Broken Time-reversal Symmetry Research Articles

Tunable hybrid-order Weyl semimetal via staggered magnetic flux

We investigate a hybrid-order Weyl semimetal (HOWS) constructed by stacking the two-dimensional kagome lattice with staggered magnetic flux. By adjusting the magnitude of flux, higher-order topological phases are tunably intertwined with the first-order topological Chern insulators, which is governed by the evolution of Weyl points. Meanwhile the surface Fermi arcs undergo topological Lifshitz transition. Notably, due to the breaking of time-reversal symmetry (TRS), a novel split of a quadratic double Weyl point occurs, giving rise to additional three type-II Weyl points hybridizing with one type-I node. This phenomenon plays a crucial role in realizing high-Chern-number phases with C=±2 and reveals a new mechanism for the emergence of type-II Weyl fermions in topological kagome semimetals. We anticipate that this study will stimulate further investigation into the unique physics of kagome materials and Weyl semimetals.

Unconventional superconductivity in chiral molecule-TaS2 hybrid superlattices.

Chiral superconductors, a unique class of unconventional superconductors in which the complex superconducting order parameter winds clockwise or anticlockwise in the momentum space1, represent a topologically non-trivial system with intrinsic time-reversal symmetry breaking (TRSB) and direct implications for topological quantum computing2,3. Intrinsic chiral superconductors are extremely rare, with only a few arguable examples, including UTe2, UPt3 and Sr2RuO4 (refs. 4-7). It has been suggested that chiral superconductivity may exist in non-centrosymmetric superconductors8,9, although such non-centrosymmetry is uncommon in typical solid-state superconductors. Alternatively, chiral molecules with neither mirror nor inversion symmetry have been widely investigated. We suggest that an incorporation of chiral molecules into conventional superconductor lattices could introduce non-centrosymmetry and help realize chiral superconductivity10. Here we explore unconventional superconductivity in chiral molecule intercalated TaS2 hybrid superlattices. Our studies reveal an exceptionally large in-plane upper critical field Bc2,|| well beyond the Pauli paramagnetic limit, a robust π-phase shift in Little-Parks measurements and a field-free superconducting diode effect (SDE). These experimental signatures of unconventional superconductivity suggest that the intriguing interplay between crystalline atomic layers and the self-assembled chiral molecular layers may lead to exotic topological materials. Our study highlights that the hybrid superlattices could lay a versatile path to artificial quantum materials by combining a vast library of layered crystals of rich physical properties with the nearly infinite variations of molecules of designable structural motifs and functional groups11.

Thermal conductivity of nonunitary triplet superconductors: application to UTe2

Considerable evidence shows that the heavy fermion material UTe2 is a spin-triplet superconductor, possibly manifesting time-reversal symmetry breaking, as measured by Kerr effect below the critical temperature, in some samples. Such signals can arise due to a chiral orbital state or possible nonunitary pairing. Although experiments at low temperatures appear to be consistent with point nodes in the spectral gap, the detailed form of the order parameter and even the nodal positions are not yet determined. Thermal conductivity measurements can extend to quite low temperatures, and varying the heat current direction should be able to provide information on the order parameter structure. Here, we derive a general expression for the thermal conductivity of a spin-triplet superconductor and use it to compare the low-temperature behavior of various states proposed for UTe2.

Optical manipulation of the charge-density-wave state in RbV3Sb5.

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents1-4. The recently discovered kagome superconductors AV3Sb5 (where A is K, Rb or Cs)5,6 display an exotic charge-density-wave (CDW) state andhave emerged as astrong candidate for materialshosting a loop currentphase. The idea that the CDW breaks time-reversal symmetry7-14 is, however, being intensely debated due to conflicting experimental data15-17. Here we use laser-coupled scanning tunnelling microscopy to study RbV3Sb5. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong nonlinear electron-phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry breaking. We show that the simplest CDW that satisfies these constraints is an out-of-phase combination of bond charge order and loop currents that we dub a congruent CDW flux phase. Our laser scanning tunnelling microscopy data open the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials.

Anomalous supercurrent and diode effect in locally perturbed topological Josephson junctions

The simultaneous breaking of time-reversal and inversion symmetry can lead to peculiar effects in Josephson junctions, such as the anomalous Josephson effect or supercurrent rectification, which is a dissipationless analog of the diode effect. Due to their impact in new quantum technologies, it is important to find robust platforms and external means to manipulate the above-mentioned effects in a controlled way. Here, we theoretically consider a Josephson junction based on a quantum spin Hall system as the normal channel, subjected to a magnetic field in the direction defined by spin-momentum locking, and in the presence of a local tip in close proximity to one of the metallic edges in the normal region. We consider different local perturbations, model normal and magnetic tips, and study how they affect the Josephson response of the device. In particular, we argue that magnetic tips are a useful tool that allows for tunability of both ϕ0 response and supercurrent rectification.

Coexistence of Ferromagnetism and Superconductivity at KTaO3 Heterointerfaces.

The coexistence of superconductivity and ferromagnetism is a long-standing issue in superconductivity due to the antagonistic nature of these two ordered states. Experimentally identifying and characterizing novel heterointerface superconductors that coexist with magnetism presents significant challenges. Here, we report the observation of two-dimensional long-range ferromagnetic order in a KTaO3 heterointerface superconductor, showing the coexistence of superconductivity and ferromagnetism. Remarkably, our direct current superconducting quantum interference device measurements reveal an in-plane magnetization hysteresis loop persisting above room temperature. Moreover, first-principles calculations and X-ray magnetic circular dichroism measurements provide decisive insights into the origin of the observed robust ferromagnetism, attributing it to oxygen vacancies that localize electrons in nearby Ta 5d states. Our findings suggest KTaO3 heterointerfaces as time-reversal symmetry breaking superconductors, injecting fresh momentum into the exploration of the intricate interplay between superconductivity and magnetism enhanced by the strong spin-orbit coupling inherent to the heavy Ta in 5d orbitals.

Second-order charge and spin transport in LaO/STO system in the presence of cubic Rashba spin orbit couplings

Under an applied electric field, certain non-centrosymmetric materials with broken time-reversal symmetry may exhibit non-reciprocal transport behavior in which the charge and spin currents contain components that are second order in the electric field. In this study, we investigate the second-order spin accumulation and charge and spin responses in the LaAlO3/SrTiO3 (LaO/STO) system with magnetic dopants under the influence of linear and cubic Rashba spin–orbit coupling (RSOC) terms. We explain the physical origin of the second-order response and perform a symmetry analysis of the first- and second-order responses for different dopant magnetization directions relative to the applied electric field. We then numerically solve the Boltzmann transport equation by extending the approach of Schliemann and Loss (2003 Phys. Rev. B 68 165311) to higher orders in the electric field. We show that the sign of the second-order responses can be switched by varying the magnetization direction of the magnetic dopants or relative strengths of the two cubic RSOC terms and explain these trends by considering the Fermi surfaces of the respective systems. These findings provide insights into the interplay of multiple SOC effects in the LaO/STO system and how the resulting first- and second-order charge and spin responses can be engineered by exploiting the symmetries of the system.

Topological pumping induced by spatiotemporal modulation of interaction

Particle-particle interaction provides a new degree of freedom to induce novel topological phenomena. Here, we propose to use spatiotemporal modulation of interaction to realize topological pumping without a single-particle counterpart. Because the modulation breaks time-reversal symmetry, the multiparticle energy bands of bound states have none-zero Chern number, and support topological bound edge states. In a Thouless pump, a bound state that uniformly occupies a topological energy band can be shifted by integer unit cells per cycle, consistent with the corresponding Chern number. We can also realize topological pumping of bound edge state from one end to another. The entanglement entropy between particles rapidly increases at transition points, which is related to the spatial spread of a bounded pair. In addition, we propose to realize hybridized pumping with fractional displacement per cycle by adding an extra tilt potential to separate topological pumping of the bound state and Bloch oscillations of single particle. Our work could trigger further studies of correlated topological phenomena that do not have a single-particle counterpart.

Spontaneous time-reversal symmetry breaking by disorder in superconductors

A growing number of superconducting materials display evidence for spontaneous time-reversal symmetry breaking (TRSB) below their critical transition temperatures. Precisely what this implies for the nature of the superconducting ground state of such materials, however, is often not straightforward to infer. We review the experimental status and survey different theoretical mechanisms for the generation of TRSB in superconductors. In cases where a TRSB complex combination of two superconducting order parameter components is realized, defects, dislocations and sample edges may generate superflow patterns that can be picked up by magnetic probes. However, even single-component condensates that do not break time-reversal symmetry in their pure bulk phases can also support signatures of magnetism inside the superconducting state. This includes, for example, the generation of localized orbital current patterns or spin-polarization near atomic-scale impurities, twin boundaries and other defects. Signals of TRSB may also arise from a superconductivity-enhanced Ruderman-Kittel-Kasuya-Yosida exchange coupling between magnetic impurity moments present in the normal state. We discuss the relevance of these different mechanisms for TRSB in light of recent experiments on superconducting materials of current interest.

Strong-coupling approach to temperature dependence of competing orders of superconductivity: Possible time-reversal symmetry breaking and nontrivial topology

Strong-coupling approach to temperature dependence of competing orders of superconductivity: Possible time-reversal symmetry breaking and nontrivial topology

Observation of valley-polarized topological phase transition in surface wave photonic crystals

Simultaneous breaking of inversion symmetry and time-reversal symmetry brings topological phases fundamental in valleytronics, i.e. unpaired Dirac points and edge states. Here, we experimentally demonstrate the valley-polarized topological phase transition of these states. In a surface wave photonic crystal platform with honeycomb lattice, we use unequal metal pillars and magnetically biased gyromagnetic ferrite disks to modulate the breaking of symmetries. Switching of the unpaired Dirac points between K and K’ valleys is observed. More importantly, we realize valley manipulation of the edge states in heterojunctions constructed by specific topological phases. Our research thus paves the way for valley-polarized devices.

High-harmonic generation in semi-Dirac and Weyl semimetals with broken time-reversal symmetry: Exploration of the merging of Weyl nodes

High-harmonic generation in semi-Dirac and Weyl semimetals with broken time-reversal symmetry: Exploration of the merging of Weyl nodes

Strain engineering the spin-valley coupling of the R-stacking sliding ferroelectric bilayer 2H-VX2 (X = S, Se, Te)

The emergence of magnetic transition metal dichalcogenides has significantly advanced the development of valleytronics due to the spontaneous breaking of time-reversal symmetry and space-inversion symmetry. However, the lack of regulation methods has prevented researchers from exploring their potential applications. Herein, we propose to use strain engineering to control the spin-valley coupling in the sliding ferroelectric bilayer 2H-VX2 (X = S, Se, Te). Four multiferroic states are constructed by combining the sliding ferroelectricity and antiferromagnetism in the R-stacking bilayer VX2, where the spin and valley polarizations are coupled together from the layer-dependent spin-polarized band structures. By applying a small external strain or pressure on the out-of-plane van der Waals direction, we predicted that there is an antiferromagnetic to magnetic transition in the bilayer VX2, leading to the interesting spin-polarized and chiral circularly polarized radiation at K+ and K- valleys, similar to those found in the magnetic monolayer. To comprehend the coupling between various degrees of freedom in these multiferroic systems, we have developed an effective k·p model. This model unveils a linear relationship between the electric polarization generated by interlayer sliding and the energy difference of the valence band maximum at K+ and K- valleys. Thus, providing an alternate method to measure the electric polarization in the sliding ferroelectrics. Based on the strong coupling between the strain, spin-valley, and electric polarization, it is likely to use the strain to control the interesting emerging properties of 2H-VX2 such as the anomalous valley Hall effect.

Anomalous-Chern Steering of Topological Nonreciprocal Guided Waves.

Nonreciprocal topological edge states based on external magnetic bias have been regarded as the last resort for genuine unidirectional wave transport, showing superior robustness over topological states with preserved time-reversal symmetry. However, fast and efficient reconfigurability of their trajectory has remained a formidable challenge due to the difficulty in controlling the spatial distribution of magnetic fields over large areas and short times. Here, thispersistent issue is solved by leveraging the rich topology of unitary scattering networks, and achieve fast steering of nonreciprocal topological transport at an interface between a Chern and an anomalous topological insulator, without having to control a magnetic field. Such interface can be drawn by doping the network with scatterers located at the center of each link, whose level of reflection is electrically tuned. With experiments in the GHz range, the possibility to actively steer the way of unidirectional edge states is demonstrated, switching the transmission path thousands of times per second in a fully-robust topological heterostructure. The approach represents a significant step towards the realization of practical reconfigurable topological meta-devices with broken time-reversal symmetry, and their application to future robust communicationtechnologies.

Photoinduced Floquet higher-orderWeyl semimetal in C6 symmetric Dirac semimetals

Abstract Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges. Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Universal scaling law for chiral antiferromagnetism

The chiral antiferromagnetic (AFM) materials, which have been widely investigated due to their rich physics, such as non-zero Berry phase and topology, provide a platform for the development of antiferromagnetic spintronics. Here, we find two distinctive anomalous Hall effect (AHE) contributions in the chiral AFM Mn3Pt, originating from a time-reversal symmetry breaking induced intrinsic mechanism and a skew scattering induced topological AHE due to an out-of-plane spin canting with respect to the Kagome plane. We propose a universal AHE scaling law to explain the AHE resistivity (ρAH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\rho }}_{AH}$$\\end{document}) in this chiral magnet, with both a scalar spin chirality (SSC)-induced skew scattering topological AHE term, ask\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${a}_{sk}$$\\end{document} and non-collinear spin-texture induced intrinsic anomalous Hall term, bin\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{b}}_{{in}}$$\\end{document}. We found that ask\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{a}}}_{{{sk}}}$$\\end{document} and bin\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{b}}}_{{{in}}}$$\\end{document} can be effectively modulated by the interfacial electron scattering, exhibiting a linear relation with the inverse film thickness. Moreover, the scaling law can explain the anomalous Hall effect in various chiral magnets and has far-reaching implications for chiral-based spintronics devices.

Quantum annealing of a frustrated magnet

Quantum annealing, which involves quantum tunnelling among possible solutions, has state-of-the-art applications not only in quickly finding the lowest-energy configuration of a complex system, but also in quantum computing. Here we report a single-crystal study of the frustrated magnet α-CoV2O6, consisting of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder. We observe quantum annealing phenomena resulting from time-reversal symmetry breaking in a tiny transverse field. Below ~ 1 K, the system exhibits no indication of approaching the lowest-energy state for at least 15 hours in zero transverse field, but quickly converges towards that configuration with a nearly temperature-independent relaxation time of ~ 10 seconds in a transverse field of ~ 3.5 mK. Our many-body simulations show qualitative agreement with the experimental results, and suggest that a tiny transverse field can profoundly enhance quantum spin fluctuations, triggering rapid quantum annealing process from topological metastable Kosterlitz-Thouless phases, at low temperatures.

The Impact of Local Strain Fields in Noncollinear Antiferromagnetic Films.

Antiferromagnets hosting structural or magnetic order that breaks time reversal symmetry are of increasing interest for "beyond von Neumann" computing applications because the topology of their band structure allows for intrinsic physical properties, exploitable in integrated memory and logic function. One such group are the noncollinear antiferromagnets. Essential for domain manipulation is the existence of small net moments found routinely when the material is synthesized in thin film form and attributed to symmetry breaking caused by spin canting, either from the Dzyaloshinskii-Moriya interaction or from strain. Although the spin arrangement of these materials makes them highly sensitive to strain, there is little understanding about the influence of local strain fields caused by lattice defects on global properties, such as magnetization and anomalous Hall effect. This premise is investigated by examining noncollinear antiferromagnetic films that are either highly lattice mismatched or closely matched to their substrate. In either case, edge dislocation networks are generated and for the former case, these extend throughout the entire film thickness, creating large local strain fields. These strain fields allow for finite intrinsic magnetization in seemingly structurally relaxed films and influence the antiferromagnetic domain state and the intrinsic anomalous Hall effect.

X-Ray Magnetic Circular Dichroism in Altermagnetic α-MnTe.

Altermagnetism is a recently identified magnetic symmetry class combining characteristics of conventional collinear ferromagnets and antiferromagnets, that were regarded as mutually exclusive, and enabling phenomena and functionalities unparalleled in either of the two traditional elementary magnetic classes. In this work we use symmetry, abinitio theory, and experiments to explore x-ray magnetic circular dichroism (XMCD) in the altermagnetic class. As a representative material for our XMCD study we choose α-MnTe with compensated antiparallel magnetic order in which an anomalous Hall effect has been already demonstrated. We predict and experimentally confirm a characteristic XMCD line shape for compensated moments lying in a plane perpendicular to the light propagation vector. Our results highlight the distinct phenomenology in altermagnets of this time-reversal symmetry breaking response, and its potential utility for element-specific spectroscopy and microscopy.

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities.

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.