Altermagnetic lifting of Kramers spin degeneracy.

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3-7 to topological quantum matter8-14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin15. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin-orbit coupling (SOC)16-19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic20,21, that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization20-23. Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25.

EuCd_{2}As_{2}: A Magnetic Semiconductor.

EuCd_{2}As_{2} is now widely accepted as a topological semimetal in which a Weyl phase is induced by an external magnetic field. We challenge this view through firm experimental evidence using a combination of electronic transport, optical spectroscopy, and excited-state photoemission spectroscopy. We show that the EuCd_{2}As_{2} is in fact a semiconductor with a gap of 0.77 eV. We show that the externally applied magnetic field has a profound impact on the electronic band structure of this system. This is manifested by a huge decrease of the observed band gap, as large as 125 meV at 2 T, and, consequently, by a giant redshift of the interband absorption edge. However, the semiconductor nature of the material remains preserved. EuCd_{2}As_{2} is therefore a magnetic semiconductor rather than a Dirac or Weyl semimetal, as suggested by ab initio computations carried out within the local spin-density approximation.

Evidence of a Coulomb-Interaction-Induced Lifshitz Transition and Robust Hybrid Weyl Semimetal in T_{d}-MoTe_{2}.

Using soft x-ray angle-resolved photoemission spectroscopy we probed the bulk electronic structure of T_{d}-MoTe_{2}. We found that on-site Coulomb interaction leads to a Lifshitz transition, which is essential for a precise description of the electronic structure. A hybrid Weyl semimetal state with a pair of energy bands touching at both type-I and type-II Weyl nodes is indicated by comparing the experimental data with theoretical calculations. Unveiling the importance of Coulomb interaction opens up a new route to comprehend the unique properties of MoTe_{2}, and is significant for understanding the interplay between correlation effects, strong spin-orbit coupling and superconductivity in this van der Waals material.

Selective Probing of Hidden Spin-Polarized States in Inversion-Symmetric Bulk MoS_{2}.

Spin- and angle-resolved photoemission spectroscopy is used to reveal that a large spin polarization is observable in the bulk centrosymmetric transition metal dichalcogenide MoS_{2}. It is found that the measured spin polarization can be reversed by changing the handedness of incident circularly polarized light. Calculations based on a three-step model of photoemission show that the valley and layer-locked spin-polarized electronic states can be selectively addressed by circularly polarized light, therefore providing a novel route to probe these hidden spin-polarized states in inversion-symmetric systems as predicted by Zhang et al. [Nat. Phys. 10, 387 (2014).NPAHAX1745-247310.1038/nphys2933].

Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3.

Two-dimensional electron gases (2DEGs) forming at the interfaces of transition metal oxides exhibit a range of properties, including tunable insulator-superconductor-metal transitions, large magnetoresistance, coexisting ferromagnetism and superconductivity, and a spin splitting of a few meV (refs 10, 11). Strontium titanate (SrTiO3), the cornerstone of such oxide-based electronics, is a transparent, non-magnetic, wide-bandgap insulator in the bulk, and has recently been found to host a surface 2DEG (refs 12-15). The most strongly confined carriers within this 2DEG comprise two subbands, separated by an energy gap of 90 meV and forming concentric circular Fermi surfaces. Using spin- and angle-resolved photoemission spectroscopy (SARPES), we show that the electron spins in these subbands have opposite chiralities. Although the Rashba effect might be expected to give rise to such spin textures, the giant splitting of almost 100 meV at the Fermi level is far larger than anticipated. Moreover, in contrast to a simple Rashba system, the spin-polarized subbands are non-degenerate at the Brillouin zone centre. This degeneracy can be lifted by time-reversal symmetry breaking, implying the possible existence of magnetic order. These results show that confined electronic states at oxide surfaces can be endowed with novel, non-trivial properties that are both theoretically challenging to anticipate and promising for technological applications.

Observation of Fermi-Arc Spin Texture in TaAs.

We have investigated the spin texture of surface Fermi arcs in the recently discovered Weyl semimetal TaAs using spin- and angle-resolved photoemission spectroscopy. The experimental results demonstrate that the Fermi arcs are spin polarized. The measured spin texture fulfills the requirement of mirror and time-reversal symmetries and is well reproduced by our first-principles calculations, which gives strong evidence for the topologically nontrivial Weyl semimetal state in TaAs. The consistency between the experimental and calculated results further confirms the distribution of chirality of the Weyl nodes determined by first-principles calculations.

A tunable topological insulator in the spin helical Dirac transport regime.

Helical Dirac fermions-charge carriers that behave as massless relativistic particles with an intrinsic angular momentum (spin) locked to its translational momentum-are proposed to be the key to realizing fundamentally new phenomena in condensed matter physics. Prominent examples include the anomalous quantization of magneto-electric coupling, half-fermion states that are their own antiparticle, and charge fractionalization in a Bose-Einstein condensate, all of which are not possible with conventional Dirac fermions of the graphene variety. Helical Dirac fermions have so far remained elusive owing to the lack of necessary spin-sensitive measurements and because such fermions are forbidden to exist in conventional materials harbouring relativistic electrons, such as graphene or bismuth. It has recently been proposed that helical Dirac fermions may exist at the edges of certain types of topologically ordered insulators-materials with a bulk insulating gap of spin-orbit origin and surface states protected against scattering by time-reversal symmetry-and that their peculiar properties may be accessed provided the insulator is tuned into the so-called topological transport regime. However, helical Dirac fermions have not been observed in existing topological insulators. Here we report the realization and characterization of a tunable topological insulator in a bismuth-based class of material by combining spin-imaging and momentum-resolved spectroscopies, bulk charge compensation, Hall transport measurements and surface quantum control. Our results reveal a spin-momentum locked Dirac cone carrying a non-trivial Berry's phase that is nearly 100 per cent spin-polarized, which exhibits a tunable topological fermion density in the vicinity of the Kramers point and can be driven to the long-sought topological spin transport regime. The observed topological nodal state is shown to be protected even up to 300 K. Our demonstration of room-temperature topological order and non-trivial spin-texture in stoichiometric Bi(2)Se(3).M(x) (M(x) indicates surface doping or gating control) paves the way for future graphene-like studies of topological insulators, and applications of the observed spin-polarized edge channels in spintronic and computing technologies possibly at room temperature.

Spin-orbital entanglement and the breakdown of singlets and triplets in Sr2RuO4 revealed by spin- and angle-resolved photoemission spectroscopy.

Spin-orbit coupling has been conjectured to play a key role in the low-energy electronic structure of Sr2RuO4. By using circularly polarized light combined with spin- and angle-resolved photoemission spectroscopy, we directly measure the value of the effective spin-orbit coupling to be 130±30 meV. This is even larger than theoretically predicted and comparable to the energy splitting of the dxy and dxz,yz orbitals around the Fermi surface, resulting in a strongly momentum-dependent entanglement of spin and orbital character in the electronic wavefunction. As demonstrated by the spin expectation value ⟨sk⃗·s-k⃗⟩ calculated for a pair of electrons with zero total momentum, the classification of the Cooper pairs in terms of pure singlets or triplets fundamentally breaks down, necessitating a description of the unconventional superconducting state of Sr2RuO4 in terms of these newly found spin-orbital entangled eigenstates.

Excitation of coherent phonons in the one-dimensional Bi(114) surface.

We present time-resolved photoemission experiments from a peculiar bismuth surface, Bi(114). The strong one-dimensional character of this surface is reflected in the Fermi surface, which consists of spin-polarized straight lines. Our results show that the depletion of the surface state and the population of the bulk conduction band after the initial optical excitation persist for very long times. The disequilibrium within the hot electron gas along with strong electron-phonon coupling cause a displacive excitation of coherent phonons, which in turn are reflected in coherent modulations of the electronic states. Beside the well-known A(1g) bulk phonon mode at 2.76 THz, the time-resolved photoelectron spectra reveal a second mode at 0.72 THz which can be attributed to an optical surface phonon mode along the atomic rows of the Bi(114) surface.

Elemental topological insulator with tunable Fermi level: strained α-Sn on InSb(001).

We report on the epitaxial fabrication and electronic properties of a topological phase in strained α-Sn on InSb. The topological surface state forms in the presence of an unusual band order not based on direct spin-orbit coupling, as shown in density functional and GW slab-layer calculations. Angle-resolved photoemission including spin detection probes experimentally how the topological spin-polarized state emerges from the second bulk valence band. Moreover, we demonstrate the precise control of the Fermi level by dopants.

Fermi nesting between atomic wires with strong spin-orbit coupling.

The mutual interplay between superlattice structures, band filling factors, and spin-orbit coupling results in a highly correlated electronic spin and charge state found for an array of atomic Pb wires grown on Si(557). By means of spin- and angle-resolved photoemission spectroscopy, the spin texture close to the Fermi surface was found to be alternating and equidistant; thus, Fermi nesting occurs in between bands with the same spin helicity, giving rise to spin-polarized charge-density waves in the direction across the wires. An out-of-phase superposition of both Rashba channels is manifested by an extraordinary large Rashba splitting of Δk0=0.2 Å(-1)=g/2, where g is a reciprocal lattice vector defined by the interwire distance and fits into the model of spin-density waves in antiferromagnetically ordered chain structures. The implications towards spin-polarized transport along the wires will be discussed.

Three-dimensional spin rotations at the Fermi surface of a strongly spin-orbit coupled surface system.

The spin texture of the metallic two-dimensional electron system (sqrt[3]×sqrt[3])-Au/Ge(111) is revealed by fully three-dimensional spin-resolved photoemission, as well as by density functional calculations. The large hexagonal Fermi surface, generated by the Au atoms, shows a significant splitting due to spin-orbit interactions. The planar components of the spin exhibit a helical character, accompanied by a strong out-of-plane spin component with alternating signs along the six Fermi surface sections. Moreover, in-plane spin rotations toward a radial direction are observed close to the hexagon corners. Such a threefold-symmetric spin pattern is not described by the conventional Rashba model. Instead, it reveals an interplay with Dresselhaus-like spin-orbit effects as a result of the crystalline anisotropies.

Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi2Se3.

We report a Rashba spin splitting of a two-dimensional electron gas in the topological insulator Bi(2)Se(3) from angle-resolved photoemission spectroscopy. We further demonstrate its electrostatic control, and show that spin splittings can be achieved which are at least an order-of-magnitude larger than in other semiconductors. Together these results show promise for the miniaturization of spintronic devices to the nanoscale and their operation at room temperature.

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

Constrained by the Nielsen-Ninomiya no-go theorem, in all so-far experimentally determined Weyl semimetals (WSMs) the Weyl points (WPs) always appear in pairs in the momentum space with no exception. As a consequence, Fermi arcs occur on surfaces which connect the projections of the WPs with opposite chiral charges. However, this situation can be circumvented in the case of unpaired WP, without relevant surface Fermi arc connecting its surface projection, appearing singularly, while its Berry curvature field is absorbed by nontrivial charged nodal walls. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show experimentally that a singular Weyl point emerges in PtGa at the center of the Brillouin zone (BZ), which is surrounded by closed Weyl nodal walls located at the BZ boundaries and there is no Fermi arc connecting its surface projection. Our results reveal that nontrivial band crossings of different dimensionalities can emerge concomitantly in condensed matter, while their coexistence ensures the net topological charge of different dimensional topological objects to be zero. Our observation extends the applicable range of the original Nielsen-Ninomiya no-go theorem which was derived from zero dimensional paired WPs with opposite chirality.

Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3.

We show that the strongly spin-orbit coupled materials Bi2Te3 and Sb2Te3 and their derivatives belong to the Z2 topological-insulator class. Using a combination of first-principles theoretical calculations and photoemission spectroscopy, we directly show that Bi2Te3 is a large spin-orbit-induced indirect bulk band gap (delta approximately 150 meV) semiconductor whose surface is characterized by a single topological spin-Dirac cone. The electronic structure of self-doped Sb2Te3 exhibits similar Z2 topological properties. We demonstrate that the dynamics of spin-Dirac fermions can be controlled through systematic Mn doping, making these materials classes potentially suitable for topological device applications.

Entanglement and manipulation of the magnetic and spin-orbit order in multiferroic Rashba semiconductors.

Entanglement of the spin-orbit and magnetic order in multiferroic materials bears a strong potential for engineering novel electronic and spintronic devices. Here, we explore the electron and spin structure of ferroelectric α-GeTe thin films doped with ferromagnetic Mn impurities to achieve its multiferroic functionality. We use bulk-sensitive soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) to follow hybridization of the GeTe valence band with the Mn dopants. We observe a gradual opening of the Zeeman gap in the bulk Rashba bands around the Dirac point with increase of the Mn concentration, indicative of the ferromagnetic order, at persistent Rashba splitting. Furthermore, subtle details regarding the spin-orbit and magnetic order entanglement are deduced from spin-resolved ARPES measurements. We identify antiparallel orientation of the ferroelectric and ferromagnetic polarization, and altering of the Rashba-type spin helicity by magnetic switching. Our experimental results are supported by first-principles calculations of the electron and spin structure.

Observation of correlated spin-orbit order in a strongly anisotropic quantum wire system.

Quantum wires with spin-orbit coupling provide a unique opportunity to simultaneously control the coupling strength and the screened Coulomb interactions where new exotic phases of matter can be explored. Here we report on the observation of an exotic spin-orbit density wave in Pb-atomic wires on Si(557) surfaces by mapping out the evolution of the modulated spin-texture at various conditions with spin- and angle-resolved photoelectron spectroscopy. The results are independently quantified by surface transport measurements. The spin polarization, coherence length, spin dephasing rate and the associated quasiparticle gap decrease simultaneously as the screened Coulomb interaction decreases with increasing excess coverage, providing a new mechanism for generating and manipulating a spin-orbit entanglement effect via electronic interaction. Despite clear evidence of spontaneous spin-rotation symmetry breaking and modulation of spin-momentum structure as a function of excess coverage, the average spin polarization over the Brillouin zone vanishes, indicating that time-reversal symmetry is intact as theoretically predicted.

Fermi states and anisotropy of Brillouin zone scattering in the decagonal Al-Ni-Co quasicrystal.

Quasicrystals (QCs) are intermetallic alloys that have excellent long-range order but lack translational symmetry in at least one dimension. The valence band electronic structure near the Fermi energy EF in such materials is of special interest since it has a direct relation to their unusual physical properties. However, the Fermi surface (FS) topology as well as the mechanism of QC structure stabilization are still under debate. Here we report the first observation of the three-dimensional FS and valence band dispersions near EF in decagonal Al70Ni20Co10 (d-AlNiCo) QCs using soft X-ray angle-resolved photoemission spectroscopy. We show that the FS, formed by dispersive Al sp-states, has a multicomponent character due to a large contribution from high-order bands. Moreover, we discover that the magnitude of the gap at the FS related to the interaction with Brillouin zone boundary (Hume-Rothery gap) critically differs for the periodic and quasiperiodic directions.

Direct observation of the spin texture in SmB6 as evidence of the topological Kondo insulator.

Topological Kondo insulators have been proposed as a new class of topological insulators in which non-trivial surface states reside in the bulk Kondo band gap at low temperature due to strong spin-orbit coupling. In contrast to other three-dimensional topological insulators, a topological Kondo insulator is truly bulk insulating. Furthermore, strong electron correlations are present in the system, which may interact with the novel topological phase. By applying spin- and angle-resolved photoemission spectroscopy, here we show that the surface states of SmB6 are spin polarized. The spin is locked to the crystal momentum, fulfilling time reversal and crystal symmetries. Our results provide strong evidence that SmB6 can host topological surface states in a bulk insulating gap stemming from the Kondo effect, which can serve as an ideal platform for investigating of the interplay between novel topological quantum states with emergent effects and competing orders induced by strongly correlated electrons.

Observation of a topological crystalline insulator phase and topological phase transition in Pb(1-x)Sn(x)Te.

A topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction-driven band inversion. The topological phase in the Bi(1-x)Sb(x) system is due to an odd number of band inversions. A related spin-orbit system, the Pb(1-x)Sn(x)Te, has long been known to contain an even number of inversions based on band theory. Here we experimentally investigate the possibility of a mirror symmetry-protected topological crystalline insulator phase in the Pb(1-x)Sn(x)Te class of materials that has been theoretically predicted to exist in its end compound SnTe. Our experimental results show that at a finite Pb composition above the topological inversion phase transition, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order distinct from that observed in Bi(1-x)Sb(x). Our observation of the spin-polarized Dirac surface states in the inverted Pb(1-x)Sn(x)Te and their absence in the non-inverted compounds related via a topological phase transition provide the experimental groundwork for opening the research on novel topological order in quantum devices.