arXiv subjects

Moritz M. Hirschmann

Publications and source records attributed to Moritz M. Hirschmann.

At least 19 recordsLinked to original sources

arXiv2026

Engineering Dirac interface states

We develop a low-energy theory of interface states in anisotropic multivalley Dirac systems whose masses and kinetic parameters are allowed to vary across an interface. For sharp interfaces, current-conserving matching conditions yield analytic expressions for the existence, localization and dispersion of the bound states. We show that the interface velocity is determined by the weighted tangential kinetic terms on the two sides of the seam. Their cancellation can suppress the linear velocity and generate an interface band that is flat to leading order near the projected Dirac point. For the special antisymmetric configuration in which both the Dirac mass and the tangential kinetic coefficient reverse sign with unchanged magnitude, the transparent sharp-interface solution is exactly dispersionless for all conserved momenta within the linear Dirac theory, while the surrounding bulk bands remain dispersive. We extend the theory to smooth interfaces, where the modified bound-state envelope changes the linear interface velocity through a spatial average of the tangential kinetic coefficient. We also investigate quadratic corrections in the kinetic $\sigma_x$ and $\sigma_y$ channels. To first order in their coefficients and through linear order in the interface momentum, these terms shift the interface-state energy but produce no additional correction to the linear velocity. Finally, we combine continuum and lattice models to show how interface modes from distinct valleys hybridize and how the resulting dispersions depend on microscopic interface properties. Our results establish design principles for controlling the dispersion, localization, and hybridization of Dirac interface states. We further examine two graphene-based mass-domain-wall models as experimentally inspired examples of dispersive copropagating and counterpropagating interface states.

cond-mat.mtrl-sci↗

arXiv2026

Collinear ferromagnetism with reduced moment length in kagome magnet Nd3Ru4Al12

We determine the magnetic ground state of the kagome lattice magnet Nd3Ru4Al12 by single-crystal neutron diffraction, supported by experiments with polarized neutrons. We identify this material as a collinear ferromagnet ("hex-FM") with uniform moment length mc = 2.1 {\mu}B/Nd and ordering vector Q = 0, in contrast to a previous, seminal report that proposed unequal moment lengths on two Nd sites, here called the "ortho-FM" state. Our analysis of the flipping ratio in polarized neutron scattering is consistent with the hex-FM state. The results provide a microscopic basis for understanding the large fluctuation-induced Hall and Nernst responses near TC = 41 K, as previously reported for Nd3Ru4Al12.

cond-mat.str-el↗

arXiv2026

Symmetry-Enforced Nodal $f$-Wave Magnets

Owing to their relevance for spintronics, electronic band splitting and spin-polarization textures in magnets are active areas of research. In non-collinear magnets, alternating spin textures can arise both for isolated bands and for intersecting band pairs with nodal splitting. This raises the question of whether $p,f,...$-wave magnets should be defined by their spin polarization or their band splitting. To resolve this ambiguity, we introduce spin-space symmetries that couple the spin polarization and splitting textures for all bands. Focusing on the nodal $f$-wave magnet, we construct a tight-binding model of itinerant electrons on a honeycomb bilayer coupled to a non-collinear magnetic texture. Analytic expressions for spin polarization and splitting reveal the dependence on hopping and exchange coupling. We predict a canting-induced spin conductivity arising from the nodal structure of the splitting. Furthermore, the $f$-wave magnet in the bulk can induce $p$-wave magnetism on the surface. This surface $p$-wave character leads to a bulk-forbidden Edelstein effect with $f$-wave anisotropy.

cond-mat.mes-hall↗

arXiv2025

Spiral-induced Anomalous Hall Effect from Odd-parity Spin-nodal Lines

Spin spirals represent a fundamental class of noncollinear yet coplanar magnetic structures that give rise to diverse emergent phenomena reflecting spin chirality. We investigate metallic systems hosting commensurate spin spirals and uncover an unconventional anomalous Hall effect (AHE) induced by spiral magnetism. The spin spiral introduces odd-parity spin splitting with polarization perpendicular to the helical plane, forming spin-nodal lines in the electronic structure. In the presence of spin-orbit coupling, we find that these nodal lines become gapped by finite magnetization, concentrating the Berry curvature near the gap and generating a distinctive AHE. We identify the interplay among the spin-orbit coupling, helical plane orientation, and magnetization direction as the key ingredient for this spiral-induced AHE, which is expected to occur across a wide range of materials hosting commensurate spin spirals.

cond-mat.mes-hall↗

arXiv2025

Topological Metal-Insulator Transition within the Ferromagnetic state

A major challenge in condensed matter physics is integrating topological phenomena with correlated electron physics to leverage both types of states for next-generation quantum devices. Metal-insulator transitions (MITs) are central to bridging these two domains while simultaneously serving as 'on-off' switches for electronic states. Here, we demonstrate how the prototypical material of K2Cr8O16 undergoes a ferromagnetic MIT accompanied by a change in band topology. Through inelastic x-ray and neutron scattering experiments combined with first-principles theoretical calculations, we demonstrate that this transition is not driven by a Peierls mechanism, given the lack of phonon softening. Instead, we establish the transition as a topological MIT within the ferromagnetic phase (topological-FM-MIT) with potential axionic properties, where electron correlations play a key role in stabilizing the insulating state. This work pioneers the discovery of a topological-FM-MIT and represents a fundamentally new class of topological phase transitions, revealing a unique pathway through which magnetism, topology, and electronic correlations interact.

cond-mat.str-el↗

arXiv2025

Quantum geometry and low-frequency optical conductivity of nodal planes

Nodal planes, two-dimensional symmetry-enforced band crossings, can carry a topological charge, similar to Weyl points. While the transport properties of Weyl points are well understood, those of nodal planes remain largely unexplored. These properties are influenced not only by the Berry curvature, but also by other quantum geometric quantities. In this work we study the quantum geometry - specifically the Berry curvature and quantum metric - and the linear optical conductivity of topological nodal planes. We introduce a low-energy model and investigate its low-frequency optical responses to determine the unique signatures of nodal planes. By comparing these findings to the optical response in a tight-binding model with a topological nodal plane, we observe consistent low-frequency behavior with a cubic power law. This paves the way for the experimental detection of nodal planes through optical conductivity measurements for which we suggest suitable materials, most promisingly the material group $X$Mo$_3$S$_3$ ($X$ = Rb, K, Cs).

cond-mat.mes-hall↗

arXiv2025

Metallic $p$-wave magnet with commensurate spin helix

Antiferromagnetic states with spin-split electronic structure give rise to novel spintronic, magnonic, and electronic phenomena despite (near-) zero net magnetization. The simplest odd-parity spin splitting - $p$-wave - was originally proposed to emerge from a collective instability in interacting electron systems. Recent theory identifies a distinct route to realise $p$-wave spin-split electronic bands without strong correlations, termed $p$-wave magnetism. Here we demonstrate an experimental realisation of a metallic $p$-wave magnet. The odd-parity spin splitting of delocalised conduction electrons arises from their coupling to an antiferromagnetic texture of localised magnetic moments: a coplanar spin helix whose magnetic period is an even multiple of the chemical unit cell, as revealed by X-ray scattering experiments. This texture breaks space inversion symmetry but preserves time-reversal ($T$) symmetry up to a half-unit-cell translation - thereby fulfilling the symmetry conditions for $p$-wave magnetism. Consistent with theoretical predictions, our $p$-wave magnet exhibits a characteristic anisotropy in the electronic conductivity. Relativistic spin-orbit coupling and a tiny spontaneous net magnetization further break $T$ symmetry, resulting in a giant anomalous Hall effect (AHE, $\sigma_{xy}>600\,$S/cm, Hall angle $>3\,\%$), for an antiferromagnet. Our model calculations show that the spin nodal planes found in the electronic structure of $p$-wave magnets are readily gapped by a small perturbation to induce the AHE.

cond-mat.str-el↗

arXiv2024

Weak $\mathbb{Z}_2$ Supertopology

Crystal symmetries can enforce all bands of a material to be topological, a property that is commonly referred to as ``supertopology". Here, we determine the symmetry-enforced $\mathbb{Z}_2$ supertopologies of non-magnetic centrosymmetric materials with weak and strong spin-orbit coupling (SOC). For weak (i.e., negligible) SOC, crystal symmetries can enforce Dirac nodal lines protected by a $\pi$-Berry phase, while for strong SOC, crystal symmetries can give rise to nontrival weak $\mathbb{Z}_2$ topologies in 2D subplanes of the 3D Brillouin zone. We catalogue all centrosymmetric space groups whose symmetries enforce these $\mathbb{Z}_2$ supertopologies. Suitable material realizations are identified and experimental signatures of the supertopologies, such as quantum spin Hall states, are being discussed.

cond-mat.mtrl-sci↗

arXiv2024

Lattice-commensurate skyrmion texture in a centrosymmetric breathing kagome magnet

Skyrmion lattices (SkL) in centrosymmetric materials typically have a magnetic period on the nanometer-scale, so that the coupling between magnetic superstructures and the underlying crystal lattice cannot be neglected. Here, we reveal the commensurate locking of a SkL to the atomic lattice in Gd$_3$Ru$_4$Al$_{12}$ via high-resolution resonant elastic x-ray scattering (REXS). Weak easy-plane magnetic anisotropy, demonstrated here by a combination of ferromagnetic resonance and REXS, penalizes placing a skyrmion core on a site of the atomic lattice. Under these conditions, a commensurate SkL, locked to the crystal lattice, is stable at finite temperatures -- but gives way to a competing incommensurate ground state upon cooling. We discuss the role of Umklapp-terms in the Hamiltonian for the formation of this lattice-locked state, its magnetic space group, the role of slight discommensurations, or (line) defects in the magnetic texture, and contrast our findings with the case of SkLs in noncentrosymmetric material platforms.

cond-mat.str-el↗

arXiv2024

Non-coplanar helimagnetism in the layered van-der-Waals metal DyTe$_3$

Magnetic materials with highly anisotropic chemical bonding can be exfoliated to realize ultrathin sheets or interfaces with highly controllable optical or spintronics responses, while also promising novel cross-correlation phenomena between electric polarization and the magnetic texture. The vast majority of these van-der-Waals magnets are collinear ferro-, ferri-, or antiferromagnets, with a particular scarcity of lattice-incommensurate helimagnets of defined left- or right-handed rotation sense, or helicity. Here we use polarized neutron scattering to reveal cycloidal, or conical, magnetic structures in DyTe$_3$, with coupled commensurate and incommensurate order parameters, where covalently bonded double-slabs of dysprosium square nets are separated by highly metallic tellurium layers. Based on this ground state and its evolution in a magnetic field as probed by small-angle neutron scattering (SANS), we establish a one-dimensional spin model with off-diagonal on-site terms, spatially modulated by the unconventional charge order in DyTe$_3$. The CDW-driven term couples to antiferromagnetism, or to the net magnetization in applied magnetic field, and creates a complex magnetic phase diagram indicative of competing interactions in an easily cleavable helimagnet. Our work paves the way for twistronics research, where helimagnetic layers can be combined to form complex spin textures on-demand, using the vast family of rare earth chalcogenides and beyond.

cond-mat.mtrl-sci↗

arXiv2023

Correlation Induced Magnetic Topological Phases in Mixed-Valence Compound SmB6

SmB6 is a mixed-valence compound with flat f-electron bands that have a propensity to magnetism. Here, using a realistic Gamma8 quartet model, we investigate the dynamical spin susceptibility and describe the in-gap collective mode observed in neutron scattering experiments. We show that as the Sm valence increases with pressure, the magnetic correlations enhance and SmB6 undergoes a first-order phase transition into a metallic antiferromagnetic state, whose symmetry depends on the model parameters. The magnetic orderings give rise to distinct band topologies: while the A-type order leads to an overlap between valence and conduction bands in the form of Dirac nodal lines, the G-type order has a negative indirect gap with weak Z2 indices. We also consider the spin polarized phase under a strong magnetic field, and find that it exhibits Weyl points as well as nodal lines close to the Fermi level. The magnetic phases show markedly different surface states and tunable bulk transport properties, with important implications for experiments. Our theory predicts that a magnetic order can be stabilized also by lifting the Gamma8 cubic symmetry, thus explaining the surface magnetism reported in SmB6.

cond-mat.str-el↗

arXiv2023

Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level

Two common difficulties in the design of topological quantum materials are that the desired features lie too far from the Fermi level and are spread over a too-large energy range. Doping-induced states at the Fermi level provide a solution, where nontrivial topological properties are enforced by the doping-reduced symmetry. To show this, we consider a regular placement of dopants in a lattice of space group (SG) 176 ($P6\text{}_3/m$), which reduces the symmetry to SG 143 ($P3$). Our two- and four-band models feature double Weyl points, Chern bands, Van Hove singularities, nontrivial multiband quantum geometry due to mixed orbital character, and singular flat bands. We relate these features to density-functional theory (DFT) calculations for dopant and vacancy bands of lead apatite Pb$_{10}($PO$_4)_6$O and Pb$_{10}($PO$_4)_6($OH$)_2$, the van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$, the semiconductor SiC, and the 2D dichalcogenide MoS$_2$.

cond-mat.mes-hall↗

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↗

arXiv2022

Creating and controlling Dirac fermions, Weyl fermions, and nodal lines in the magnetic antiperovskite Eu$_3$PbO

The band topology of magnetic semimetals is of interest both from the fundamental science point of view and with respect to potential spintronics and memory applications. Unfortunately, only a handful of suitable topological semimetals with magnetic order have been discovered so far. One such family that hosts these characteristics is the antiperovskites, A$_3$BO, a family of 3D Dirac semimetals. The A=Eu$^{2+}$ compounds magnetically order with multiple phases as a function of applied magnetic field. Here, by combining band structure calculations with neutron diffraction and magnetic measurements, we establish the antiperovskite Eu$_3$PbO as a new topological magnetic semimetal. This topological material exhibits a multitude of different topological phases with ordered Eu moments which can be easily controlled by an external magnetic field. The topological phase diagram of Eu$_3$PbO includes an antiferromagnetic Dirac phase, as well as ferro- and ferrimagnetic phases with both Weyl points and nodal lines. For each of these phases, we determine the bulk band dispersions, the surface states, and the topological invariants by means of $\textit{ab-initio}$ and tight-binding calculations. Our discovery of these topological phases introduces Eu$_3$PbO as a new platform to study and manipulate the interplay of band topology, magnetism, and transport.

cond-mat.mtrl-sci↗

arXiv2022

Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry

We discover three-dimensional intertwined Weyl phases, by developing a theory to create topological phases. The theory is based on intertwining existing topological gapped and gapless phases protected by the same crystalline symmetry. The intertwined Weyl phases feature both unconventional Weyl semimetallic (monopole charge>1) and higher-order topological phases, and more importantly, their exotic intertwining. While the two phases are independently stabilized by the same symmetry, their intertwining results in the specific distribution of them in the bulk. The construction mechanism allows us to combine different kinds of unconventional Weyl semimetallic and higher-order topological phases to generate distinct phases. Remarkably, on 2D surfaces, the intertwining causes the Fermi-arc topology to change in a periodic pattern against surface orientation. This feature provides a characteristic and feasible signature to probe the intertwining Weyl phases. Moreover, we provide guidelines for searching candidate materials, and elaborate on emulating the intertwined double-Weyl phase in cold-atom experiments.

cond-mat.mes-hall↗

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

Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet

Following over a decade of intense efforts to enable major progress in spintronics devices and quantum information technology by means of materials in which the electronic structure exhibits non-trivial topological properties, three key challenges are still unresolved. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, to identify generic topological degeneracies in large, multi-sheeted Fermi surfaces. Combining de Haas - van Alphen spectroscopy with density functional theory and band-topology calculations, we report here that the non-symmorphic symmetries in ferromagnetic MnSi generate nodal planes (NPs), which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs on the FS of MnSi that may be controlled with a magnetic field suggests the existence of similar properties, amenable for technological exploitation, in a large number of materials.

cond-mat.str-el↗

arXiv2021

Network of topological nodal planes, multifold degeneracies, and Weyl points in CoSi

We report the identification of symmetry-enforced nodal planes (NPs) in CoSi providing the missing topological charges in an entire network of band-crossings comprising in addition multifold degeneracies and Weyl points, such that the fermion doubling theorem is satisfied. In our study we have combined measurements of Shubnikov-de Haas (SdH) oscillations in CoSi with material-specific calculations of the electronic structure and Berry curvature, as well as a general analysis of the band topology of space group (SG) 198. The observation of two nearly dispersionless SdH frequency branches provides unambiguous evidence of four Fermi surface sheets at the R point that reflect the symmetry-enforced orthogonality of the underlying wave functions at the intersections with the NPs. Hence, irrespective of the spin-orbit coupling strength, SG198 features always six- and fourfold degenerate crossings at R and $Γ$ that are intimately connected to the topological charges distributed across the network.

cond-mat.str-el↗