Pressure-induced topological phase transition in noncentrosymmetric elemental tellurium

Observation of edge states derived from topological helix chains

Introducing the concept of topology has revolutionized materials classification, leading to the discovery of topological insulators and Dirac-Weyl semimetals1-3. One of the most fundamental theories underpinning topological materials is the Su-Schrieffer-Heeger (SSH) model4,5, which was developed in 1979-decades before the recognition of topological insulators-to describe conducting polymers. Distinct from the vast majority of known topological insulators with two and three dimensions1-3, the SSH model predicts a one-dimensional analogue of topological insulators, which hosts topological bound states at the endpoints of a chain4-8. To establish this unique and pivotal state, it is crucial to identify the low-energy excitations stemming from bound states, but this has remained unknown in solids because of the absence of suitable platforms. Here we report unusual electronic states that support the emergent bound states in elemental tellurium, the single helix of which was recently proposed to realize an extended version of the SSH chain9,10. Using spin- and angle-resolved photoemission spectroscopy with a micro-focused beam, we have shown spin-polarized in-gap states confined to the edges of the (0001) surface. Our density functional theory calculations indicate that these states are attributed to the interacting bound states originating from the one-dimensional array of SSH tellurium chains. Helices in solids offer a promising experimental platform for investigating exotic properties associated with the SSH chain and exploring topological phases through dimensionality control.

Topological phase transition and tunable surface states in YBi

A unique co-existence of extremely large magnetoresistance (XMR) and topological characteristics in non-magnetic rare-earth monopnictides has stimulated intensive research on these materials. Yttrium monobismuthide (YBi) has been reported to exhibit XMR up to 105% but its topological properties still need clarification. Here we use the hybrid density functional theory to probe the structural, electronic, and topological properties of YBi in detail. We observe that YBi is topologically trivial semimetal at ambient pressure which is in accordance with reported experimental results. The topological phase transitions i.e. trivial to non-trivial are obtained with volumetric pressure of 6.5 GPa and 3% of epitaxial strain. These topological phase transitions are well within the structural phase transition of YBi (24.5 GPa). The topological non-trivial state is characterized by band inversions amongY-dband andBi-pband atΓ-andX-pointwhich is further verified with the help of surface band structure along (001) plane. The Z2topological invariants are calculated with the help of product of parities and evolution of Wannier charge centers. The occurrence of non-trivial phase in YBi with a relatively small epitaxial strain, which a thin film geometry can naturally have, make it an ideal candidate to probe inter-relationship between XMR and non-trivial topology.

Reversible non-volatile electronic switching in a near-room-temperature van der Waals ferromagnet

Non-volatile phase-change memory devices utilize local heating to toggle between crystalline and amorphous states with distinct electrical properties. Expanding on this kind of switching to two topologically distinct phases requires controlled non-volatile switching between two crystalline phases with distinct symmetries. Here, we report the observation of reversible and non-volatile switching between two stable and closely related crystal structures, with remarkably distinct electronic structures, in the near-room-temperature van der Waals ferromagnet Fe5-δGeTe2. We show that the switching is enabled by the ordering and disordering of Fe site vacancies that results in distinct crystalline symmetries of the two phases, which can be controlled by a thermal annealing and quenching method. The two phases are distinguished by the presence of topological nodal lines due to the preserved global inversion symmetry in the site-disordered phase, flat bands resulting from quantum destructive interference on a bipartite lattice, and broken inversion symmetry in the site-ordered phase.

Strain-induced topological phase transition in ferromagnetic Janus monolayer MnSbBiS2Te2

We investigate a strain-induced topological phase transition in the ferromagnetic Janus monolayer MnSbBiS2Te2 using first-principles calculations. The electronic, magnetic, and topological properties are studied under biaxial strain within the range of -8 to +8%. The ground state of monolayer MnSbBiS2Te2 is metallic with an out-of-plane magnetic easy axis. A band gap is opened when a compressive strain between -4% and -7% is applied. We observe a topological phase transition at a biaxial strain of -5%, where the material becomes a Chern insulator exhibiting a quantum anomalous hall (QAH) effect. We find that biaxial strain and spin-orbit coupling (SOC) are responsible for the topological phase transition in MnSbBiS2Te2. In addition, we find that biaxial strain can alter the direction of the magnetic easy axis of MnSbBiS2Te2. The Curie temperature is calculated using the Heisenberg model and is found to be 24 K. This study could pave the way to the design of topological materials with potential applications in spintronics, quantum computing, and dissipationless electronics.

Manipulating Topological Phases in Magnetic Topological Insulators

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications.

Tellurium crystal pumped with ultrafast 10 µm pulses demonstrates a giant nonlinear optical response

The nonresonant nonlinear optical response of bulk tellurium (Te) is studied using 220 fs 10 µm laser pulses with photon energy roughly three times smaller than the band gap energy. The Kerr nonlinearity is found to be extremely large (n2,eff = 3.0-6.0 × 10-12 cm2/W), nearly 100 times larger than that of GaAs, depending on crystal orientation. Multiphoton absorption is observed at intensities >109 W/cm2 indicating the importance of free carriers to the overall nonlinear optical response. The large values of the nonlinear susceptibilities of Te open up possibilities of designing thin film elements for mid- and long-wavelength infrared nonlinear photonics.

Coexistence of logarithmic and SdH quantum oscillations in ferromagnetic Cr-doped tellurium single crystals

We report the synthesis of transition-metal-doped ferromagnetic elemental single-crystal semiconductors with quantum oscillations using the physical vapor transport method. The 7.7 atom% Cr-doped Te crystals (Cr:Te) show ferromagnetism, butterfly-like negative magnetoresistance in the low temperature (<3.8 K) and low field (<0.15 T) region, and high Hall mobility, e.g. 1320 cm²V^-1s^-1at 30 K and 350 cm²V^-1s^-1at 300 K, implying that Cr:Te crystals are ferromagnetic elemental semiconductors. WhenB// [001] // I, the maximum negative MR is ∼-27% atT= 20 K andB= 8 T. In the low temperature semiconducting region, Cr:Te crystals show strong discrete scale invariance dominated logarithmic quantum oscillations when the direction of the magnetic fieldBis parallel to the [100] crystallographic direction (B// [100]) and show Landau quantization dominated Shubnikov-de Haas oscillations forB// [210] direction, which suggests the broken rotation symmetry of the Fermi pockets in the Cr:Te crystals. The findings of coexistence of multiple quantum oscillations and ferromagnetism in such an elemental quantum material may inspire more study of narrow bandgap semiconductors with ferromagnetism and quantum phenomena.

Chiral phonons: circularly polarized Raman spectroscopy and ab initio calculations in a chiral crystal tellurium

Recently, phonons with chirality (chiral phonons) have attracted significant attention. Chiral phonons exhibit angular and pseudoangular momenta. In circularly polarized Raman spectroscopy, the peak split of the Γ 3 $$ {\Gamma}_3 $$ mode is detectable along the principal axis of the chiral crystal in the backscattering configuration. In addition, peak splitting occurs when the pseudoangular momenta of the incident and scattered circularly polarized light are reversed. Until now, chiral phonons in binary crystals have been observed, whereas those in unary crystals have not been observed. Here, we observe chiral phonons in a chiral unary crystal Te. The pseudoangular momentum of the phonon is obtained in Te by an ab initio calculation. From this calculation, we verified the conservation law of pseudoangular momentum in Raman scattering. From this conservation law, we determined the handedness of the chiral crystals. We also evaluated the true chirality of the phonons using a measure with symmetry similar to that of an electric toroidal monopole.

Intrinsic Torques Emerging from Anomalous Velocity in Magnetic Textures

Momentum-space topology of electrons under strong spin-orbit coupling contributes to the electrically induced torques exerting on magnetic textures insensitively to disorder or thermal fluctuation. We present a direct connection between band topology and the torques by classifying the whole torques phenomenologically. As well as the intrinsic anomalous Hall effect, the torques also emerge intrinsically from the anomalous velocity of electrons regardless of a nonequilibrium transport current. We especially point out the intrinsic contribution arising exclusively in magnetic textures, which we call the "topological Hall torque (THT)." The THT emerges in bulk crystals without any interface or surface structures. We numerically demonstrate the enhancement of the THT in comparison with the conventional spin-transfer torque in the bulk metallic ferromagnet, which accounts for the giant current-induced torque measured in ferromagnetic SrRuO_{3}.

Coupling Charge and Topological Reconstructions at Polar Oxide Interfaces

In oxide heterostructures, different materials are integrated into a single artificial crystal, resulting in a breaking of inversion symmetry across the heterointerfaces. A notable example is the interface between polar and nonpolar materials, where valence discontinuities lead to otherwise inaccessible charge and spin states. This approach paved the way for the discovery of numerous unconventional properties absent in the bulk constituents. However, control of the geometric structure of the electronic wave functions in correlated oxides remains an open challenge. Here, we create heterostructures consisting of ultrathin SrRuO_{3}, an itinerant ferromagnet hosting momentum-space sources of Berry curvature, and LaAlO_{3}, a polar wide-band-gap insulator. Transmission electron microscopy reveals an atomically sharp LaO/RuO_{2}/SrO interface configuration, leading to excess charge being pinned near the LaAlO_{3}/SrRuO_{3} interface. We demonstrate through magneto-optical characterization, theoretical calculations and transport measurements that the real-space charge reconstruction drives a reorganization of the topological charges in the band structure, thereby modifying the momentum-space Berry curvature in SrRuO_{3}. Our results illustrate how the topological and magnetic features of oxides can be manipulated by engineering charge discontinuities at oxide interfaces.

Radial Spin Texture of the Weyl Fermions in Chiral Tellurium

Trigonal tellurium, a small-gap semiconductor with pronounced magneto-electric and magneto-optical responses, is among the simplest realizations of a chiral crystal. We have studied by spin- and angle-resolved photoelectron spectroscopy its unconventional electronic structure and unique spin texture. We identify Kramers-Weyl, composite, and accordionlike Weyl fermions, so far only predicted by theory, and show that the spin polarization is parallel to the wave vector along the lines in k space connecting high-symmetry points. Our results clarify the symmetries that enforce such spin texture in a chiral crystal, thus bringing new insight in the formation of a spin vectorial field more complex than the previously proposed hedgehog configuration. Our findings thus pave the way to a classification scheme for these exotic spin textures and their search in chiral crystals.

Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium

The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5 and HfTe5 The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop "Weyl semiconductors" provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.

Radial Spin Texture in Elemental Tellurium with Chiral Crystal Structure

The chiral crystal is characterized by a lack of mirror symmetry and inversion center, resulting in the inequivalent right- and left-handed structures. In the noncentrosymmetric crystal structure, the spin and momentum of electrons are expected to be locked in the reciprocal space with the help of the spin-orbit interaction. To reveal the spin textures of chiral crystals, we investigate the spin and electronic structure in a p-type semiconductor, elemental tellurium, with the simplest chiral structure by using spin- and angle-resolved photoemission spectroscopy. Our data demonstrate that the highest valence band crossing the Fermi level has a spin component parallel to the electron momentum around the Brillouin zone corners. Significantly, we have also confirmed that the spin polarization is reversed in the crystal with the opposite chirality. The results indicate that the spin textures of the right- and left-handed chiral crystals are hedgehoglike, leading to unconventional magnetoelectric effects and nonreciprocal phenomena.