Observation of Out-of-Plane Spin Texture in a SrTiO_{3}(111) Two-Dimensional Electron Gas

Observation of giant non-reciprocal charge transport from quantum Hall states in a topological insulator

Symmetry breaking in quantum materials is of great importance and can lead to non-reciprocal charge transport. Topological insulators provide a unique platform to study non-reciprocal charge transport due to their surface states, especially quantum Hall states under an external magnetic field. Here we report the observation of non-reciprocal charge transport mediated by quantum Hall states in devices composed of the intrinsic topological insulator Sn-Bi1.1Sb0.9Te2S, which is attributed to asymmetric scattering between quantum Hall states and Dirac surface states. A giant non-reciprocal coefficient of up to 2.26 × 105 A-1 is found. Our work not only reveals the properties of non-reciprocal charge transport of quantum Hall states in topological insulators but also paves the way for future electronic devices.

Enhanced Nonlinear Response by Manipulating the Dirac Point at the (111) LaTiO_{3}/SrTiO_{3} Interface

Tunable spin-orbit interaction (SOI) is an important feature for future spin-based devices. In the presence of a magnetic field, SOI induces an asymmetry in the energy bands, which can produce nonlinear transport effects (V∼I^{2}). Here, we focus on such effects to study the role of SOI in the (111) LaTiO_{3}/SrTiO_{3} interface. This system is a convenient platform for understanding the role of SOI since it exhibits a single-band Hall response through the entire gate-voltage range studied. We report a pronounced rise in the nonlinear longitudinal resistance at a critical in-plane field H_{cr}. This rise disappears when a small out-of-plane field component is present. We explain these results by considering the location of the Dirac point formed at the crossing of the spin-split energy bands. An in-plane magnetic field pushes this point outside of the Fermi contour, and consequently changes the symmetry of the Fermi contours and intensifies the nonlinear transport. An out-of-plane magnetic field opens a gap at the Dirac point, thereby significantly diminishing the nonlinear effects. We propose that magnetoresistance effects previously reported in interfaces with SOI could be comprehended within our suggested scenario.

Large Nonlinear Transverse Conductivity and Berry Curvature in KTaO3 Based Two-Dimensional Electron Gas

Two-dimensional electron gas (2DEG) at oxide interfaces exhibits various exotic properties stemming from interfacial inversion and symmetry breaking. In this work, we report large nonlinear transverse conductivities in the LaAlO3/KTaO3 interface 2DEG under zero magnetic field. Skew scattering was identified as the dominant origin based on the cubic scaling of nonlinear transverse conductivity with linear longitudinal conductivity and 3-fold symmetry. Moreover, gate-tunable nonlinear transport with pronounced peak and dip was observed and reproduced by our theoretical calculation. These results indicate the presence of Berry curvature hotspots and thus a large Berry curvature triplet at the oxide interface. Our theoretical calculations confirm the existence of large Berry curvatures from the avoided crossing of multiple 5d-orbit bands, orders of magnitude larger than that in transition-metal dichalcogenides. Nonlinear transport offers a new pathway to probe the Berry curvature at oxide interfaces and facilitates new applications in oxide nonlinear electronics.

Designing spin and orbital sources of Berry curvature at oxide interfaces

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO₃/SrTiO₃ interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

Anisotropic superconductivity at KTaO3(111) interfaces

A two-dimensional, anisotropic superconductivity was recently found at the KTaO₃(111) interfaces. The nature of the anisotropic superconducting transition remains a subject of debate. To investigate the origins of the observed behavior, we grew epitaxial KTaO₃(111)-based heterostructures. We show that the superconductivity is robust against the in-plane magnetic field and violates the Pauli limit. We also show that the Cooper pairs are more resilient when the bias is along [11[Formula: see text]] (I ∥ [11[Formula: see text]]) and the magnetic field is along [1[Formula: see text]0] (B ∥ [1[Formula: see text]0]). We discuss the anisotropic nature of superconductivity in the context of electronic structure, orbital character, and spin texture at the KTaO₃(111) interfaces. The results point to future opportunities to enhance superconducting transition temperatures and critical fields in crystalline, two-dimensional superconductors with strong spin-orbit coupling.

Room-Temperature Gate-Tunable Nonreciprocal Charge Transport in Lattice-Matched InSb/CdTe Heterostructures

Symmetry manipulation can be used to effectively tailor the physical order in solid-state systems. With the breaking of both the inversion and time-reversal symmetries, nonreciprocal magneto-transport may arise in nonmagnetic systems to enrich spin-orbit effects. Here, the observation of unidirectional magnetoresistance (UMR) in lattice-matched InSb/CdTe films is investigated up to room temperature. Benefiting from the strong built-in electric field of 0.13 V nm^-1 in the heterojunction region, the resulting Rashba-type spin-orbit coupling and quantum confinement result in a distinct sinusoidal UMR signal with a nonreciprocal coefficient that is 1-2 orders of magnitude larger than most non-centrosymmetric materials at 298 K. Moreover, this heterostructure configuration enables highly efficient gate tuning of the rectification response, wherein the UMR amplitude is enhanced by 40%. The results of this study advocate the use of narrow-bandgap semiconductor-based hybrid systems with robust spin textures as suitable platforms for the pursuit of controllable chiral spin-orbit applications.

Enhancement of the Rashba Effect in a Conducting SrTiO3 Surface by MoO3 Capping

Systems having inherent structural asymmetry retain the Rashba-type spin-orbit interaction, which ties the spin and momentum of electrons in the band structure, leading to coupled spin and charge transport. One of the electrical manifestations of the Rashba spin-orbit interaction is nonreciprocal charge transport, which could be utilized for rectifying devices. Further tuning of the Rashba spin-orbit interaction allows additional functionalities in spin-orbitronic applications. In this work, we present our study of nonreciprocal charge transport in a conducting SrTiO3 (001) surface and its significant enhancement by a capping layer. The conductive strontium titanate SrTiO3 (STO) (001) surface was created through oxygen vacancies by Ar+ irradiation, and the nonreciprocal signal was probed by angle- and magnetic field-dependent second harmonic voltage measurement with an AC current. We observed robust directional transport in the Ar+-irradiated sample at low temperatures. The magnitude of the nonreciprocal signal is highly dependent on the irradiation time as it affects the depth of the conducting layer and the impact of the topmost conducting layer. Moreover, the nonreciprocal resistance was significantly enhanced by simply adding a MoO3 capping layer on the conductive STO surface. These results show a simple methodology for tuning and investigating the Rashba effect in a conductive STO surface, which could be adopted for various two-dimensional (2D) conducting layers for spin-orbitronic applications.

Controlled large non-reciprocal charge transport in an intrinsic magnetic topological insulator MnBi2Te4

Symmetries, quantum geometries and electronic correlations are among the most important ingredients of condensed matters, and lead to nontrivial phenomena in experiments, for example, non-reciprocal charge transport. Of particular interest is whether the non-reciprocal transport can be manipulated. Here, we report the controllable large non-reciprocal charge transport in the intrinsic magnetic topological insulator MnBi₂Te₄. The current direction relevant resistance is observed at chiral edges, which is magnetically switchable, edge position sensitive and stacking sequence controllable. Applying gate voltage can also effectively manipulate the non-reciprocal response. The observation and manipulation of non-reciprocal charge transport reveals the fundamental role of chirality in charge transport of MnBi₂Te₄, and pave ways to develop van der Waals spintronic devices by chirality engineering.

Bilinear Magnetoresistance in HgTe Topological Insulator: Opposite Signs at Opposite Surfaces Demonstrated by Gate Control

Spin-orbit effects appearing in topological insulators (TI) and at Rashba interfaces are currently revolutionizing how we can manipulate spins and have led to several newly discovered effects, from spin-charge interconversion and spin-orbit torques to novel magnetoresistance phenomena. In particular, a puzzling magnetoresistance has been evidenced as bilinear in electric and magnetic fields. Here, we report the observation of bilinear magnetoresistance (BMR) in strained HgTe, a prototypical TI. We show that both the amplitude and sign of this BMR can be tuned by controlling with an electric gate the relative proportions of the opposite contributions of opposite surfaces. At magnetic fields of 1 T, the magnetoresistance is of the order of 1% and has a larger figure of merit than previously measured TIs. We propose a theoretical model giving a quantitative account of our experimental data. This phenomenon, unique to TI, offers novel opportunities to tune their electrical response for spintronics.

Large magnetoelectric resistance in the topological Dirac semimetal α-Sn

The spin-momentum locking of surface states in topological materials can produce a resistance that scales linearly with magnetic and electric fields. Such a bilinear magnetoelectric resistance (BMER) effect offers a new approach for information reading and field sensing applications, but the effects demonstrated so far are too weak or for low temperatures. This article reports the first observation of BMER effects in topological Dirac semimetals; the BMER responses were measured at room temperature and were substantially stronger than those reported previously. The experiments used topological Dirac semimetal α-Sn thin films grown on silicon substrates. The films showed BMER responses that are 10⁶ times larger than previously measured at room temperature and are also larger than those previously obtained at low temperatures. These results represent a major advance toward realistic BMER applications. Significantly, the data also yield the first characterization of three-dimensional Fermi-level spin texture of topological surface states in α-Sn.

Tunable Spin and Orbital Edelstein Effect at (111) LaAlO3/SrTiO3 Interface

Converting charge current into spin current is one of the main mechanisms exploited in spintronics. One prominent example is the Edelstein effect, namely, the generation of a magnetization in response to an external electric field, which can be realized in systems with lack of inversion symmetry. If a system has electrons with an orbital angular momentum character, an orbital magnetization can be generated by the applied electric field, giving rise to the so-called orbital Edelstein effect. Oxide heterostructures are the ideal platform for these effects due to the strong spin–orbit coupling and the lack of inversion symmetries. Beyond a gate-tunable spin Edelstein effect, we predict an orbital Edelstein effect an order of magnitude larger then the spin one at the (111) LaAlO3/SrTiO3 interface for very low and high fillings. We model the material as a bilayer of t2g orbitals using a tight-binding approach, whereas transport properties are obtained in the Boltzmann approach. We give an effective model at low filling, which explains the non-trivial behaviour of the Edelstein response, showing that the hybridization between the electronic bands crucially impacts the Edelstein susceptibility.

Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires

Chiral materials are an ideal playground for exploring the relation between symmetry, relativistic effects and electronic transport. For instance, chiral organic molecules have been intensively studied to electrically generate spin-polarized currents in the last decade, but their poor electronic conductivity limits their potential for applications. Conversely, chiral inorganic materials such as tellurium have excellent electrical conductivity, but their potential for enabling the electrical control of spin polarization in devices remains unclear. Here, we demonstrate the all-electrical generation, manipulation and detection of spin polarization in chiral single-crystalline tellurium nanowires. By recording a large (up to 7%) and chirality-dependent unidirectional magnetoresistance, we show that the orientation of the electrically generated spin polarization is determined by the nanowire handedness and uniquely follows the current direction, while its magnitude can be manipulated by an electrostatic gate. Our results pave the way for the development of magnet-free chirality-based spintronic devices.

Nonreciprocal Transport in a Bilayer of MnBi2Te4 and Pt

MnBi₂Te₄ (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi₂Te₃ phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.

Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions

Transport is non-reciprocal when not only the sign, but also the absolute value of the current depends on the polarity of the applied voltage. It requires simultaneously broken inversion and time-reversal symmetries, for example, by an interplay of spin-orbit coupling and magnetic field. Hitherto, observation of nonreciprocity was tied to resistivity, and dissipationless non-reciprocal circuit elements were elusive. Here we engineer fully superconducting non-reciprocal devices based on highly transparent Josephson junctions fabricated on InAs quantum wells. We demonstrate supercurrent rectification far below the transition temperature. By measuring Josephson inductance, we can link the non-reciprocal supercurrent to an asymmetry of the current-phase relation, and directly derive the supercurrent magnetochiral anisotropy coefficient. A semiquantitative model explains well the main features of our experimental data. Non-reciprocal Josephson junctions have the potential to become for superconducting circuits what pn junctions are for traditional electronics, enabling new non-dissipative circuit elements.

Emergence of spin-orbit coupled ferromagnetic surface state derived from Zak phase in a nonmagnetic insulator FeSi

FeSi is a nonmagnetic narrow-gap insulator, exhibiting peculiar charge and spin dynamics beyond a simple band structure picture. Those unusual features have been attracting renewed attention from topological aspects. Although the surface conduction was demonstrated according to size-dependent resistivity in bulk crystals, its topological characteristics and consequent electromagnetic responses remain elusive. Here, we demonstrate an inherent surface ferromagnetic-metal state of FeSi thin films and its strong spin-orbit coupling (SOC) properties through multiple characterizations of two-dimensional conductance, magnetization, and spintronic functionality. Terminated covalent bonding orbitals constitute the polar surface state with momentum-dependent spin textures due to Rashba-type spin splitting, as corroborated by unidirectional magnetoresistance measurements and first-principles calculations. As a consequence of the spin-momentum locking, nonequilibrium spin accumulation causes magnetization switching. These surface properties are closely related to the Zak phase of the bulk band topology. Our findings propose another route to explore noble metal–free materials for SOC-based spin manipulation.

Anisotropic Picosecond Spin-Photocurrent from Weyl Semimetal WTe2

The generation and detection of ultrafast spin current, preferably reaching a frequency up to terahertz, is the core of spintronics. Studies have shown that the Weyl semimetal WTe₂ is of great potential in generating spin currents. However, the prior studies have been limited to the static measurements with the in-plane spin orientation. In this work, we demonstrate a picosecond spin-photocurrent in a Td-WTe₂ thin film via a terahertz time domain spectroscopy with a circularly polarized laser excitation. The anisotropic dependence of the circular photogalvanic effect (CPGE) in the terahertz emission reveals that the picosecond spin-photocurrent is generated along the rotational asymmetry a-axis. Notably, the generated spins are aligned along the out-of-plane direction under the light normally incident to the film surface, which provides an efficient means to manipulate magnetic devices with perpendicular magnetic anisotropy. A spin-splitting band induced by intrinsic inversion symmetry breaking enables the manipulation of a spin current by modulating the helicity of the laser excitation. Moreover, CPGE nearly vanishes at a transition temperature of ∼175 K due to the carrier compensation. Our work provides an insight into the dynamic behavior of the anisotropic spin-photocurrent of Td-WTe₂ in terahertz frequencies and shows a great potential for the future development of terahertz-spintronic devices with Weyl semimetals.

Nonreciprocal transport in gate-induced polar superconductor SrTiO3

Polar conductors/superconductors with Rashba-type spin-orbit interaction are potential material platforms for quantum transport and spintronic functionalities. One of their inherent properties is the nonreciprocal transport, where the rightward and leftward currents become inequivalent, reflecting spatial inversion/time-reversal symmetry breaking. Such a rectification effect originating from the polar symmetry has been recently observed at interfaces or bulk Rashba semiconductors, while its mechanism in a polar superconductor remains elusive. Here, we report the nonreciprocal transport in gate-induced two-dimensional superconductor SrTiO₃, which is a Rashba superconductor candidate. In addition to the gigantic enhancement of nonreciprocal signals in the superconducting fluctuation region, we found kink and sharp peak structures around critical temperatures, which reflect the crossover behavior from the paraconductivity origin to the vortex origin, based on a microscopic theory. The present result proves that the nonreciprocal transport is a powerful tool for investigating the interfacial/polar superconductors without inversion symmetry, where rich exotic features are theoretically prognosticated.

Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature

The spin Hall effect (SHE) is usually observed as a bulk effect in high-symmetry crystals with substantial spin-orbit coupling (SOC), where the symmetric spin-orbit field imposes a widely encountered trade-off between spin Hall angle (θ_SH) and spin diffusion length (L_sf), and spin polarization, spin current and charge current are constrained to be mutually orthogonal. Here, we report a large θ_SH of 0.32 accompanied by a long L_sf of 2.2 μm at room temperature in a low-symmetry few-layered semimetal MoTe₂, thus identifying it as an excellent candidate for simultaneous spin generation, transport and detection. In addition, we report that longitudinal spin current with out-of-plane polarization can be generated by both transverse and vertical charge current, due to the conventional and a newly observed planar SHE, respectively. Our study suggests that manipulation of crystalline symmetries and strong SOC opens access to new charge-spin interconversion configurations and spin-orbit torques for spintronic applications.

Observation of Large Unidirectional Rashba Magnetoresistance in Ge(111)

Relating magnetotransport properties to specific spin textures at surfaces or interfaces is an intense field of research nowadays. Here, we investigate the variation of the electrical resistance of Ge(111) grown epitaxially on semi-insulating Si(111) under the application of an external magnetic field. We find a magnetoresistance term that is linear in current density j and magnetic field B, hence, odd in j and B, corresponding to a unidirectional magnetoresistance. At 15 K, for I=10  μA (or j=0.33  A m^{-1}) and B=1  T, it represents 0.5% of the zero field resistance, a much higher value compared to previous reports on unidirectional magnetoresistance (UMR). We ascribe the origin of this magnetoresistance to the interplay between the externally applied magnetic field and the pseudomagnetic field generated by the current applied in the spin-splitted subsurface states of Ge(111). This unidirectional magnetoresistance is independent of the current direction with respect to the Ge crystal axes. It progressively vanishes, either using a negative gate voltage due to carrier activation into the bulk (without spin-splitted bands), or by increasing the temperature due to the Rashba energy splitting of the subsurface states lower than ∼58k_{B}. We believe that UMR could be used as a powerful probe of the spin-orbit interaction in a wide range of materials.

Gate-tunable giant nonreciprocal charge transport in noncentrosymmetric oxide interfaces

A polar conductor, where inversion symmetry is broken, may exhibit directional propagation of itinerant electrons, i.e., the rightward and leftward currents differ from each other, when time-reversal symmetry is also broken. This potential rectification effect was shown to be very weak due to the fact that the kinetic energy is much higher than the energies associated with symmetry breaking, producing weak perturbations. Here we demonstrate the appearance of giant nonreciprocal charge transport in the conductive oxide interface, LaAlO₃/SrTiO₃, where the electrons are confined to two-dimensions with low Fermi energy. In addition, the Rashba spin-orbit interaction correlated with the sub-band hierarchy of this system enables a strongly tunable nonreciprocal response by applying a gate voltage. The observed behavior of directional response in LaAlO₃/SrTiO₃ is associated with comparable energy scales among kinetic energy, spin-orbit interaction, and magnetic field, which inspires a promising route to enhance nonreciprocal response and its functionalities in spin orbitronics.

Nonlinear Planar Hall Effect

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

Nonreciprocal charge transport at topological insulator/superconductor interface

Topological superconductor is attracting growing interest for its potential application to topological quantum computation. The superconducting proximity effect on the topological insulator surface state is one promising way to yield topological superconductivity. The superconductivity realized at the interface between Bi₂Te₃ and non-superconductor FeTe is one such candidate. Here, to detect the mutual interaction between superconductivity and topological surface state, we investigate nonreciprocal transport; i.e., current-direction dependent resistance, which is sensitive to the broken inversion symmetry of the electronic state. The largely enhanced nonreciprocal phenomenon is detected in the Bi₂Te₃/FeTe heterostructure associated with the superconducting transition. The emergent nonreciprocal signal at low magnetic fields is attributed to the current-induced modulation of supercurrent density under the in-plane magnetic fields due to the spin-momentum locking. The angular dependence of the signal reveals the symmetry of superconductivity and indicates the existence of another mechanism of nonreciprocal transport at high fields.

The superconducting proximity effect on the surface state of a topological insulator is promising to generate topological superconductivity. Here, Yasuda et al. reported enhanced nonreciprocal charge transport in a Bi₂Te₃/FeTe heterostructure with an emerging superconducting order parameter.

Nonlinear magnetotransport shaped by Fermi surface topology and convexity

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe₂, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe₂, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.

Thermal Spin Injection and Inverse Edelstein Effect of the Two-Dimensional Electron Gas at EuO-KTaO3 Interfaces

With the help of the two-dimensional electron gas (2DEG) at the LaAlO₃-SrTiO₃ interface, spin and charge currents can be interconverted. However, the conversion efficiency has been strongly depressed by LaAlO₃, which blocks spin transmission. It is therefore highly desired to explore 2DEGs sandwiched between ferromagnetic insulators that are transparent for magnons. By constructing epitaxial heterostructure with ferromagnetic EuO, which is conducting for spin current but insulating for electric current, and KTaO₃, we successfully obtained the 2DEGs, which can receive thermally injected spin current directly from EuO and convert the spin current to charge current via inverse Edelstein effect of the interface. Strong dependence of the spin Seebeck coefficient on the layer thickness of EuO is further observed and the propagation length for non-equilibrium magnons in EuO has been determined. The present work demonstrates the great potential of the 2DEGs formed by ferromagnetic oxides for spin caloritronics.