# Topological matter

• Article
| Open Access

### Magnetic topological quantum chemistry

The band topology of nonmagnetic crystals can be characterized by Topological Quantum Chemistry (TQC), whereas the band topology of magnetic crystals remains unexplored. Here, the authors extend TQC to the magnetic space groups to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids.

• Luis Elcoro
• , Benjamin J. Wieder
•  & B. Andrei Bernevig
• Article
| Open Access

### Magneto-optical spectroscopy on Weyl nodes for anomalous and topological Hall effects in chiral MnGe

Previous work has proposed that the anomalous and topological Hall effects, associated with Weyl nodes, should have a signature in optical conductivity. Here, using THz optical spectroscopy, the authors assign these two effects to optical conductivity resonances, arising near band anti-crossings, in thin films of MnGe.

• Y. Hayashi
• , Y. Okamura
•  & Y. Takahashi
• Article
| Open Access

### Dynamical symmetry indicators for Floquet crystals

A general theory for Floquet topology applicable to all crystalline symmetry groups is lacking. Here, the authors propose such a theory for noninteracting Floquet crystals and predict an inversion-protected Floquet higher-order topological phase with anomalous chiral hinge modes.

• Jiabin Yu
• , Rui-Xing Zhang
•  & Zhi-Da Song
• Article
| Open Access

### Exceptional topological insulators

Three-dimensional topological insulators have become a research focal point on topological quantum matter. Here, the authors propose the non-Hermitian analogue, the exceptional topological insulator, with anomalous surface states only existing within the topological bulk embedding.

• M. Michael Denner
• , Anastasiia Skurativska
•  & Titus Neupert
• Article
| Open Access

### Quantum anomalous Hall edge channels survive up to the Curie temperature

The quantum anomalous Hall effect has so far been limited to temperature of the order of 20 mK. Here, Fijalkowski et al. report the existence of chiral edge channels up to the Curie temperature of bulk ferromagnetism of the magnetic topological insulator with a multi-terminal Corbino geometry.

• Kajetan M. Fijalkowski
• , Nan Liu
•  & Laurens W. Molenkamp
• Article
| Open Access

### Topological phase transition in chiral graphene nanoribbons: from edge bands to end states

Graphene nanoribbons are potential systems for engineering topological phases of matter, but the pre-required gapped phases are difficult to find. Here, the authors show that chiral graphene nanoribbons undergo a transition from metallic to topological insulators, and then to trivial band insulators as they are narrowed down to nanometer widths.

• Jingcheng Li
• , Sofia Sanz
•  & Jose Ignacio Pascual
• Article
| Open Access

### Realization of topological Mott insulator in a twisted bilayer graphene lattice model

Magic-angle twisted bilayer graphene exhibits a quantum anomalous Hall effect at 3/4 filling; however, its mechanism is debated. Here, the authors show that such a phase can be realized in a lattice model of twisted bilayer graphene in the strong coupling limit, and interpret the results in terms of a topological Mott insulator phase.

• Bin-Bin Chen
• , Yuan Da Liao
•  & Zi Yang Meng
• Article
| Open Access

### Evidence of two-dimensional flat band at the surface of antiferromagnetic kagome metal FeSn

Transition metal kagome compounds have been shown to host flat bands in their bulk electronic spectrum. Here, using planar tunnelling spectroscopy supported by first-principles calculations, the authors report the signature of a novel type of flat band at the surface of antiferromagnetic kagome metal FeSn.

• Minyong Han
• , Hisashi Inoue
•  & Joseph G. Checkelsky
• Article
| Open Access

### Design and realization of topological Dirac fermions on a triangular lattice

Atomic monolayers of large-gap quantum spin Hall insulators are challenging to synthesize. Here, the authors realize massive Dirac fermions emerging from Bloch wave-function interference on a triangular lattice and achieve topologically non-trivial domains with unprecedented spatial extension.

• Maximilian Bauernfeind
• , Jonas Erhardt
•  & Giorgio Sangiovanni
• Article
| Open Access

### Observation of higher-order non-Hermitian skin effect

Though non-Hermitian physics has contributed toward the advance of research in quantum, electronic and classical systems, previous work focused on zero- or one-dimensional systems. Here, the authors report higher-order non-Hermitian skin effects in a 2D acoustic higher-order topological insulator.

• Xiujuan Zhang
• , Yuan Tian
•  & Yan-Feng Chen
• Article
| Open Access

### Fractionalized conductivity and emergent self-duality near topological phase transitions

Conventional quantum particles can break up into fractionalized excitations under the right conditions; however, their direct experimental observation is challenging. Here, the authors predict strong optical conductivity signatures of such excitations in the vicinity of a topological phase transition.

• Yan-Cheng Wang
• , Meng Cheng
•  & Zi Yang Meng
• Article
| Open Access

### Quantized classical response from spectral winding topology

Quantized response has so far eluded classical system beyond linear response theory. Here, the authors predict that a quantized classical response, arising from fundamental mathematical properties of the Green’s function, shows up in steady-state response of a non-Hermitian system without invoking a linear response theory.

• Linhu Li
• , Sen Mu
•  & Jiangbin Gong
• Article
| Open Access

### Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under low heat flow

Skyrmions are a type of topological spin texture that great potential across a wide variety of technological applications. Here, Yu et al. study the thermally driven motion of Skyrmions and find a minimum temperature gradient for the motion of skyrmions two orders of magnitude smaller than for domain walls.

• Xiuzhen Yu
• , Fumitaka Kagawa
•  & Yoshinori Tokura
• Article
| Open Access

### Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene

Twisted monolayer-bilayer graphene is an attractive platform to study the interplay between topology, magnetism and correlations in the flat bands. Here, using electrical transport measurements, the authors uncover a rich correlated phase diagram and identify a new insulating state that can be explained by intervalley coherence with broken time reversal symmetry.

• Minhao He
• , Ya-Hui Zhang
•  & Matthew Yankowitz
• Article
| Open Access

### Optical N-invariant of graphene’s topological viscous Hall fluid

Graphene is the archetype for realizing two-dimensional topological phases of matter. Here, the authors introduce a new topological classification connected to polarization transport, where the topological number is revealed in the spatiotemporal dispersion of the susceptibility tensor.

• Todd Van Mechelen
• , Wenbo Sun
•  & Zubin Jacob
• Article
| Open Access

### Guided accumulation of active particles by topological design of a second-order skin effect

Sustainable strategies for shepherding active particles are at the heart of many prospective applications. Here, Palacios et al. use the emerging topological properties of a microfluidic maze array to passively guide self-propelled colloids from the interior to the edges of the device.

• Lucas S. Palacios
• , Serguei Tchoumakov
• Article
| Open Access

### Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator

The antiferromagnetic topological insulator MnBi2Te4 exhibits Chern and axion insulator phases at low magnetic field; however, its behaviour in high magnetic field has remained unexplored. Here, using transport measurements at high magnetic field, the authors report a zero Hall plateau composed of two counter-propagating edge channels.

• Chang Liu
• , Yongchao Wang
•  & Yayu Wang
• Article
| Open Access

### Large linear non-saturating magnetoresistance and high mobility in ferromagnetic MnBi

Ferromagnetic systems rarely display a large or non-saturating magnetoresistance, due to the low Fermi velocity of the predominant charge carrier. Here, the authors show that MnBi, a ferromagnet, bucks this trend, showing both large and non-saturating magnetoresistance, and high charge carrier motilities.

• Yangkun He
• , Jacob Gayles
•  & Claudia Felser
• Article
| Open Access

### Evidence for higher order topology in Bi and Bi0.92Sb0.08

The experimental realization of higher order topological insulator (HOTI) in solid state materials remains elusive. Here, Aggarwal et al. reveal hinge states on three edges of both Bi and Bi0.92Sb0.08 (110) islands, supporting them as a class of HOTI.

• Leena Aggarwal
• , Penghao Zhu
• Article
| Open Access

### Experimental observation of topological Z2 exciton-polaritons in transition metal dichalcogenide monolayers

In this work light and matter have been coupled in a strong interaction between exciton resonances and topological photonic bands. The authors herein demonstrate a Z2 spin-Hall topological polaritonic phase enabling new coupling schemes in valleytronics and spintronics.

• Mengyao Li
• , Ivan Sinev
•  & Alexander B. Khanikaev
• Article
| Open Access

### Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co3Sn2S2

Magnetic Weyl semimetals in the 2D limit may behave like 2D Chern insulators and host the quantum anomalous Hall effect at high temperatures. Here, the authors report the observation of linearly dispersing topological states confined to the edges of the kagome Co3Sn terraces in the magnetic Weyl system Co3Sn2S2.

• Sean Howard
• , Lin Jiao
• Article
| Open Access

### Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

Despite the discovery of Majorana zero modes (MZM) in iron-based superconductors, sample inhomogeneity may destroy MZMs during braiding. Here, authors observe MZM in impurity-assisted vortices due to tuning of the bulk Dirac fermions in a homogeneous superconductor LiFeAs.

• Lingyuan Kong
• , Lu Cao
•  & Hong Ding
• Article
| Open Access

### Spin-valley locking and bulk quantum Hall effect in a noncentrosymmetric Dirac semimetal BaMnSb2

Valley dependent spin polarization called spin-valley locking appears in absence of magnetism but it is limited to rare examples of transition metal dichalcogenides. Here, the authors report evidence of spin-valley locking and stacked quantum Hall effect in a bulk Dirac semimetal BaMnSb2.

• J. Y. Liu
• , J. Yu
•  & Z. Q. Mao
• Article
| Open Access

### Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

Recent advances in the identification and growth of antiferromagnetic topological insulators open the way to the manipulation of the chiral edge states that are topologically required at their step edges and domain walls. Here, the authors propose a quantum point junction formed by two types of edge states and discuss its applications in electron quantum optics.

• Nicodemos Varnava
• , Justin H. Wilson
•  & David Vanderbilt
• Article
| Open Access

### Observation of a singular Weyl point surrounded by charged nodal walls in PtGa

In all experimentally observed Weyl semimetals so far, the Weyl points always appear in pairs in the momentum space. Here, the authors report one unpaired Weyl point without surface Fermi arc emerging at the center of the Brillouin zone, which is surrounded by charged Weyl nodal walls in PtGa.

• J.-Z. Ma
• , Q.-S. Wu
•  & M. Shi
• Article
| Open Access

### Vortex states in an acoustic Weyl crystal with a topological lattice defect

Here, the authors introduce a 3D Weyl metamaterial hosting modes bound to a 1D topological lattice defect. The modes carry nonzero orbital angular momentum locked to the direction of propagation, and they experimentally demonstrate the ability to emit acoustic vortices into free space.

• Qiang Wang
• , Yong Ge
•  & Y. D. Chong
• Article
| Open Access

### Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs

Weyl semimetals exhibit Berry flux monopoles in momentum-space, but direct experimental evidence has remained elusive. Here, the authors reveal topologically non-trivial winding of the orbital-angular-momentum at the Weyl nodes and a chirality-dependent spin-angular-momentum of the Weyl bands, as a direct signature of the Berry flux monopoles in TaAs.

• M. Ünzelmann
• , H. Bentmann
•  & F. Reinert
• Article
| Open Access

### Wavefront dislocations reveal the topology of quasi-1D photonic insulators

Topological properties are defined from singularities of the wave functions delocalised in the bulk of the material, but most experimental manifestations remain indirect. Here, the authors observe a wavefront dislocation as a direct evidence of the phase singularity of the delocalised wave functions in 1D microwave photonic insulators.

• Clément Dutreix
• , Matthieu Bellec
•  & Fabrice Mortessagne
• Article
| Open Access

### Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators

Experimentally detectable signature of an axion insulator remains elusive. Here, the authors predict a topological phase diagram of MnBi2Te4/(Bi2Te3)n heterostructure, where the chiral hinge mode induced by the surface anomalous Hall conductivity is identified as a signature of an axion insulator state.

• Mingqiang Gu
• , Jiayu Li
•  & Qihang Liu
• Article
| Open Access

### Observation of domain wall bimerons in chiral magnets

Domain wall skyrmions have been proposed but the experimental observation has been difficult. Here, the authors report experimental discovery of domain wall bimerons due to the interplay between magnetic anisotropy and Dzyaloshinskii-Moriya interaction in chiral magnet Co-ZnMn(110) thin films.

• Tomoki Nagase
• , Yeong-Gi So
•  & Masahiro Nagao
• Article
| Open Access

### Quantized spin Hall conductance in a magnetically doped two dimensional topological insulator

The quantum spin Hall effect is expected not to survive the presence of magnetic impurities. Here, authors report full quantization at very low temperatures in HgTe quantum wells alloyed with a few percent of magnetic Mn atoms, due to Kondo screening.

• Saquib Shamim
• , Wouter Beugeling
•  & Laurens W. Molenkamp
• Article
| Open Access

### Origin of the quasi-quantized Hall effect in ZrTe5

A 3D quantum Hall effect has been reported in Dirac semimetal ZrTe5 due to a magnetic-field-driven Fermi surface instability. Here, the authors show evidence of quasi-quantized Hall response without Fermi surface instability, but they argue that it is due to the interplay of the intrinsic properties of ZrTe5 electronic structure and Dirac semi-metallic character.

• S. Galeski
• , T. Ehmcke
•  & J. Gooth
• Article
| Open Access

### Non-Abelian three-loop braiding statistics for 3D fermionic topological phases

Non-Abelian statistics plays a crucial role towards realizing topological quantum computation. Here, the authors discover new types of non-Abelian three-loop braiding statistics that can only be realized in 3D interacting fermionic systems.

• Jing-Ren Zhou
• , Qing-Rui Wang
•  & Zheng-Cheng Gu
• Article
| Open Access

### Kramers nodal line metals

Chiral crystals with spin-orbit coupling (SOC) termed Kramers Weyl semimetals possess Weyl points at time-reversal invariant momenta. Here, the authors propose a new class of topological materials with doubly degenerate lines connecting time-reversal invariant momenta in achiral noncentrosymmetric materials with SOC.

• Ying-Ming Xie
• , Xue-Jian Gao
•  & K. T. Law
• Article
| Open Access

### Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Superconductivity induced on a topological insulator’s surface may realize Majorana modes. Here, Herbrych et al. predict that a large Coulomb interaction helps develop a spiral spin order, which is a topological state at the edge of a canonical superconductor with orbital degrees of freedom.

• J. Herbrych
• , M. Środa
•  & E. Dagotto
• Article
| Open Access

### Observation of topological superconductivity in a stoichiometric transition metal dichalcogenide 2M-WS2

Topological superconductors are potentially important for future quantum computation, but they are very rare in nature. Here, the authors observe topological surface states acquiring a nodeless superconducting gap with similar magnitude as that of the bulk states in 2M-WS2, suggesting an intrinsic topological superconductor.

• Y. W. Li
• , H. J. Zheng
•  & Y. L. Chen
• Article
| Open Access

### Andreev reflection of fractional quantum Hall quasiparticles

Andreev reflection is normally known to occur at a metal-superconductor interface. Here, Hashisaka et al. observe an Andreev-like process in a narrow junction between fractional and integer quantum Hall states originating from a topological quantum many-body effect instead of superconductivity.

• M. Hashisaka
• , T. Jonckheere
•  & K. Muraki
• Article
| Open Access

### Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

The broken-symmetry edge states that are the hallmark of the quantum Hall effect in graphene have eluded spatial measurements. Here, the authors spatially map the quantum Hall broken-symmetry edge states using atomic force microscopy and show a gapped ground state proceeding from the bulk through to the quantum Hall edge boundary.

• Sungmin Kim
• , Johannes Schwenk
•  & Joseph A. Stroscio
• Article
| Open Access

### Spectroscopy of a tunable moiré system with a correlated and topological flat band

Twisted double bilayer graphene hosts flat bands that can be tuned with an electric field. Here, by using gate-tuned scanning tunneling spectroscopy, the authors demonstrate the tunability of the flat band and reveal spectral signatures of correlated electron states and the topological nature of the flat band.

• Xiaomeng Liu
• , Cheng-Li Chiu
•  & Ali Yazdani
• Article
| Open Access

### Nanoscale real-time detection of quantum vortices at millikelvin temperatures

Previous work has shown the detection of quantum turbulence with mechanical resonators but with limited spatial and temporal resolution. Here, the authors demonstrate real-time detection of single quantum vortices in superfluid 4He with millisecond and micron resolution at temperatures of 10 millikelvin.

• A. Guthrie
• , S. Kafanov
•  & D. E. Presnov
• Article
| Open Access

### Intrinsic coupling between spatially-separated surface Fermi-arcs in Weyl orbit quantum Hall states

The spatial distribution of the quantized transport due to the presence of Weyl orbits in topological semimetals remains elusive. Here, the authors report concomitant modulation of doubly-degenerate quantum Hall states, evidencing intrinsic coupling between two spatially separated surface states in the Weyl orbits of a Dirac semimetal film.

• Shinichi Nishihaya
• , Masaki Uchida
•  & Masashi Kawasaki
• Article
| Open Access

### Intercalated architecture of MA2Z4 family layered van der Waals materials with emerging topological, magnetic and superconducting properties

The discovery of a new two-dimensional van der Waals layered MoSi2N4 material inspires many attentions. Here, the authors report intercalation strategies to explore a much wider range of MA2Z4 family and predict amount of materials accessible to experimental verifications with emergent topological, magnetic or Ising superconductivity properties.

• Lei Wang
• , Yongpeng Shi
•  & Xing-Qiu Chen
• Article
| Open Access

### Discovery of $${\hat{\boldsymbol{C}}}_2$$ rotation anomaly in topological crystalline insulator SrPb

New class of topological crystalline insulators (TCI) have been proposed, but are yet to be experimentally evidenced. Here, the authors evidence two massless Dirac fermions protected by the combination of time-reversal symmetry T and Ĉ2y on the (010) surface of SrPb, confirming the Ĉ2 rotation anomaly in the new class of TCIs.

• Wenhui Fan
• , Simin Nie
•  & Hong Ding
• Article
| Open Access

### Giant c-axis nonlinear anomalous Hall effect in Td-MoTe2 and WTe2

Certain materials without inversion symmetry may allow for a nonlinear anomalous Hall effect with conserved time reversal symmetry. Here, the authors report an extremely large c-axis nonlinear anomalous Hall effect in the non-centrosymmetric Td phase of MoTe2 and WTe2 without intrinsic magnetic order that is dominated by extrinsic scattering.

• Archana Tiwari
• , Fangchu Chen
• Article
| Open Access

### Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers

The influence of spin-orbit coupling on the hybridization of Shiba states in dimers of magnetic atoms on superconducting surfaces remains unexplored. Here, the authors reveal a splitting of atomic Shiba orbitals due to spin-orbit coupling and broken inversion symmetry in antiferromagnetically coupled Mn dimers placed on a Nb(110) surface.

• Philip Beck
• , Lucas Schneider
•  & Roland Wiesendanger
• Article
| Open Access

### Non-Hermitian route to higher-order topology in an acoustic crystal

Losses, due to their non-Hermitian nature, are generally disregarded or even considered harmful when looking for non-trivial topological phases. Here, the authors experimentally demonstrate that higher-order topology can emerge as a result of introducing losses in an acoustic crystal.

• He Gao
• , Haoran Xue
•  & Baile Zhang
• Article
| Open Access

### Manipulating Weyl quasiparticles by orbital-selective photoexcitation in WTe2

Photoexcitation in Weyl semimetals is recently reported to induce topological phase transitions useful for ultrafast switching devices. Here, the authors predict that the symmetry of the atomic orbitals comprising the Weyl bands in response to linear light polarization allows for not only annihilation but also separation of Weyl quasiparticles.

• Meng-Xue Guan
• , En Wang
•  & Sheng Meng
• Article
| Open Access

### Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2

Weak topological insulators (WTI) remain difficult to be observed in experiments. Here, the authors discover a WTI state in RhBi2, where the topological surface states with saddle points result in a van Hove singularity along the (100) direction near Fermi energy.

• Kyungchan Lee
• , Gunnar F. Lange
• Article
| Open Access

### High-frequency rectifiers based on type-II Dirac fermions

High-frequency rectifiers at terahertz regime are pivotal components in modern communication, whereas the drawbacks in semiconductor junctions-based devices inhibit their usages. Here, the authors report electromagnetic rectification with high signal-to-noise ratio driven by chiral Bloch-electrons in type-II Dirac semimetal NiTe2-based device allowing for efficient THz detection.

• Libo Zhang
• , Zhiqingzi Chen
•  & Wei Lu
• Article
| Open Access

### Fragility of surface states in topological superfluid 3He

Surface states in topological quantum matter are protected by their band structure. Here, on confined superfluid 3He as a model for topological superconductors, the authors report experimental evidence on the fragility of surface Andreev bound states with respect to the details of surface scattering.

• P. J. Heikkinen
• , A. Casey
•  & J. Saunders