Revealing hidden spin polarization in centrosymmetric van der Waals materials on ultrafast timescales

One of the key challenges for spintronic and quantum technologies is to achieve active control of the spin angular momentum of electrons in nanoscale materials on ultrafast, femtosecond timescales. While conventional ferromagnetic materials and materials supporting spin texture suffer both from conceptional limitations in miniaturization and inefficiency of optical and electronic manipulation, non-magnetic centrosymmetric layered materials with hidden spin polarization may offer an alternative pathway to manipulate the spin degree of freedom by external stimuli. Here we demonstrate an approach for generating transient spin polarization on a femtosecond timescale in the otherwise spin-unpolarized band structure of the centrosymmetric 2H-stacked group VI transition metal dichalcogenide WSe2. Using ultrafast optical excitation of a fullerene layer grown on top of WSe2, we trigger an ultrafast interlayer electron transfer from the fullerene layer into the WSe2 crystal. The resulting transient charging of the C60/WSe2 interface leads to a substantial interfacial electric field that by means of spin-layer-valley locking ultimately creates ultrafast spin polarization without the need of an external magnetic field. Our findings open a novel pathway for true optical engineering of spin functionalities such as the sub-picosecond generation and manipulation of ultrafast spin currents in 2D heterostructures.

Quantum oscillations evidence for topological bands in kagome metal ScV6Sn6

Metals with kagome lattice provide bulk materials to host both the flat-band and Dirac electronic dispersions. A new family of kagome metals is recently discovered inAV6Sn6. The Dirac electronic structures of this material needs more experimental evidence to confirm. In the manuscript, we investigate this problem by resolving the quantum oscillations in both electrical transport and magnetization in ScV6Sn6. The revealed orbits are consistent with the electronic band structure models. Furthermore, the Berry phase of a dominating orbit is revealed to be aroundπ, providing direct evidence for the topological band structure, which is consistent with calculations. Our results demonstrate a rich physics and shed light on the correlated topological ground state of this kagome metal.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

Chiral anomaly and Weyl orbit in three-dimensional Dirac semimetal Cd3As2grown on Si

Preparing Cd3As2, which is a three-dimensional (3D) Dirac semimetal in certain crystal orientation, on Si is highly desirable as such a sample may well be fully compatible with existing Si CMOS technology. However, there is a dearth of such a study regarding Cd3As2films grown on Si showing the chiral anomaly. Here,for the first time, we report the novel preparation and fabrication technique of a Cd3As2(112) film on a Si (111) substrate with a ZnTe (111) buffer layer which explicitly shows the chiral anomaly with a nontrivial Berry's phase ofπ. Despite the Hall carrier density (n3D≈9.42×1017cm-3) of our Cd3As2film, which is almost beyond the limit for the portents of a 3D Dirac semimetal to emerge, we observe large linear magnetoresistance in a perpendicular magnetic field and negative magnetoresistance in a parallel magnetic field. These results clearly demonstrate the chiral magnetic effect and 3D Dirac semimetallic behavior in our silicon-based Cd3As2film. Our tailoring growth of Cd3As2on a conventional substrate such as Si keeps the sample quality, while also achieving a low carrier concentration.

Magnetoresistive-coupled transistor using the Weyl semimetal NbP

Semiconductor transistors operate by modulating the charge carrier concentration of a channel material through an electric field coupled by a capacitor. This mechanism is constrained by the fundamental transport physics and material properties of such devices-attenuation of the electric field, and limited mobility and charge carrier density in semiconductor channels. In this work, we demonstrate a new type of transistor that operates through a different mechanism. The channel material is a Weyl semimetal, NbP, whose resistivity is modulated via a magnetic field generated by an integrated superconductor. Due to the exceptionally large electron mobility of this material, which reaches over 1,000,000 cm2/Vs, and the strong magnetoresistive coupling, the transistor can generate significant transconductance amplification at nanowatt levels of power. This type of device can enable new low-power amplifiers, suitable for qubit readout operation in quantum computers.

Tunable Chirality-Dependent Nonlinear Electrical Responses in 2D Tellurium

Tellurium (Te) is an elemental semiconductor with a simple chiral crystal structure. Te in a two-dimensional (2D) form synthesized by a solution-based method shows excellent electrical, optical, and thermal properties. In this work, the chirality of hydrothermally grown 2D Te is identified and analyzed by hot sulfuric acid etching and high-angle tilted high-resolution scanning transmission electron microscopy. The gate-tunable nonlinear electrical responses, including the nonreciprocal electrical transport in the longitudinal direction and the nonlinear planar Hall effect in the transverse direction, are observed in 2D Te under a magnetic field. Moreover, the nonlinear electrical responses have opposite signs in left- and right-handed 2D Te due to the opposite spin polarizations ensured by the chiral symmetry. The fundamental relationship between the spin-orbit coupling and the crystal symmetry in two enantiomers provides a viable platform for realizing chirality-based electronic devices by introducing the degree of freedom of chirality into electron transport.

CoTe2 : A Quantum Critical Dirac Metal with Strong Spin Fluctuations

Quantum critical points separating weak ferromagnetic and paramagnetic phases trigger many novel phenomena. Dynamical spin fluctuations not only suppress the long-range order, but can also lead to unusual transport and even superconductivity. Combining quantum criticality with topological electronic properties presents a rare and unique opportunity. Here, by means of ab initio calculations and magnetic, thermal, and transport measurements, it is shown that the orthorhombic CoTe₂ is close to ferromagnetism, which appears suppressed by spin fluctuations. Calculations and transport measurements reveal nodal Dirac lines, making it a rare combination of proximity to quantum criticality and Dirac topology.

Evidences of Topological Surface States in the Nodal-Line Semimetal SnTaS2 Nanoflakes

Exploring the topological surface state of a topological semimetal by the transport technique has always been a big challenge because of the overwhelming contribution of the bulk state. In this work, we perform systematic angular-dependent magnetotransport measurements and electronic band calculations on SnTaS₂ crystals, a layered topological nodal-line semimetal. Distinct Shubnikov-de Haas quantum oscillations were observed only in SnTaS₂ nanoflakes when the thickness was below about 110 nm, and the oscillation amplitudes increased significantly with decreasing thickness. By analysis of the oscillation spectra, together with the theoretical calculation, a two-dimensional and topological nontrivial nature of the surface band is unambiguously identified, providing direct transport evidence of drumhead surface state for SnTaS₂. Our comprehensive understanding of the Fermi surface topology of the centrosymmetric superconductor SnTaS₂ is crucial for further research on the interplay of superconductivity and nontrivial topology.

Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn6Sn6, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

The Singularity Paramagnetic Peak of Bi0.3Sb1.7Te3 with p-type Surface State

The magnetization measurement was performed in the Bi_0.3Sb_1.7Te₃ single crystal. The magnetic susceptibility revealed a paramagnetic peak independent of the experimental temperature variation. It is speculated to be originated from the free-aligned spin texture at the Dirac point. The ARPES reveals that the Fermi level lies below the Dirac point. The Fermi wavevector extracted from the de Haas-van Alphen oscillation is consistent with the energy dispersion in the ARPES. Our experimental results support that the observed paramagnetic peak in the susceptibility curve does not originate from the free-aligned spin texture at the Dirac point.

Tip-induced superconductivity

It is widely believed that topological superconductivity, a hitherto elusive phase of quantum matter, can be achieved by inducing superconductivity in topological materials. In search of such topological superconductors, certain topological insulators (like, Bi₂Se₃) were successfully turned into superconductors by metal-ion (Cu, Pd, Sr, Nb etc) intercalation. Superconductivity could be induced in topological materials through applying pressure as well. For example, a pressure-induced superconducting phase was found in the topological insulator Bi₂Se₃. However, in all such cases, no conclusive signature of topological superconductivity was found. In this review, we will discuss about another novel way of inducing superconductivity in a non-superconducting topological material-by creating a mesoscopic interface on the material with a non-superconducting, normal metallic tip where the mesoscopic interface becomes superconducting. Such a phase is now known as a tip-induced superconducting (TISC) phase. This was first realized on Cd₃As₂in India. Following that, a large number of other topological materials were shown to display TISC. Since the TISC phase emerges only at a confined region under a mesoscopic point contact, traditional bulk tools for characterizing superconductivity cannot be employed to detect/confirm such a phase. On the other hand, such a point contact geometry is ideal for probing the possible existence of a temperature and magnetic field dependent superconducting energy gap and a temperature and magnetic field dependent critical current. We will review the details of the experimental signatures that can be used to prove the existence of superconductivity even when the 'text-book' tests for detecting superconductivity cannot be performed. Then, we will review various systems where a TISC phase could be realized.

Rare Earth Engineering in RMn_{6}Sn_{6} (R=Gd-Tm, Lu) Topological Kagome Magnets

Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.

Kramers nodal line metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Rashba valleys and quantum Hall states in few-layer black arsenic

Exciting phenomena may emerge in non-centrosymmetric two-dimensional electronic systems when spin-orbit coupling (SOC)¹ interplays dynamically with Coulomb interactions^2,3, band topology^4,5 and external modulating forces^6-8. Here we report synergetic effects between SOC and the Stark effect in centrosymmetric few-layer black arsenic, which manifest as particle-hole asymmetric Rashba valley formation and exotic quantum Hall states that are reversibly controlled by electrostatic gating. The unusual findings are rooted in the puckering square lattice of black arsenic, in which heavy 4p orbitals form a Brillouin zone-centred Γ valley with p_z symmetry, coexisting with doubly degenerate D valleys of p_x origin near the time-reversal-invariant momenta of the X points. When a perpendicular electric field breaks the structure inversion symmetry, strong Rashba SOC is activated for the p_x bands, which produces spin-valley-flavoured D^± valleys paired by time-reversal symmetry, whereas Rashba splitting of the Γ valley is constrained by the p_z symmetry. Intriguingly, the giant Stark effect shows the same p_x-orbital selectiveness, collectively shifting the valence band maximum of the D^± Rashba valleys to exceed the Γ Rashba top. Such an orchestrating effect allows us to realize gate-tunable Rashba valley manipulations for two-dimensional hole gases, hallmarked by unconventional even-to-odd transitions in quantum Hall states due to the formation of a flavour-dependent Landau level spectrum. For two-dimensional electron gases, the quantization of the Γ Rashba valley is characterized by peculiar density-dependent transitions in the band topology from trivial parabolic pockets to helical Dirac fermions.

Quantized thermoelectric Hall effect induces giant power factor in a topological semimetal

Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric Hall effect in the topological Weyl semimetal (WSM) tantalum phosphide (TaP). An ultrahigh longitudinal thermopower \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{xx} \sim 1.1 \times 10^3 \, \mu \, {\mathrm{V}} \, {\mathrm{K}}^{ - 1}$$\end{document}Sxx~1.1×103μVK−1 and giant power factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 525 \, \mu \, {\mathrm{W}} \, {\mathrm{cm}}^{ - 1} \, {\mathrm{K}}^{ - 2}$$\end{document}~525μWcm−1K−2 are observed at ~40 K, which is largely attributed to the quantized thermoelectric Hall effect. Our work highlights the unique quantized thermoelectric Hall effect realized in a WSM toward low-temperature energy harvesting applications.

Theories predict a large thermopower and a quantized thermoelectric Hall conductivity in topological semimetals. Here, the authors observe an ultrahigh longitudinal thermopower and a giant power factor attributed to the quantized thermoelectric Hall effect in a Weyl semimetal TaP.

Discerning the Nature of Neutrinos: Decoherence and Geometric Phases

We present new approaches to distinguish between Dirac and Majorana neutrinos. The first is based on the analysis of the geometric phases associated to neutrinos in matter, the second on the effects of decoherence on neutrino oscillations. In the former we compute the total and geometric phase for neutrinos, and find that they depend on the Majorana phase and on the parametrization of the mixing matrix. In the latter, we show that Majorana neutrinos might violate CPT symmetry, whereas Dirac neutrinos preserve CPT. A phenomenological analysis is also reported showing the possibility to highlight the distinctions between Dirac and Majorana neutrinos.

Quantum transport evidence of Weyl fermions in an epitaxial ferromagnetic oxide

Magnetic Weyl semimetals have novel transport phenomena related to pairs of Weyl nodes in the band structure. Although the existence of Weyl fermions is expected in various oxides, the evidence of Weyl fermions in oxide materials remains elusive. Here we show direct quantum transport evidence of Weyl fermions in an epitaxial 4d ferromagnetic oxide SrRuO₃. We employ machine-learning-assisted molecular beam epitaxy to synthesize SrRuO₃ films whose quality is sufficiently high to probe their intrinsic transport properties. Experimental observation of the five transport signatures of Weyl fermions—the linear positive magnetoresistance, chiral-anomaly-induced negative magnetoresistance, π phase shift in a quantum oscillation, light cyclotron mass, and high quantum mobility of about 10,000 cm²V⁻¹s⁻¹—combined with first-principles electronic structure calculations establishes SrRuO₃ as a magnetic Weyl semimetal. We also clarify the disorder dependence of the transport of the Weyl fermions, which gives a clear guideline for accessing the topologically nontrivial transport phenomena.

Despite various predictions, the evidence of Weyl fermions in oxide materials remains elusive. Here, the authors show evidence of Weyl fermions in quantum transport measurements in an epitaxial ferromagnetic oxide SrRuO₃.

Breakdown of Ohm's law and nontrivial Berry phase in magnetic Weyl semimetal Co3Sn2S2

The concept of realization of Weyl points close to the Fermi level in materials with broken time-reversal symmetry has significant theoretical and technological ramifications. Here, we review the investigation of magneto-transport measurements in single crystals of magnetic Weyl semimetal Co3Sn2S2. We see a turn-on like behaviour followed by saturation in resistivity under magnetic field in the low temperature region which is allocated to the topological surface states. A non-saturating magnetoresistance, linear at high fields, is observed at low temperatures where applied magnetic field is transverse to the current direction. The linear negative magnetoresistance at low magnetic fields (B < 0.1 T) provides evidence for time reversal symmetry breaking in Co3Sn2S2. Chiral anomaly in Weyl metallic state in Co3Sn2S2 is confirmed from the breakdown of Ohm's law in the electronic transport. Shubnikov de Haas (SdH) oscillation measurement has unveiled the multiple sub-bands on the Fermi surface that corresponds to a non-trivial Berry phase. The non-linear behaviour in Hall resistivity validates the existence of two type of charge carriers with equal electron and hole densities. Strong temperature dependence of carrier mobilities reflects the systematic violation of Kohler's rule in Co3Sn2S2. Our findings open avenues to study kagome-lattice based magnetic Weyl semimetals that unfurl the basic topological aspects leading to significant ramification for spintronics.

Anisotropic Quantum Transport through a Single Spin Channel in the Magnetic Semiconductor EuTiO3

Magnetic semiconductors are a vital component in the understanding of quantum transport phenomena. To explore such delicate, yet fundamentally important, effects, it is crucial to maintain a high carrier mobility in the presence of magnetic moments. In practice, however, magnetization often diminishes the carrier mobility. Here, it is shown that EuTiO₃ is a rare example of a magnetic semiconductor that can be desirably grown using the molecular beam epitaxy to possess a high carrier mobility exceeding 3000 cm² V^-1 s^-1 at 2 K, while intrinsically hosting a large magnetization value, 7 μ_B per formula unit. This is demonstrated by measuring the Shubnikov-de Haas (SdH) oscillations in the ferromagnetic state of EuTiO₃ films with various carrier densities. Using first-principles calculations, it is shown that the observed SdH oscillations originate genuinely from Ti 3d-t_2g states which are fully spin-polarized due to their energetical proximity to the in-gap Eu 4f bands. Such an exchange coupling is further shown to have a profound effect on the effective mass and fermiology of the Ti 3d-t_2g electrons, manifested by a directional anisotropy in the SdH oscillations. These findings suggest that EuTiO₃ film is an ideal magnetic semiconductor, offering a fertile field to explore quantum phenomena suitable for spintronic applications.

Planar Hall effect and anisotropic magnetoresistance in polar-polar interface of LaVO3-KTaO3 with strong spin-orbit coupling

Among the perovskite oxide family, KTaO₃ (KTO) has recently attracted considerable interest as a possible system for the realization of the Rashba effect. In this work, we report a novel conducting interface by placing KTO with another insulator, LaVO₃ (LVO) and report planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) measurements. This interface exhibits a signature of strong spin-orbit coupling. Our experimental observations of two fold AMR and PHE at low magnetic fields (B) is similar to those obtained for topological systems and can be intuitively understood using a phenomenological theory for a Rashba spin-split system. Our experimental data show a B² dependence of AMR and PHE at low magnetic fields that could also be explained based on our model. At high fields (~8 T), we see a two fold to four fold transition in the AMR that could not be explained using only Rashba spin-split energy spectra.

Two dimensional electron gas (2DEG) at oxide interfaces is promising in modern electronic devices. Here, Wadehra et al. realize 2DEG at a novel interface composed of LaVO₃ and KTaO₃, where strong spin-orbit coupling and relativistic nature of the electrons in the 2DEG, leading to anisotropic magnetoresistance and planar Hall effect.

Pressure-induced topological phase transition in noncentrosymmetric elemental tellurium

Recent progress in understanding the electronic band topology and emergent topological properties encourage us to reconsider the band structure of well-known materials including elemental substances. Controlling such a band topology by external field is of particular interest from both fundamental and technological viewpoints. Here we report possible signatures of the pressure-induced topological phase transition from a semiconductor to a Weyl semimetal in elemental tellurium probed by transport measurements. Pressure variation of the periods of Shubnikov-de Haas oscillations, as well as oscillation phases, shows an anomaly around the pressure theoretically predicted for topological phase transition. This behavior is consistent with the pressure-induced band deformation and resultant band-crossing effect. Moreover, effective cyclotron mass is reduced toward the critical pressure, potentially reflecting the emergence of massless linear dispersion. The present result paves the way for studying the electronic band topology in well-known compounds and topological phase transition by the external field.

Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and the g Factor in Spin-Orbit Coupled Solids

We propose a fully quantum approach to nonperturbatively calculate the spin-split Landau levels and g factor of various spin-orbit coupled solids based on the k·p theory in the matrix mechanics representation. The new method considers the detailed band structure and the multiband effect of spin-orbit coupling irrespective of the magnetic-field strength. We show an application of this method to PbTe, a typical Dirac electron system. Contrary to popular belief, we show that the spin-splitting parameter M, which is the ratio of the Zeeman to cyclotron energy, exhibits a remarkable magnetic-field dependence. This field dependence can rectify the existing discrepancy between experimental and theoretical results. We also show that M evaluated from the fan diagram plot is different from that determined as the ratio of the Zeeman to cyclotron energy, which also overturns common belief.

Nontrivial quantum oscillation geometric phase shift in a trivial band

Quantum oscillations provide a notable visualization of the Fermi surface of metals, including associated geometrical phases such as Berry's phase, that play a central role in topological quantum materials. Here we report the existence of a new quantum oscillation phase shift in a multiband system. In particular, we study the ABA-trilayer graphene, the band structure of which is composed of a weakly gapped linear Dirac band, nested within a quadratic band. We observe that Shubnikov-de Haas (SdH) oscillations of the quadratic band are shifted by a phase that sharply departs from the expected 2π Berry's phase and is inherited from the nontrivial Berry's phase of the linear band. We find this arises due to an unusual filling enforced constraint between the quadratic band and linear band Fermi surfaces. Our work indicates how additional bands can be exploited to tease out the effect of often subtle quantum mechanical geometric phases.

Nontrivial topology of bulk HgSe from the study of cyclotron effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations

In this paper, the authors report the results of an experimental study of effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations of transverse magnetoresistance in an extended electron concentration region from 8.8  ×  10¹⁵ cm^-3 to 4.3  ×  10¹⁸ cm^-3 in single crystals of mercury selenide. The revealed features indicate that Weyl semimetal phase may exist in HgSe at low electron density. The most significant result is the discovery of an abrupt change of Berry phase [Formula: see text] at electron concentration [Formula: see text] 2  ×  10¹⁸ cm^-3, which we explain in terms of a manifestation of topological Lifshitz transition in HgSe that occurs by tuning Fermi energy via doping.

Quantum Oscillations from Nontrivial States in Quasi-Two-Dimensional Dirac Semimetal ZrTe5 Nanowires

Recently discovered Dirac semimetal ZrTe5 bulk crystal, exhibits nontrivial conducting states in each individual layer, holding great potential for novel spintronic applications. Here, to reveal the transport properties of ZrTe5, we fabricated ZrTe5 nanowires (NWs) devices, with much larger surface-to-volume ratio than bulk materials. Quantum oscillations induced by the two-dimensional (2D) nontrivial conducting states have been observed from these NWs and a finite Berry phase of ~π is obtained by the analysis of Landau-level fan diagram. More importantly, the absence of the Aharonov-Bohm (A-B) oscillations, along with the SdH oscillations, suggests that the electrons only conduct inside each layer. And the intralayer conducting is suppressed because of the weak connection between adjacent layers. Our results demonstrate that ZrTe5 NWs can serve as a suitable quasi-2D Dirac semimetal with high mobility (~85000 cm2V-1s-1) and large nontrivial conductance contribution (up to 8.68%).

Experimental Observation of Hidden Berry Curvature in Inversion-Symmetric Bulk 2H-WSe_{2}

We investigate the hidden Berry curvature in bulk 2H-WSe_{2} by utilizing the surface sensitivity of angle resolved photoemission (ARPES). The symmetry in the electronic structure of transition metal dichalcogenides is used to uniquely determine the local orbital angular momentum (OAM) contribution to the circular dichroism (CD) in ARPES. The extracted CD signals for the K and K^{'} valleys are almost identical, but their signs, which should be determined by the valley index, are opposite. In addition, the sign is found to be the same for the two spin-split bands, indicating that it is independent of spin state. These observed CD behaviors are what are expected from Berry curvature of a monolayer of WSe_{2}. In order to see if CD-ARPES is indeed representative of hidden Berry curvature within a layer, we use tight binding analysis as well as density functional calculation to calculate the Berry curvature and local OAM of a monolayer WSe_{2}. We find that measured CD-ARPES is approximately proportional to the calculated Berry curvature as well as local OAM, further supporting our interpretation.

Design of Highly Efficient Thermoelectric Materials: Tailoring Reciprocal-Space Properties by Real-Space Modification

Although restricted by the poor performance at present, thermoelectric materials for power-generation devices and solid-state Peltier coolers still possess unlimited vitality, thus capturing considerable attention. Understanding and manipulating the electrical and thermal transport mechanisms in thermoelectrics play significant roles in tailoring the properties of various thermoelectric materials. The transport behavior of electrons and phonons are closely related to the chemical composition and structure, which are defined in real space. Meanwhile, transport properties are also contingent on the band structure and phonon spectrum, both of which are represented in the reciprocal-space first Brillouin zone. Real space and reciprocal space are bridged by the Fourier transform, and the combination of real-space and reciprocal-space properties will provide more possibilities for regulating transport characteristics. Herein, a compendious discussion of the internal connection between real space and reciprocal space, and the underlying physics and chemistry is presented. Then, how the relationship between real and reciprocal space provides additional insights to govern electrical and thermal transport parameters is elaborated upon, thereby enabling the discovery and optimization of thermoelectric materials. In conclusion, specific challenges and feasible directions are discussed.

Pressure-induced phase transitions and superconductivity in a black phosphorus single crystal

We report a thorough study of the transport properties of the normal and superconducting states of black phosphorus (BP) under magnetic field and high pressure with a large-volume apparatus that provides hydrostatic pressure to induce transitions from the layered A17 phase to the layered A7 phase and to the cubic phase of BP. Quantum oscillations can be observed at P ≥ 1 GPa in both resistivity and Hall voltage, and their evolutions with pressure in the A17 phase imply a continuous enlargement of Fermi surface. A significantly large magnetoresistance (MR) at low temperatures is observed in the A7 phase that becomes superconducting below a superconducting transition temperature Tc ∼ 6-13 K. Tc increases continuously with pressure on crossing the A7 to the cubic phase boundary. The strong MR effect can be fit by a modified Kohler's rule. A correlation between Tc and fitting parameters suggests that phonon-mediated interactions play dominant roles in driving the Cooper pairing, which is further supported by our density functional theory (DFT) calculations. The change of effective carrier mobility in the A17 phase under pressure derived from the MR effect is consistent with that obtained from the temperature dependence of the quantum oscillations. In situ single-crystal diffraction under high pressure indicates a total structural reconstruction instead of simple stretching of the A17 phase layers in the A17-to-A7-phase transition. This finding helps us to interpret transport properties on crossing the phase transition under high pressure.

Tip-induced or enhanced superconductivity: a way to detect topological superconductivity

Topological materials, hosting topological nontrivial electronic band, have attracted widespread attentions. As an application of topology in physics, the discovery and study of topological materials not only enrich the existing theoretical framework of physics, but also provide fertile ground for investigations on low energy excitations, such as Weyl fermions and Majorana fermions, which have not been observed yet as fundamental particles. These quasiparticles with exotic physical properties make topological materials the cutting edge of scientific research and a new favorite of high tech. As a typical example, Majorana fermions, predicted to exist in the edge state of topological superconductors, are proposed to implement topological error-tolerant quantum computers. Thus, the detection of topological superconductivity has become a frontier in condensed matter physics and materials science. Here, we review a way to detect topological superconductivity triggered by the hard point contact: tip-induced superconductivity (TISC) and tip-enhanced superconductivity (TESC). The TISC refers to the superconductivity induced by a non-superconducting tip at the point contact on non-superconducting materials. We take the elaboration of the chief experimental achievement of TISC in topological Dirac semimetal Cd₃As₂ and Weyl semimetal TaAs as key components of this article for detecting topological superconductivity. Moreover, we also briefly introduce the main results of another exotic effect, TESC, in superconducting Au₂Pb and Sr₂RuO₄ single crystals, which are respectively proposed as the candidates of helical topological superconductor and chiral topological superconductor. Related results and the potential mechanism are conducive to improving the comprehension of how to induce and enhance the topological superconductivity.

Vanishing quantum oscillations in Dirac semimetal ZrTe5

One of the characteristics of topological materials is their nontrivial Berry phase. Experimental determination of this phase largely relies on a phase analysis of quantum oscillations. We study the angular dependence of the oscillations in a Dirac material [Formula: see text] and observe a striking spin-zero effect (i.e., vanishing oscillations accompanied with a phase inversion). This indicates that the Berry phase in [Formula: see text] remains nontrivial for arbitrary field direction, in contrast with previous reports. The Zeeman splitting is found to be proportional to the magnetic field based on the condition for the spin-zero effect in a Dirac band. Moreover, it is suggested that the Dirac band in [Formula: see text] is likely transformed into a line node other than Weyl points for the field directions at which the spin zero occurs. The results underline a largely overlooked spin factor when determining the Berry phase from quantum oscillations.

A possible candidate for triply degenerate point fermions in trigonal layered PtBi2

Triply degenerate point (TP) fermions in tungsten–carbide-type materials (e.g., MoP), which represent new topological states of quantum matter, have generated immense interest recently. However, the TPs in these materials are found to be far below the Fermi level, leading to the TP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically predict the existence of TP fermions with TP points close to the Fermi level in trigonal layered PtBi₂ by ab initio calculations, and experimentally verify the predicted band topology by magnetotransport measurements under high magnetic fields up to 40 T. Analyses of both the pronounced Shubnikov–de Haas and de Haas–van Alphen oscillations reveal the existence of six principal Fermi pockets. Our experimental results, together with those from ab initio calculations, reveal the interplay between transport behaviors and unique electronic structures, and support the existence of TP fermions in trigonal layered PtBi₂.

Triply degenerate point (TP) fermions have been reported in MoP but the TPs are far below the Fermi level. Here, Guo et al. predict and verify the possible existence of TP fermions in trigonal layered PtBi₂, where the TP points are close to the Fermi level.

Magnetoresistance and valley degree of freedom in bulk bismuth

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.

Evidence for a Dirac nodal-line semimetal in SrAs3

Dirac nodal-line semimetals with the linear bands crossing along a line or loop, represent a new topological state of matter. Here, by carrying out magnetotransport measurements and performing first-principle calculations, we demonstrate that such a state has been realized in high-quality single crystals of SrAs₃. We obtain the nontrivial π Berry phase by analysing the Shubnikov-de Haas quantum oscillations. We also observe a robust negative longitudinal magnetoresistance induced by the chiral anomaly. Accompanying first-principles calculations identifies that a single hole pocket enclosing the loop nodes is responsible for these observations.

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

Nonzero Berry phase in quantum oscillations from giant Rashba-type spin splitting in LaTiO3/SrTiO3 heterostructures

The manipulation of the spin degrees of freedom in a solid has been of fundamental and technological interest recently for developing high-speed, low-power computational devices. There has been much work focused on developing highly spin-polarized materials and understanding their behavior when incorporated into so-called spintronic devices. These devices usually require spin splitting with magnetic fields. However, there is another promising strategy to achieve spin splitting using spatial symmetry breaking without the use of a magnetic field, known as Rashba-type splitting. Here we report evidence for a giant Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃. Analysis of the magnetotransport reveals anisotropic magnetoresistance, weak anti-localization and quantum oscillation behavior consistent with a large Rashba-type splitting. It is surprising to find a large Rashba-type splitting in 3d transition metal oxide-based systems such as the LaTiO₃/SrTiO₃ interface, but it is promising for the development of a new kind of oxide-based spintronics.

Rashba-type splitting is an effective way to manipulate the spin degrees of freedom in a solid without external magnetic field. Here, the authors demonstrate a strong Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃ which is promising for the development of oxide-based spintronics.

Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-Line Semimetals

Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial π Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W=Zr/Hf, H=Si/Ge, M=S/Se/Te). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu_{3}PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help explore transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.

Evidence for Layered Quantized Transport in Dirac Semimetal ZrTe5

ZrTe₅ is an important semiconductor thermoelectric material and a candidate topological insulator. Here we report the observation of Shubnikov-de Hass (SdH) oscillations accompanied by quantized Hall resistance in bulk ZrTe₅ crystal, with a mobility of 41,000 cm²V⁻¹s⁻¹. We have found that the quantum oscillations does not originate from the surface states, but from the bulk states. Each single layer ZrTe₅ acted like an independent 2D electron system in the quantum Hall regime having the same carrier density and mobilities, while the bulk of the sample exhibits a multilayered quantum Hall effect.

Evolution of the Fermi surface of BiTeCl with pressure

We report measurements of Shubnikov-de Haas oscillations in the giant Rashba semiconductor BiTeCl under applied pressures up to  ∼2.5 GPa. We observe two distinct oscillation frequencies, corresponding to the Rashba-split inner and outer Fermi surfaces. BiTeCl has a conduction band bottom that is split into two sub-bands due to the strong Rashba coupling, resulting in two spin-polarized conduction bands as well as a Dirac point. Our results suggest that the chemical potential lies above this Dirac point, giving rise to two Fermi surfaces. We use a simple two-band model to understand the pressure dependence of our sample parameters. Comparing our results on BiTeCl to previous results on BiTeI, we observe similar trends in both the chemical potential and the Rashba splitting with pressure.

Fermi surface topology and signature of surface Dirac nodes in LaBi

Novel topological state of matter is one of the rapidly growing fields in condensed matter physics research in recent times. While these materials are fascinating from the aspect of fundamental physics of relativistic particles, their exotic transport properties are equally compelling due to the potential technological applications. Extreme magnetoresistance and ultrahigh carrier mobility are two such major hallmarks of topological materials and often used as primary criteria for identifying new compounds belonging to this class. Recently, LaBi has emerged as a new system, which exhibits the above mentioned properties. However, the topological nature of its band structure remains unresolved. Here, using the magnetotransport and magnetization measurements, we have probed the bulk and surface states of LaBi. Similar to earlier reports, extremely large magnetoresistance and high carrier mobility have been observed with compensated electron and hole density. The Fermi surface properties have been analyzed from both Shubnikov-de Haas and de Haas-van Alphen oscillation techniques. In the magnetization measurement, a prominent paramagnetic singularity has been observed, which demonstrates the non-trivial nature of the surface states in LaBi. Our study unambiguously confirms that LaBi is a three-dimensional topological insulator with possible linear dispersion in the gapped bulk band structure.

Bulk Rashba Semiconductors and Related Quantum Phenomena

Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.

Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite PtBi_{2}

While pyrite-type PtBi_{2} with a face-centered cubic structure has been predicted to be a three-dimensional (3D) Dirac semimetal, experimental study of its physical properties remains absent. Here we report the angular-dependent magnetoresistance measurements of a PtBi_{2} single crystal under high magnetic fields. We observed extremely large unsaturated magnetoresistance (XMR) up to (11.2×10^{6})% at T=1.8  K in a magnetic field of 33 T, which is comparable to the previously reported Dirac materials, such as WTe_{2}, LaSb, and NbP. The crystals exhibit an ultrahigh mobility and significant Shubnikov-de Hass quantum oscillations with a nontrivial Berry phase. The analysis of Hall resistivity indicates that the XMR can be ascribed to the nearly compensated electron and hole. Our experimental results associated with the ab initio calculations suggest that pyrite PtBi_{2} is a topological semimetal candidate that might provide a platform for exploring topological materials with XMR in noble metal alloys.

Topological Phase Transition in Single Crystals of (Cd1-xZnx)3As2

Single crystals of (Cd_1−xZn_x)₃As₂ were synthesized from high-temperature solutions and characterized in terms of their structural and electrical properties. Based on the measurements of resistivity and Hall signals, we revealed a chemical-doping-controlled transition from a three-dimensional Dirac semimetal to a semiconductor with a critical point x_c ~ 0.38. We observed structural transitions from a body-center tetragonal phase to a primitive tetragonal phase then back to a body-center tetragonal phase in the solid solutions as well, which are irrelevant to the topological phase transition. This continuously tunable system controlled by chemical doping provides a platform for investigating the topological quantum phase transition of three-dimensional Dirac electrons.

Disruption of the Accidental Dirac Semimetal State in ZrTe_{5} under Hydrostatic Pressure

We study the effect of hydrostatic pressure on the magnetotransport properties of zirconium pentatelluride. The magnitude of resistivity anomaly gets enhanced with increasing pressure, but the transition temperature T^{*} is insensitive to it up to 2.5 GPa. In the case of H∥b, the quasilinear magnetoresistance decreases drastically from 3300% (9 T) at ambient pressure to 230% (9 T) at 2.5 GPa. Besides, the change of the quantum oscillation phase from topological nontrivial to trivial is revealed around 2 GPa. Both demonstrate that the pressure breaks the accidental Dirac node in ZrTe_{5}. For H∥c, in contrast, subtle changes can be seen in the magnetoresistance and quantum oscillations. In the presence of pressure, ZrTe_{5} evolves from a highly anisotropic to a nearly isotropic electronic system, which accompanies the disruption of the accidental Dirac semimetal state. It supports the assumption that ZrTe_{5} is a semi-3D Dirac system with linear dispersion along two directions and a quadratic one along the third.

Discovery of tip induced unconventional superconductivity on Weyl semimetal

Weyl fermion is a massless Dirac fermion with definite chirality, which has been long pursued since 1929. Though it has not been observed as a fundamental particle in nature, Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal, which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal, TaAs crystal possesses 12 pairs of Weyl points in the momentum space, which are topologically protected against small perturbations. Here, we report for the first time the tip induced superconductivity on TaAs crystal by point contact spectroscopy. The zero bias conductance peak as well as a conductance plateau with double conductance peaks and sharp double dips are observed in the point contact spectra simultaneously, indicating unconventional superconductivity. Our further theoretical study suggests that the induced superconductivity may have nontrivial topology. The present work opens a new route in investigating the novel superconducting states based on Weyl materials.

Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS

Whereas the discovery of Dirac- and Weyl-type excitations in electronic systems is a major breakthrough in recent condensed matter physics, finding appropriate materials for fundamental physics and technological applications is an experimental challenge. In all of the reported materials, linear dispersion survives only up to a few hundred millielectronvolts from the Dirac or Weyl nodes. On the other hand, real materials are subject to uncontrolled doping during preparation and thermal effect near room temperature can hinder the rich physics. In ZrSiS, angle-resolved photoemission spectroscopy measurements have shown an unusually robust linear dispersion (up to [Formula: see text]2 eV) with multiple nondegenerate Dirac nodes. In this context, we present the magnetotransport study on ZrSiS crystal, which represents a large family of materials (WHM with W = Zr, Hf; H = Si, Ge, Sn; M = O, S, Se, Te) with identical band topology. Along with extremely large and nonsaturating magnetoresistance (MR), [Formula: see text]1.4 [Formula: see text] 10⁵% at 2 K and 9 T, it shows strong anisotropy, depending on the direction of the magnetic field. Quantum oscillation and Hall effect measurements have revealed large hole and small electron Fermi pockets. A nontrivial [Formula: see text] Berry phase confirms the Dirac fermionic nature for both types of charge carriers. The long-sought relativistic phenomenon of massless Dirac fermions, known as the Adler-Bell-Jackiw chiral anomaly, has also been observed.

Mesoscopic superconductivity and high spin polarization coexisting at metallic point contacts on Weyl semimetal TaAs

A Weyl semimetal is a topologically non-trivial phase of matter that hosts mass-less Weyl fermions, the particles that remained elusive for more than 80 years since their theoretical discovery. The Weyl semimetals exhibit unique transport properties and remarkably high surface spin polarization. Here we show that a mesoscopic superconducting phase with critical temperature T_c=7 K can be realized by forming metallic point contacts with silver (Ag) on single crystals of TaAs, while neither Ag nor TaAs are superconductors. Andreev reflection spectroscopy of such point contacts reveals a superconducting gap of 1.2 meV that coexists with a high transport spin polarization of 60% indicating a highly spin-polarized supercurrent flowing through the point contacts on TaAs. Therefore, apart from the discovery of a novel mesoscopic superconducting phase, our results also show that the point contacts on Weyl semimetals are potentially important for applications in spintronics.

Topological states of matter with unique transport properties hold the potential to realize unexpected phenomena. Here, Aggarwal et al. report the coexistence of a superconducting phase and a high transport spin polarization at metallic point contacts on Weyl semimetal TaAs.

Coexistence of topological Dirac fermions on the surface and three-dimensional Dirac cone state in the bulk of ZrTe5 single crystal

Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T < 2 K) by controlling impurity and defects.

Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS

Magnetoresistance (MR), the change of a material's electrical resistance in response to an applied magnetic field, is a technologically important property that has been the topic of intense study for more than a quarter century. We report the observation of an unusual "butterfly"-shaped titanic angular magnetoresistance (AMR) in the nonmagnetic Dirac material, ZrSiS, which we find to be the most conducting sulfide known, with a 2-K resistivity as low as 48(4) nΩ⋅cm. The MR in ZrSiS is large and positive, reaching nearly 1.8 × 10⁵ percent at 9 T and 2 K at a 45° angle between the applied current (I || a) and the applied field (90° is H || c). Approaching 90°, a "dip" is seen in the AMR, which, by analyzing Shubnikov de Haas oscillations at different angles, we find to coincide with a very sharp topological phase transition unlike any seen in other known Dirac/Weyl materials. We find that ZrSiS has a combination of two-dimensional (2D) and 3D Dirac pockets comprising its Fermi surface and that the combination of high-mobility carriers and multiple pockets in ZrSiS allows for large property changes to occur as a function of angle between applied fields. This makes it a promising platform to study the physics stemming from the coexistence of 2D and 3D Dirac electrons as well as opens the door to creating devices focused on switching between different parts of the Fermi surface and different topological states.

Visualising Berry phase and diabolical points in a quantum exciton-polariton billiard

Diabolical points (spectral degeneracies) can naturally occur in spectra of two-dimensional quantum systems and classical wave resonators due to simple symmetries. Geometric Berry phase is associated with these spectral degeneracies. Here, we demonstrate a diabolical point and the corresponding Berry phase in the spectrum of hybrid light-matter quasiparticles-exciton-polaritons in semiconductor microcavities. It is well known that sufficiently strong optical pumping can drive exciton-polaritons to quantum degeneracy, whereby they form a macroscopically populated quantum coherent state similar to a Bose-Einstein condensate. By pumping a microcavity with a spatially structured light beam, we create a two-dimensional quantum billiard for the exciton-polariton condensate and demonstrate a diabolical point in the spectrum of the billiard eigenstates. The fully reconfigurable geometry of the potential walls controlled by the optical pump enables a striking experimental visualization of the Berry phase associated with the diabolical point. The Berry phase is observed and measured by direct imaging of the macroscopic exciton-polariton probability densities.

Direct comparison of current-induced spin polarization in topological insulator Bi2Se3 and InAs Rashba states

Three-dimensional topological insulators (TIs) exhibit time-reversal symmetry protected, linearly dispersing Dirac surface states with spin–momentum locking. Band bending at the TI surface may also lead to coexisting trivial two-dimensional electron gas (2DEG) states with parabolic energy dispersion. A bias current is expected to generate spin polarization in both systems, although with different magnitude and sign. Here we compare spin potentiometric measurements of bias current-generated spin polarization in Bi₂Se₃(111) where Dirac surface states coexist with trivial 2DEG states, and in InAs(001) where only trivial 2DEG states are present. We observe spin polarization arising from spin–momentum locking in both cases, with opposite signs of the measured spin voltage. We present a model based on spin dependent electrochemical potentials to directly derive the sign expected for the Dirac surface states, and show that the dominant contribution to the current-generated spin polarization in the TI is from the Dirac surface states.

Spin-polarized states arising from either Rashba splitting or topological effects are expected to produce current-induced spin polarization with different magnitude and sign. Here, Li et al. observe current-generated spin polarization in both Bi₂Se₃ (111) and InAs (001) films, with opposite signs of the spin voltage.