Nontrivial Band Topology Research Articles

Pressure engineering of intertwined phase transitions in lanthanide monopnictide NdSb

Coexistence of non-trivial band topology and intrinsic magnetic order not only leads to emergent phenomena but also allows for the tunability of the exotic properties from different degrees of freedom. By performing transport measurements at synergetic extreme conditions, here we report on pressure engineering of intertwined structural, magnetic, and topological phase transitions in an antiferromagnetic Dirac semimetal NdSb. We show that the original antiferromagnetic state is strengthened in the low-pressure region while destabilized upon further compression close to the critical pressure where a structural transition from Fm-3m phase to P4/mmm phase takes place at PC∼18 GPa, forming a yurt-shaped evolution in response to magnetic field, pressure and temperature. Concomitant with the structural transition, NdSb simultaneously carries on a magnetic transition to the ferromagnetic state. Moreover, theoretical calculations unravel that the ferromagnetic tetragonal phase presents nontrivial features of Weyl fermions. These findings offer new important insight into the microscopic interplay among lattice, spin, and relativistic fermions in lanthanide monopnictides.

Nontrivial band topology coupled thermoelectrics in VSe2/MoSe2 van der Waals magnetic Weyl semimetal

The correlation between topological and thermoelectrics promotes numerous interesting electronic phenomena and sets the stage for efficient thermopower devices. Herein, we report nontrivial band topology of 1T–VSe2/1H–MoSe2 van der Waals system and also probe its thermoelectric (TE) characteristics on the basis of first-principle calculations. The crossover of bands, which creates a close loop near Fermi level along M–K high symmetry points, gets inverted at former crossing points of bands, under spin–orbit coupling effect. The calculated Chern Number C = 1 supports the nontrivial band topology whereas the broken time reversal symmetry asserts its magnetic Weyl semimetallic behavior. The nontrivial band topology falls under the category of Type-I Weyl band crossing. We delve into the TE characteristics of the proposed topological material by employing constant relaxation time approximation. The heterostructure shows high electrical conductivity of order 106 S m−1 at both 300 K and 1200 K, and a low magnitude of Seebeck coefficient (S) value of 79.3 μV K−1 near room temperature. Such interplay between the topological phase and TE characteristics can lay foundation for next-generation topological-TE devices.

Twisted nodal wires and three-dimensional quantum spin Hall effect in distorted square-net compounds

Recently, square-net materials have attracted lots of attention for the Dirac semimetal phase with negligible spin-orbit coupling (SOC) gap, e.g., ZrSiS/LaSbTe and ${\mathrm{CaMnSb}}_{2}$. In this paper, we demonstrate that the Jahn-Teller effect enlarges the nontrivial SOC gap in the distorted structure, e.g., LaAsS and ${\mathrm{SrZnSb}}_{2}$. Its distorted $X$ square-net layer ($X=$ P, As, Sb, Bi) resembles a quantum spin Hall (QSH) insulator. Since these QSH layers are simply stacked in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ direction and weakly coupled, three-dimensional QSH effect can be expected in these distorted materials, such as insulating compounds ${\mathrm{CeAs}}_{1+x}{\mathrm{Se}}_{1\ensuremath{-}y}$ and ${\mathrm{EuCdSb}}_{2}$. Our detailed calculations show that it hosts two twisted nodal wires without SOC [each consists of two noncontractible time-reversal symmetry- and inversion symmetry-protected nodal lines touching at a fourfold degenerate point], while with SOC it becomes a topological crystalline insulator with symmetry indicators $(000;2)$ and mirror Chern numbers $(0,0)$. The nontrivial band topology is characterized by a generalized spin Chern number ${C}_{s+}=2$ when there is a gap between two sets of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{s}}_{x}$ eigenvalues. The nontrivial topology of these materials can be well reproduced by our tight-binding model and the calculated spin Hall conductivity is quantized to ${\ensuremath{\sigma}}_{yz}^{x}=(\frac{\ensuremath{\hbar}}{e})\frac{{G}_{x}{e}^{2}}{\ensuremath{\pi}h}$ with ${G}_{x}$ a reciprocal lattice vector.

Pressure-induced superconductivity and nontrivial band topology in compressed γ-InSe

We performed high-pressure electrical transport and Raman measurements on a two-dimensional rhombohedral semiconductor \ensuremath{\gamma}-InSe. Our results confirm two structural phase transitions at high pressure. More interestingly, a domelike superconducting transition with maximum ${T}_{c}$ around 2.3 K is discovered when the compound transforms to the cubic CsCl phase above 40 GPa. Our first-principles calculations indicate that the high-pressure superconducting phase possesses nontrivial topological band structure in the vicinity of the Fermi level. These results show that the physical properties in this material strongly depend on its structure, which provides insights into the interplay between superconductivity and topological physics. Our work suggests promising emergent phenomena in this material and other related III-VI semiconductors under high-pressure conditions.

Ferromagnetic MnBi4Te7 obtained with low-concentration Sb doping: A promising platform for exploring topological quantum states

The tuning of the magnetic phase, chemical potential, and structure is crucial to observe diverse exotic topological quantum states in $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{m}$ $(m=0--3)$. Here we show a ferromagnetic (FM) phase with a chiral crystal structure in $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{4}{\mathrm{Te}}_{7}$, obtained via tuning the growth conditions and Sb concentration. Unlike previously reported $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{4}{\mathrm{Te}}_{7}$, which exhibits FM transitions only at high Sb doping levels, our samples show FM transitions $({T}_{\mathrm{C}}=13.5\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ at 15%--27% doping levels. Furthermore, our single-crystal x-ray-diffraction structure refinements find Sb doping leads to a chiral structure with the space group of $P3$, contrasted with the centrosymmetric $P\overline{3}m1$ crystal structure of the parent compound ${\mathrm{MnBi}}_{4}{\mathrm{Te}}_{7}$. Through angle-resolved photoemission spectroscopy measurements, we also demonstrated that the nontrivial band topology is preserved in the Sb-doped FM samples. Given that the nontrivial band topology of this system remains robust for low Sb doping levels, our success in making FM $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{4}{\mathrm{Te}}_{7}$ with $x=0.15$, 0.175, 0.2, and 0.27 paves the way for realizing the predicted topological quantum states, such as the axion insulator and Weyl semimetals. Additionally, we also observed magnetic glassy behavior in both antiferromagnetic ${\mathrm{MnBi}}_{4}{\mathrm{Te}}_{7}$ and FM $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{4}{\mathrm{Te}}_{7}$ samples, which we believe originates from cluster spin-glass phases coexisting with long-range antiferromagnetic/FM orders. We have also discussed how the antisite Mn ions impact the interlayer magnetic coupling and how FM interlayer coupling is stabilized in this system.

Valley-polarized quantum anomalous Hall insulator in monolayer

The coexistence of an intrinsic ferrovalley (FV) and nontrivial band topology attracts intensive interest, both for its fundamental physics and for its potential applications, namely a valley-polarized quantum anomalous Hall insulator (VQAHI). Here, based on first-principles calculations by using a generalized gradient approximation plus a U (GGA + U) approach, the VQAHI induced by electronic correlation or strain can occur in monolayer . For perpendicular magnetic anisotropy (PMA), the FV to half-valley-metal (HVM) to quantum anomalous Hall (QAH) to HVM to FV transitions can be driven by increasing the electron correlation U. However, there are no special QAH states and valley polarization for in-plane magnetic anisotropy. By calculating the actual magnetic anisotropy energy (MAE), the VQAHI can indeed exist between two HVM states due to PMA, a unit Chern number/a chiral edge state and spontaneous valley polarization. The increasing U can induce VQAHI, which can be explained by a sign-reversible Berry curvature or a band inversion between d xy / and orbitals. Even though the real U falls outside the range, the VQAHI can be achieved by strain. Taking U = 2.25 eV as a concrete case, the monolayer can change from a common ferromagentic (FM) semiconductor to VQAHI under about 0.985 compressive strain. It is noted that the edge states of VQAHI are chiral-spin-valley locking, which can achieve complete spin and valley polarizations for low-dissipation electronic devices. Both the energy band gap and the valley splitting of VQAHI in monolayer are higher than the thermal energy of room temperature (25 meV), which is key for device applications at room temperature . It is found that the electronic correlation or strain have important effects on the Curie temperature of monolayer . These results can be readily extended to other monolayer (M = Ru, Os; X/Y = Cl, Br I). Our work emphasizes the importance of electronic correlation and PMA to study FV materials, and provides a pathway to realize VQAHI.

Layered opposite Rashba spin-orbit coupling in bilayer graphene: Loss of spin chirality, symmetry breaking, and topological transition

Inversion symmetry in bilayer graphene allows for layered opposite Rashba spin-orbit coupling (LO-RSOC) -- the situation when the RSOC has the same magnitude but the opposite sign in two coupled spatially separated layers. We show that the LO-RSOC results in the loss of spin chirality in the momentum space, in contrast to the common uniform RSOC. This chirality loss makes it difficult to experimentally establish whether the LO-RSOC (on the scale of 10 meV) exists, because the band structure is insensitive to it. To solve this problem, we propose to identify the LO-RSOC either by gating to break the inversion symmetry or by magnetic field to break the time-reversal symmetry. Remarkably, we observe the transition between trivial and non-trivial band topology as the system deviates from the LO Rashba state. Ab inito calculations suggest that bilayer graphene encapsulated by two monolayers of Au is a candidate to be a LO Rashba system.

Observation of Reentrant Correlated Insulators and Interaction-Driven Fermi-Surface Reconstructions at One Magnetic Flux Quantum per Moiré Unit Cell in Magic-Angle Twisted Bilayer Graphene.

The discovery of flat bands with nontrivial band topology in magic-angle twisted bilayer graphene (MATBG) has provided a unique platform to study strongly correlated phenomena including superconductivity, correlated insulators, Chern insulators, and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hofstadter spectrum. Here, we report on a detailed magnetotransport study of a MATBG device in external magnetic fields of up to B=31 T, corresponding to one magnetic flux quantum per moiré unit cell Φ_{0}. At Φ_{0}, we observe reentrant correlated insulators at a flat band filling factors of ν=+2 and of ν=+3, and interaction-driven Fermi-surface reconstructions at other fillings, which are identified by new sets of Landau levels originating from these. These experimental observations are supplemented by theoretical work that predicts a new set of eight well-isolated flat bands at Φ_{0}, of comparable band width, but with different topology than in zero field. Overall, our magnetotransport data reveal a qualitatively new Hofstadter spectrum in MATBG, which arises due to the strong electronic correlations in the reentrant flat bands.

Anomalous thermoelectric effects and quantum oscillations in the kagome metal CsV3Sb5

The kagome metal compounds $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\text{K}$, Rb, and Cs) feature a wealth of phenomena including nontrivial band topology, charge density wave (CDW), and superconductivity. One intriguing property is the time-reversal symmetry breaking in the CDW state without local moments, which leads to anomalous transport responses. Here, we report the investigation of magnetothermoelectric effects on high-quality ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ single crystals. A large anomalous Nernst effect (ANE) is observed at temperatures below 30 K and can be enhanced by the high mobility. Multiple Fermi surfaces with small effective masses are revealed by quantum oscillations in the Nernst and Seebeck signals. Furthermore, we discover a magnetic breakdown effect across the two smallest Fermi surfaces, with a gap around 20 meV between them. We propose that the two Fermi surfaces are split from a Dirac band by the CDW gap. These results indicate the large ANE originates from the CDW modulated nontrivial band structure as well as the extrinsic contributions. A second phase transition below the CDW transition temperature is also suggested by the strange temperature dependence of the ANE.

Theory of phonon instabilities in Weyl semimetals at high magnetic fields

The behavior of three-dimensional (3D) semimetals under strong magnetic fields is a topic of recurring interest in condensed matter physics. Recently, the advent of Weyl and Dirac semimetals has brought about an interesting platform for potentially uncovering phases of matter that combine nontrivial band topology and interactions. While electronic instabilities of such semimetals at strong magnetic fields have been explored theoretically and experimentally, the role of electron-phonon interactions therein has been largely neglected. In this paper, we study the interplay of electron-electron and electron-phonon interactions in a minimal two-node model of Weyl semimetal. Using a Kadanoff-Wilson renormalization group approach, we analyze lattice (Peierls) instabilities emerging from chiral and nonchiral Landau levels as a function of the magnetic field. We consider both the adiabatic and the nonadiabatic phonon regimes, in the presence or in the absence of improper symmetries that relate Weyl nodes of opposite chirality. We find that (i) the Cooper channel, often neglected in recent studies, can prevent purely electronic instabilities while enabling lattice instabilities that are not Bardeen-Cooper-Schrieffer-like; (ii) breaking the improper symmetry that relates the two Weyl nodes suppresses the Cooper channel, thereby increasing the critical temperature for the lattice instability; (iii) in the adiabatic phonon regime, lattice instabilities can preempt purely electronic instabilities; (iv) pseudoscalar phonons are more prone to undergo a Peierls instability than scalar phonons. In short, our study emphasizes the importance of taking electron-phonon interactions into account for a complete understanding of interacting phases of matter in Dirac and Weyl semimetals at high magnetic fields.

Pressure-induced superconductivity in the noncentrosymmetric Weyl semimetals LaAlX (X=Si,Ge)

In topological materials, Dirac fermions can split into two Weyl fermions with opposite chiralities due to the breaking of space-inversion symmetry, while in noncentrosymmetric superconductors, novel superconducting electron pairing mechanisms arise because of the antisymmetric spin-orbit coupling. In this work, we report the pressure-introduced superconductivity in a typical noncentrosymmetric Weyl semimetal $\mathrm{LaAl}X$ ($X=\mathrm{Si}$ and Ge). Superconductivity was observed at around 65 GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum ${T}_{\mathrm{c}}$ of 2.5 K (2.1 K) for LaAlSi (LaAlGe). Furthermore, the application of pressure does not destroy the nontrivial band topology of LaAlSi up to 80.4 GPa, making such materials potential candidates for realizing topological superconductivity. Our report of superconductivity in $\mathrm{LaAl}X$ ($X=\mathrm{Si}$ and Ge) will provide critical insight in noncentrosymmetric superconductors and stimulate further study on superconductivity in Weyl semimetals.

Quantum Sensing and Imaging of Spin-Orbit-Torque-Driven Spin Dynamics in the Non-Collinear Antiferromagnet Mn3 Sn.

Novel non-collinear antiferromagnets with spontaneous time-reversal symmetry breaking, non-trivial band topology, and unconventional transport properties have received immense research interest over the past decade due to their rich physics and enormous promise in technological applications. One of the central focuses in this emerging field is exploring the relationship between the microscopic magnetic structure and exotic material properties. Here, nanoscale imaging of both spin-orbit-torque-induced deterministic magnetic switching and chiral spin rotation in non-collinear antiferromagnet Mn3 Sn films using nitrogen-vacancy (NV) centers are reported. Direct evidence of the off-resonance dipole-dipole coupling between the spin dynamics in Mn3 Sn and proximate NV centers is also demonstrated by NV relaxometry measurements. These results demonstrate the unique capabilities of NV centers in accessing the local information of the magnetic order and dynamics in these emergent quantum materials and suggest new opportunities for investigating the interplay between topology and magnetism in a broad range of topological magnets.

Robust Tunable Large-Gap Quantum Spin Hall States in Monolayer Cu2S on Insulating Substrates.

Quantum spin Hall (QSH) insulators with large band gaps and dissipationless edge states are of both technological and scientific interest. Although numerous two-dimensional (2D) systems have been predicted to host the QSH phase, very few of them harbor large band gaps and retain their nontrivial band topology when they are deposited on substrates. Here, based on a first-principles analysis with hybrid functional calculations, we investigated the electronic and topological properties of inversion-asymmetric monolayer copper sulfide (Cu2S). Interestingly, we found that monolayer Cu2S possesses an intrinsic QSH phase, Rashba spin splitting, and a large band gap of 220 meV that is suitable for room-temperature applications. Most importantly, we constructed heterostructures of a Cu2S film on PtTe2, h-BN, and Cu(111) substrates and found that the topological properties remain preserved upon an interface with these substrates. Our findings suggest Cu2S as a possible platform to realize inversion-asymmetric QSH insulators with potential applications in low-dissipation electronic devices.

Microscopic evidence for anisotropic multigap superconductivity in the CsV3Sb5 kagome superconductor

The recently discovered kagome superconductor CsV3Sb5 (Tc ≃ 2.5 K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report anisotropic superconducting properties of CsV3Sb5 by means of transverse-field muon spin rotation (μSR) experiments. The fits of temperature dependences of in-plane and out-of-plane components of the magnetic penetration depth suggest that the superconducting order parameter may have a two-gap (s + s)-wave symmetry. The multiband nature of superconductivity could be further supported by the different temperature dependences of the anisotropic magnetic penetration depth γλ(T) and upper critical field {gamma }_{{{{{rm{B}}}}}_{{{{rm{c}}}}2}}(T). The relaxation rates obtained from zero field μSR experiments do not show noticeable change across the superconducting transition, indicating that superconductivity does not break time reversal symmetry.

Electron-phonon coupling in the charge density wave state of CsV3Sb5

Metallic materials with kagome lattice structure are interesting because their electronic structures can host flat bands, Dirac cones, and van Hove singularities, resulting in strong electron correlations, nontrivial band topology, charge density wave (CDW), and unconventional superconductivity. Recently, kagome lattice compounds AV$_3$Sb$_5$ (A = K, Rb, Cs) are found to have intertwined CDW order and superconductivity. The origin of the CDW has been suggested to be purely electronic, arising from Fermi-surface instabilities of van Hove singularity (saddle point) near the M points. Here we use neutron scattering experiments to demonstrate that the CDW order in CsV$_3$Sb$_5$ is associated with static lattice distortion and a sudden hardening of the B3u longitudinal optical phonon mode, thus establishing that electron-phonon coupling must also play an important role in the CDW order of AV$_3$Sb$_5$.

Higher-order topological states in locally resonant elastic metamaterials

Higher-order topological insulators (HOTIs), capable of hosting topological states over multiple dimensionalities, have received considerable attention recently, providing unprecedented platforms for robust wave manipulation. Aiming at applications of HOTIs for integrated sensing, energy harvesting, or control of structural vibration propagation, challenges remain in achieving topological states at low frequencies with ample flexibility and tunability. Here, we report the theoretical modeling and experimental realization of HOTIs in elastic locally resonant metamaterials (LRMs). By exploring the interplay between local resonance couplings and nontrivial band topology, a variety of higher-order topological corner states (TCSs) are constructed in deep sub-wavelength regime with high efficiency in energy confinement. More importantly, we reveal that the TCSs are dependent on localization mechanisms of interacting sites at interfaces, which endows our HOTIs with unique frequency-selective and dimension-switching abilities. We further design complex domain walls to demonstrate the TCSs can be selectively switched on at desired frequencies or geometric corners. Our findings not only offer effective routes for the design of deep sub-wavelength topological devices but also enrich the understandings of higher-order topological physics that can be extended to other classic systems.

Large Magnetic Gap in a Designer Ferromagnet-Topological Insulator-Ferromagnet Heterostructure.

Combining magnetism and nontrivial band topology gives rise to quantum anomalous Hall (QAH) insulators and exotic quantum phases such as the QAH effect where current flows without dissipation along quantized edge states. Inducing magnetic order in topological insulators via proximity to a magnetic material offers a promising pathway toward achieving the QAH effect at a high temperature for lossless transport applications. One promising architecture involves a sandwich structure comprising two single-septuple layers (1SL) of MnBi2 Te4 (a 2D ferromagnetic insulator) with ultrathin few quintuple layer (QL) Bi2 Te3 in the middle, and it is predicted to yield a robust QAH insulator phase with a large bandgap greater than 50 meV. Here, the growth of a 1SL MnBi2 Te4 /4QL Bi2 Te3 /1SL MnBi2 Te4 heterostructure via molecular beam epitaxy is demonstrated and the electronic structure probed using angle-resolved photoelectron spectroscopy. Strong hexagonally warped massive Dirac fermions and a bandgap of 75 ± 15 meV are observed. The magnetic origin of the gap is confirmed by the observation of the exchange-Rashba effect, as well as the vanishing bandgap above the Curie temperature, in agreement with density functional theory calculations. These findings provide insights into magnetic proximity effects in topological insulators and reveal a promising platform for realizing the QAH effect at elevated temperatures.

Euler-obstructed Cooper pairing: Nodal superconductivity and hinge Majorana zero modes

Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in 3D PT-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where PT is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is time-reversal invariant and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models. Our work presents the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing.

Statistical modeling of epitaxial thin films of an intrinsic antiferromagnetic topological insulator

Synthesis of materials demands structural analysis tools suited to the particularities of each system. Van der Waals (vdW) materials are fundamental in emerging technologies of spintronics and quantum information processing. In particular, topological insulators and, more recently, materials that allow the phenomenological exploration of the combination of non-trivial electronic band topology and magnetism. Weak vdW forces between atomic layers give rise to compositional fluctuations and structural disorder that are difficult to control, even in a typical topological insulator such as the binary compound Bi2Te3. The addition of a third element, as in MnBi2Te4, makes the epitaxy of these materials even more chaotic. In this work, statistical modeling of MnxBi2Te3+x film structures is described. It allows the simulation of X-ray diffraction in disordered MnBi2Te4/Bi2Te3 heterostructures, a necessary step towards controlling the epitaxial growth of topological insulators with intrinsic magnetic properties. On top of this, the diffraction simulation method used here can be readily applied as a general tool in the field of materials design based on stacking of vdW bonded layers of distinct elements.

A topological kagome magnet in high entropy form

Topological kagome magnets RMn6Sn6 (R = rare earth element) attract numerous interests due to their non-trivial band topology and room-temperature magnetism. Here, we report a high entropy version of kagome magnet, (Gd0.38Tb0.27Dy0.20Ho0.15)Mn6Sn6. Such a high entropy material exhibits multiple spin reorientation transitions, which is not seen in all the related parent compounds and can be understood in terms of competing magnetic interactions enabled by high entropy. Furthermore, we also observed an intrinsic anomalous Hall effect, indicating that the high entropy phase preserves the non-trivial band topology. These results suggest that high entropy may provide a route to engineer the magnetic structure and expand the horizon of topological materials.