WSM with Weyl points only 60 meV above the Fermi level ($E_F$). Owing to the low charge carrier density and large Berry curvature induced,Co$_3$Sn$_2$S$_2$ possesses both a large anomalous Hall conductivity (AHC) and a large anomalous Hall angle (AHA), which provide strong evidence for the existence of Weyl points in Co$_3$Sn$_2$S$_2$. In this work, we theoretically studied the surface topological feature of Co$_3$Sn$_2$S$_2$ and its counterpart Co$_3$Sn$_2$Se$_2$. By cleaving the sample at the weak Sn--S/Se bonds, one can achieve two different surfaces terminated with Sn and S/Se atoms, respectively. The resulting Fermi arc related states can range from the energy of the Weyl points to $E_F$--0.1 eV in the Sn-terminated surface. Therefore, it should be possible to observe the Fermi arcs in angle-resolved photoemission spectroscopy (ARPES) measurements. Furthermore, in order to simulate quasiparticle interference (QPI) in scanning tunneling microscopy (STM) measurements, we also calculated the joint density of states (JDOS) for both terminals. This work would be helpful for a comprehensive understanding of the topological properties of these two magnetic WSMs and further ARPES and STM measurements.

cond-mat.mtrl-sci↗

arXiv2020

Signature of an Ultrafast Photo-Induced Lifshitz Transition in the Nodal-Line Semimetal ZrSiTe

Here we report an ultrafast optical spectroscopic study of the nodal-line semimetal ZrSiTe. Our measurements reveal that, converse to other compounds of the family, the sudden injection of electronic excitations results in a strongly coherent response of an $A_{1g}$ phonon mode which dynamically modifies the distance between Zr and Te atoms and Si layers. "Frozen phonon" DFT calculations, in which band structures are calculated as a function of nuclear position along the phonon mode coordinate, show that large displacements along this mode alter the material's electronic structure significantly, forcing bands to approach and even cross the Fermi energy. The incoherent part of the time domain response reveals that a delayed electronic response at low fluence discontinuously evolves into an instantaneous one for excitation densities larger than $3.43 \times 10^{17}$ cm$^{-3}$. This sudden change of the dissipative channels for electronic excitations is indicative of an ultrafast Lifshitz transition which we tentatively associate to a change in topology of the Fermi surface driven by a symmetry preserving $A_{1g}$ phonon mode.

cond-mat.mtrl-sci↗

arXiv2020

Emerging chiral edge states from the confinement of a magnetic Weyl semimetal in Co$_3$Sn$_2$S$_2$

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.

cond-mat.str-el↗

arXiv2019

Influence of point defects on the electronic and topological properties of monolayer WTe$_2$

In some topological insulators, such as graphene and WTe$_2$, band inversion originates from chemical bonding and space group symmetry, in contrast to materials such as Bi$_2$Se$_3$, where the band inversion derives from relativistic effects in the atoms. In the former, band inversion is susceptible to changes of the chemical environment, e.g. by defects, while the latter are less affected by defects due to the larger energy scale associated with atomic relativistic effects. Motivated by recent experiments, we study the effect of Te-vacancies and Te-adatoms on the electronic properties of WTe$_2$. We find that the Te-vacancies have a formation energy of $2.21$ eV, while the formation energy of the Te-adatoms is much lower with $0.72$ eV. The vacancies strongly influence the band structure and we present evidence that band inversion is already reversed at the nominal composition of WTe$_{1.97}$. In contrast, we show that the adatoms do not change the electronic structure in the vicinity of the Fermi level and thus the topological properties. Our findings indicate that Te-adatoms should be present in thin films that are grown in a Te-rich environment, and we suggest that they have been observed in scanning tunneling microscopy experiments.

cond-mat.mtrl-sci↗

arXiv2019

Superconducting order parameter of the nodal-line semimetal NaAlSi

Nodal-line semimetals are topologically non-trivial states of matter featuring band crossings along a closed curve, i.e. nodal-line, in momentum space. Through a detailed analysis of the electronic structure, we show for the first time that the normal state of the superconductor NaAlSi, with a critical temperature of $T_{\rm c} \approx$ 7 K, is a nodal-line semimetal, where the complex nodal-line structure is protected by non-symmorphic mirror crystal symmetries. We further report on muon spin rotation experiments revealing that the superconductivity in NaAlSi is truly of bulk nature, featuring a fully gapped Fermi-surface. The temperature-dependent magnetic penetration depth can be well described by a two-gap model consisting of two $s$-wave symmetric gaps with $Δ_1 =$ 0.6(2) meV and $Δ_2 =$ 1.39(1) meV. The zero-field muon experiment indicates that time-reversal symmetry is preserved in the superconducting state. Our observations suggest that notwithstanding its topologically non-trivial band structure, NaAlSi may be suitably interpreted as a conventional London superconductor, while more exotic superconducting gap symmetries cannot be excluded. The intertwining of topological electronic states and superconductivity renders NaAlSi a prototypical platform to search for unprecedented topological quantum phases.

cond-mat.supr-con↗

arXiv2019

Modular Arithmetic with Nodal Lines: Drumhead Surface States in ZrSiTe

We study the electronic structure of the nodal line semimetal ZrSiTe both experimentally and theoretically. We find two different surface states in ZrSiTe - topological drumhead surface states and trivial floating band surface states. Using the spectra of Wilson loops, we show that a non-trivial Berry phase that exists in a confined region within the Brillouin Zone gives rise to the topological drumhead-type surface states. The $\mathbb{Z}_2$ structure of the Berry phase induces a $\mathbb{Z}_2$ 'modular arithmetic' of the surface states, allowing surface states deriving from different nodal lines to hybridize and gap out, which can be probed by a set of Wilson loops. Our findings are confirmed by \textit{ab-initio} calculations and angle-resolved photoemission experiments, which are in excellent agreement with each other and the topological analysis. This is the first complete characterization of topological surface states in the family of square-net based nodal line semimetals and thus fundamentally increases the understanding of the topological nature of this growing class of topological semimetals.

cond-mat.mes-hall↗

arXiv2019

Extremely high conductivity observed in the triple point topological metal MoP

Weyl and Dirac fermions have created much attention in condensed matter physics and materials science. Recently, several additional distinct types of fermions have been predicted. Here, we report ultra-high electrical conductivity in MoP at low temperature, which has recently been established as a triple point Fermion material. Here we show that the electrical resistivity is 6 n-ohm cm at 2 K with a large mean free path of 11 microns. de Haas-van Alphen oscillations reveal spin splitting of the Fermi surfaces. In contrast to noble metals with similar conductivity and number of carriers, the magnetoresistance in MoP does not saturate up to 9 T at 2 K. Interestingly, the momentum relaxing time of the electrons is found to be more than 15 times larger than the quantum coherence time. This difference between the scattering scales shows that momentum conserving scattering dominates in MoP at low temperatures.

cond-mat.mtrl-sci↗