Zeeman Spin Splitting Research Articles

The external electric field induces Rashba and Zeeman spin splitting in non-polar MXene Lu2CF2 monolayers for spintronics application

For the application of the spintronics devices, large Rashba spin splitting and Zeeman spin splitting are required. However, the absence of spin splitting in the non-polar MXene Lu2CT2 (T = F, OH) with mirror symmetry limits the functionality of the spintronics applications. In this paper, by the density functional theory calculation, the effect of the electric field on the electronic properties along with the spin polarization of MXene Lu2CT2 (T = F, OH) are investigated. For Lu2CF2, the electric field can effectively regulate the energy band structures resulting in the indirect-direct band gap transition and semiconductor-metal transition. The spin splitting and spin polarization that are not observed in the situation of the intrinsic systems are established due to the breaking of the mirror symmetry by a suitable external electric field, which is sufficient to support the spintronics functionality. Furthermore, the electric field can effectively control the in-plane Rashba spin splitting and out-of-plane Zeeman spin splitting. The parameters of Rashba and the warping coefficients are comprehensively studied by using the effective k·p model. Therefore, our results provide a possible way to induce and tune Rashba spin splitting and Zeeman spin splitting in the MXene by an external electric field, which is useful for spintronic devices.

Perfect Zeeman Anisotropy in Rotationally Symmetric Quantum Dots with Strong Spin-Orbit Interaction.

In nanoscale structures with rotational symmetry, such as quantum rings, the orbital motion of electrons combined with a spin-orbit interaction can produce a very strong and anisotropic Zeeman effect. Since symmetry is sensitive to electric fields, ring-like geometries provide an opportunity to manipulate magnetic properties over an exceptionally wide range. In this work, we show that it is possible to form rotationally symmetric confinement potentials inside a semiconductor quantum dot, resulting in electron orbitals with large orbital angular momentum and strong spin-orbit interactions. We find complete suppression of Zeeman spin splitting for magnetic fields applied in the quantum dot plane, similar to the expected behavior of an ideal quantum ring. Spin splitting reappears as orbital interactions are activated with symmetry-breaking electric fields. For two valence electrons, representing a common basis for spin-qubits, we find that modulating the rotational symmetry may offer new prospects for realizing tunable protection and interaction of spin-orbital states.

Electric field-tuneable crossing of hole Zeeman splitting and orbital gaps in compressively strained germanium semiconductor on silicon

With the emergence of the quantum computing era, the spin physics of engineered semiconductor materials with large and tuneable effective g*-factor, which is a measure of the interaction between the magnetic field and the spin of the particle, has become of great interest because it offers new physics and engineering tools for spin’s manipulation and its addressable control. Here we suggest a semi-empirical method to determine out of plane effective g*-factor in high mobility 2D hole heterostructures. We experimentally study the electric-field tuneablity of effective g*-factor of holes in a strained germanium quantum well heterostructure. As a result of the material’s engineering, the g*-factor can be tuned in a large range from 13 to 24 that corresponds to the tuneable Zeeman spin splitting of heavy holes in the range from smaller, to equal, and to larger than the orbital Landau level quantization gap.

Weak Dispersion of Exciton Landé Factor with Band Gap Energy in Lead Halide Perovskites: Approximate Compensation of the Electron and Hole Dependences.

The optical properties of lead halide perovskite semiconductors in vicinity of the bandgap are controlled by excitons, so that investigation of their fundamental properties is of critical importance. The exciton Landé or g-factor gX is the key parameter, determining the exciton Zeeman spin splitting in magnetic fields. The exciton, electron, and hole carrier g-factors provide information on the band structure, including its anisotropy, and the parameters contributing to the electron and hole effective masses. Here, gX is measured by reflectivity in magnetic fields up to 60T for lead halide perovskite crystals. The materials band gap energies at a liquid helium temperature vary widely across the visible spectral range from 1.520 up to 3.213eV in hybrid organic-inorganic and fully inorganic perovskites with different cations and halogens: FA0.9Cs0.1PbI2.8Br0.2, MAPbI3, FAPbBr3, CsPbBr3, and MAPb(Br0.05Cl0.95)3. The exciton g-factors are found to be nearly constant, ranging from +2.3 to +2.7. Thus, the strong dependences of the electron and hole g-factors on the bandgap roughly compensate each other when combining to the exciton g-factor. The same is true for the anisotropies of the carrier g-factors, resulting in a nearly isotropic exciton g-factor. The experimental data are compared favorably with model calculation results.

Enhanced performance of Janus XMSiY2 (X=S, Se; M=Mo, W; and Y=N, P) monolayers for photocatalytic water splitting via strain engineering

In this article, using first-principles calculations, we propose XMSiY2 (X = S, Se; M = Mo, W; and Y=N, P) monolayers as a Janus form of MA2Z4 family and investigate their electronic, spintronic, and photocatalytic properties. The obtained band structures show that XMSiY2 monolayers are semiconductors with bandgaps ranging from 1.21 eV to 2.98 eV. Considering spin-orbit coupling, we observe that broken out-of-plane symmetry in the XMSiY2 structures leads to Rashba spin-splitting at the Γ point and lack of inversion symmetry results in Zeeman spin-splitting at the K point of the valence bands. The monolayers with W atom exhibit larger Zeeman spin-splitting (up to 0.479 eV for SeWSiP2) which indicates that XWSiY2 monolayers are promising materials for spintronic and valleytronic applications. Assisted by the large work function difference (Δ&varphi) between two surfaces of the Janus XMSiY2 monolayers, all the proposed structures satisfy the band alignment requirement for overall water splitting. Benefiting from strong solar absorption, large carrier mobility (up to 104 cm2 V−1 s−1) and huge difference between electron and hole mobilities, XMSiY2 monolayers are predicted to be high performance photocatalysts. Lastly, the effect of biaxial strain on the photocatalytic properties of the proposed monolayers is comprehensively investigated and it is found that compressive strain helps XMSiY2 structures to act as great photocatalysts for overall water splitting in an expanded range of pH. In addition, tensile strain can broaden and intensify the solar light absorption spectrum of XMSiY2 monolayers to achieve high performance photocatalysts.

Superconductivity in a Magnetic Rashba Semimetal EuAuBi

We report the observation of superconductivity with multiple magnetic ordering and Rashba-type spin-orbit coupling in a layered polar semimetal EuAuBi. Magnetic transition is observed at 4 K, followed by a superconducting transition at 2.2 K, which is sensitive to the crystal surface conditions. The upper critical field Hc2 of 9.8 T for the out-of-plane field is three times higher than that for the in-plane field, which can be associated with the two-dimensional structure or the surface state. On the basis of first-principles calculations, it is found that the characteristic Hc2 possibly reflects the anisotropic modification of the Fermi surface by the effective combination of Rashba-type spin splitting and Zeeman spin splitting enhanced by Eu moments.

Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, g mu _B B, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in nu for the R_{xx} minimum, e.g., from nu = 11/7 to nu = 8/5, and a corresponding change in the R_{xy}, e.g., from R_{xy}/R_{K} = (11/7)^{-1} to R_{xy}/R_{K} = (8/5)^{-1}, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the nu = 4/3 and nu = 7/5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of R_{xy} at the R_{xx} minima- the latter occurring for nu = 4/3, 7/5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same nu and R_{xy}, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

Zeeman Effect in Centrosymmetric Antiferromagnetic Semiconductors Controlled by an Electric Field.

Centrosymmetric antiferromagnetic semiconductors, although abundant in nature, seem less promising than ferromagnets and ferroelectrics for practical applications in semiconductor spintronics. As a matter of fact, the lack of spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these materials. Here, we propose a paradigm to harness electronic spin in centrosymmetric antiferromagnets via Zeeman spin splitting of electronic energy levels-termed as the spin Zeeman effect-which is controlled by an electric field. By symmetry analysis, we identify 21 centrosymmetric magnetic point groups that accommodate such a spin Zeeman effect. We further predict by first principles that two antiferromagnetic semiconductors, Fe_{2}TeO_{6} and SrFe_{2}S_{2}O, are excellent candidates showcasing Zeeman splittings as large as ∼55 and ∼30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover, the electronic spin magnetization associated to the splitting energy levels can be switched by reversing the electric field. Our Letter thus sheds light on the electric-field control of electronic spin in antiferromagnets, which broadens the scope of application of centrosymmetric antiferromagnetic semiconductors.

Spin and valley degrees of freedom in a bilayer graphene quantum point contact: Zeeman splitting and interaction effects

We present a study on the lifting of degeneracy of the size-quantized energy levels in an electrostatically defined quantum point contact in bilayer graphene by the application of in-plane magnetic fields. We observe a Zeeman spin splitting of the first three subbands, characterized by effective Land\'e $g$ factors that are enhanced by confinement and interactions. In the gate-voltage dependence of the conductance, a shoulderlike feature below the lowest subband appears, which we identify as a 0.7 anomaly stemming from the interaction-induced lifting of the band degeneracy. We employ a phenomenological model of the 0.7 anomaly to the gate-defined channel in bilayer graphene subject to in-plane magnetic field. Based on the qualitative theoretical predictions for the conductance evolution with increasing magnetic field, we conclude that the assumption of an effective spontaneous spin splitting is capable of describing our observations, while the valley degree of freedom remains degenerate.

Reentrant Bloch ferromagnetism

An interacting electron liquid in two (2D) and three (3D) dimensions may undergo a paramagnetic-to-ferromagnetic quantum spin polarization transition at zero applied magnetic field, driven entirely by exchange interactions, as the system density ($n$) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field ($B$), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, $B\ensuremath{\sim}{n}^{p}$. For $p<{p}_{c}$, with ${p}_{c}=1(2/3)$ in $2(3)\mathrm{D}$, the system remains either fully spin polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin polarized or fully spin polarized. However, for $p>{p}_{c}$, the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second-order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first-order transition back to the fully spin-polarized phase again with a single Fermi surface.

Quantum Hall effect and Shubnikov–de Haas oscillations in a high-mobility p -type PbTe quantum well

We present here the magnetotransport experiment performed with a magnetic field up to 30 T on a 10 nm-wide $p$-type PbTe quantum well. Pronounced Shubnikov--de Haas oscillations and the integer quantum Hall effect are clearly observed, demonstrating the transport of a confined two-dimensional hole gas with negligible parallel conduction at low temperatures. The sequence of filling factors can be explained by considering the magnetic field evolution of Landau levels derived from two longitudinal and one oblique occupied subbands and taking Zeeman spin splitting into account. During illumination, the total carrier density of the system is raised by 15%, which leads to a plateau sequence in the integer quantum Hall effect with higher filling factors in comparison to the dark condition.

Giant Transition-State Quasiparticle Spin-Hall Effect in an Exchange-Spin-Split Superconductor Detected by Nonlocal Magnon Spin Transport.

Although recent experiments and theories have shown a variety of exotic transport properties of nonequilibrium quasiparticles (QPs) in superconductor (SC)-based devices with either Zeeman or exchange spin-splitting, how a QP interplays with magnon spin currents remains elusive. Here, using nonlocal magnon spin-transport devices where a singlet SC (Nb) on top of a ferrimagnetic insulator (Y3Fe5O12) serves as a magnon spin detector, we demonstrate that the conversion efficiency of magnon spin to QP charge via inverse spin-Hall effect (iSHE) in such an exchange-spin-split SC can be greatly enhanced by up to 3 orders of magnitude compared with that in the normal state, particularly when its interface superconducting gap matches the magnon spin accumulation. Through systematic measurements by varying the current density and SC thickness, we identify that superconducting coherence peaks and exchange spin-splitting of the QP density-of-states, yielding a larger spin excitation while retaining a modest QP charge-imbalance relaxation, are responsible for the giant QP iSHE. The latter exchange-field-modified QP relaxation is experimentally proved by spatially resolved measurements with varying the separation of electrical contacts on the spin-split Nb.

Chiral two-dimensional p -wave superfluid from s -wave pairing in the Bose-Einstein-condensate regime

Twodimensional spin-orbit-coupled Fermi gases subject to s-wave pairing can be driven into a topological phase by increasing the Zeeman spin splitting beyond a critical value. In the topological phase, the system exhibits the hallmarks of chiral p-wave superfluidity, including exotic Majorana excitations. Previous theoretical studies of this realization of a twodimensional topological Fermi superfluid have focused on the BCS regime where the s-wave Cooper pairs are only weakly bound and, hence, the induced chiral p-wave order parameter has a small magnitude. Motivated by the goal to identify potential new ways for the experimental realization of robust topological superfluids in ultra-cold atom gases, we study the BCS-to-BEC crossover driven by increasing the Cooper-pair binding energy for this system. In particular, we obtain phase diagrams in the parameter space of two-particle bound-state energy and Zeeman spin-splitting energy. Ordinary characteristics of the BCS-to-BEC crossover, in particular the shrinking and eventual disappearance of the Fermi surface, are observed in the nontopological phase. In contrast, the topological phase retains all features of chiral p-wave superfluidity, including a well-defined underlying Fermi surface, even for large s-wave pair-binding energies. Compared to the BCS limit, the topological superfluid in the BEC regime turns out to be better realizable even for only moderate magnitude of spin-orbit coupling because the chiral p-wave order parameter is generally larger and remnants of s-wave pairing are suppressed. We identify optimal parameter ranges that can aid further experimental investigations and elucidate the underlying physical reason for the persistence of the chiral p-wave superfluid.

Zeeman spin-splitting in the (010) β-Ga2O3 two-dimensional electron gas

Through magnetotransport measurements and analysis of the observed Shubnikov de-Haas oscillations in (010) (AlxGa1-x)2O3/Ga2O3 heterostructures, spin-splitting of the Landau levels in the (010) Ga2O3 two-dimensional electron gas (2DEG) has been studied. Analysis indicates that the spin-splitting results from the Zeeman effect. By fitting both the first and second harmonics of the oscillations as a function of magnetic field, we determine the magnitude of the Zeeman splitting to be 0.4 ħωc, with a corresponding effective g-factor of 2.7, for the magnetic field perpendicular to the 2DEG.

Non-Abelian Majorana fermions in topological s-wave Fermi superfluids

By solving the Bogoliubov–de Gennes equations analytically, we derive the fermionic zero-modes satisfying the Majorana property that exist in vortices of a two-dimensional s-wave Fermi superfluid with spin–orbit coupling and Zeeman spin-splitting. The Majorana zero-mode becomes normalisable and exponentially localised to the vicinity of the vortex core when the superfluid is topologically non-trivial. We calculate the energy splitting due to Majorana hybridisation and identify that the s-wave Majorana vortices obey non-Abelian statistics.

Quantum FFLO State in Clean Layered Superconductors

We investigate the influence of Landau quantization on the superconducting instability for a pure layered superconductor in the magnetic field directed perpendicular to the layers. We demonstrate that the quantization corrections to the Cooper-pairing kernel with finite Zeeman spin splitting promote the formation of the nonuniform state in which the order parameter is periodically modulated along the magnetic field, i.e., between the layers (Fulde-Ferrell-Larkin-Ovchinnikov [FFLO] state). The conventional uniform state experiences such a quantization-induced FFLO instability at low temperatures even in a common case of predominantly orbital suppression of superconductivity when the Zeeman spin splitting is expected to have a relatively weak effect. The maximum relative FFLO temperature is given by the ratio of the superconducting transition temperature and the Fermi energy. This maximum is realized when the ratio of the spin-spitting energy and the Landau-level separation is half-integer. These results imply that the FFLO states may exist not only in the Pauli-limited superconductors but also in very clean materials with small Zeeman spin-splitting energy. We expect that the described quantization-promoted FFLO instability is a general phenomenon, which may be found in materials with different electronic spectra and order-parameter symmetries.

Quasiparticle gaps in multiprobe Majorana nanowires

We theoretically study a spin-orbit-coupled nanowire proximitized by a superconductor in the presence of an externally applied Zeeman field ("Majorana nanowire") with zero-energy Majorana bound states localized at the two ends of the wire when the Zeeman spin splitting is large enough for the system to enter the topological phase. The specific physics of interest in the current work is the effect of having several tunnel probes attached to the wire along its length. Such tunnel probes should allow, as a matter of principle, one to observe both the predicted bulk superconducting gap closing and opening associated with the topological quantum phase transition as well as the Majorana bound states at the wire ends showing up as zero-bias conductance peaks, depending on which probes are used for the tunneling spectroscopy measurement. Because of the possible invasive nature of the tunnel probes, producing local potential fluctuations in the nanowire, we find the physical situation to be quite complex. In particular, depending on the details of the tunnel barrier operational at the probes, the Majorana nanowire could manifest additional low-energy Andreev bound states which will manifest their own almost-zero-bias peaks, complicating the interpretation of the tunneling data in multiprobe Majorana nanowires. We use two complementary microscopic models to simulate the probes, finding that the tunneling conductance spectrum depends rather sensitively on the details of the tunnel barriers at the probes. We apply our general analysis to simulate a recent multiprobe nanowire experiment commenting on the nature of the quasiparticle gaps likely controlling the experimental observations.

Josephson Current Anomalies in Spin-Orbit Nanowires

We study the anomalous Josephson effect in a nanowire with Rashba spin-orbit interaction and Zeeman spin splitting, contacted with two s-wave superconducting leads with either one or two open conducting channels in the wire. In both cases, we find that the Josephson current is zero at a value φ 0 ≠ 0, π of the phase difference between the order parameter of the leads. While in the former case the critical current is direction independent, in the latter case we observe an asymmetry between I c+ (the maximum Josephson current from left to right) and I c - up to about 20%.

Interplay between orbital-quantization effects and the Fulde-Ferrell-Larkin-Ovchinnikov instability in multiple-band layered superconductors

We explore superconducting instability for a clean two-band layered superconductor with deep and shallow bands in the magnetic field applied perpendicular to the layers. In the shallow band, the quasiclassical approximation is not applicable, and Landau quantization has to be accounted for exactly. The electronic spectrum of this band in the magnetic field is composed of the one-dimensional Landau-level minibands. With increasing magnetic field the system experiences series of Lifshitz transitions when the chemical potential enters and exits the minibands. These transitions profoundly influence the shape of the upper critical field at low temperatures. In addition, the Zeeman spin splitting may cause the nonuniform state with interlayer modulation of the superconducting order parameter (Fulde-Ferrell-Larkin-Ovchinnikov state). Typically, the quantization effects in the shallow band strongly promote the formation of this state. The uniform state remains favorable only in the exceptional resonance cases when the spin-splitting energy exactly matches the Landau-level spacing. Furthermore, for specific relations between electronic spectrum parameters, the alternating FFLO state may realize, in which the order parameter changes sign between the neighboring layers. For all above cases, the reentrant high-field superconducting states may emerge at low temperatures if the shallow band has significant contribution to the Cooper pairing.

Asymmetric g Tensor in Low-Symmetry Two-Dimensional Hole Systems

The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin-3/2 hole systems compared to typical spin-1/2 electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman spin splitting. We have investigated this anisotropy in GaAs/AlAs quantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a non-diagonal tensor $g$ that manifests itself in unusual precessional motion as well as distinct dependencies of hole spin dynamics on the direction of the magnetic field $\vec{B}$. We quantify the individual components of the tensor $g$ for [113]-, [111]- and [110]-grown samples. We complement the experiments by a comprehensive theoretical study of Zeeman splitting in in-plane and out-of-plane fields $\vec{B}$. To this end, we develop a detailed multiband theory for the tensor $g$. Using perturbation theory, we derive transparent analytical expressions for the components of the tensor $g$ that we complement with accurate numerical calculations based on our theoretical framework. We obtain very good agreement between experiment and theory. Our study demonstrates that the tensor $g$ is neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude.