Band Spin-orbit Splitting Research Articles

Spin-orbit-splitting-driven nonlinear Hall effect in NbIrTe4

The Berry curvature dipole (BCD) serves as a one of the fundamental contributors to emergence of the nonlinear Hall effect (NLHE). Despite intense interest due to its potential for new technologies reaching beyond the quantum efficiency limit, the interplay between BCD and NLHE has been barely understood yet in the absence of a systematic study on the electronic band structure. Here, we report NLHE realized in NbIrTe4 that persists above room temperature coupled with a sign change in the Hall conductivity at 150 K. First-principles calculations combined with angle-resolved photoemission spectroscopy (ARPES) measurements show that BCD tuned by the partial occupancy of spin-orbit split bands via temperature is responsible for the temperature-dependent NLHE. Our findings highlight the correlation between BCD and the electronic band structure, providing a viable route to create and engineer the non-trivial Hall effect by tuning the geometric properties of quasiparticles in transition-metal chalcogen compounds.

Observation of weak localization in dual-gated bilayer MoS2

We investigate the magnetoresistance of a dual-gated bilayer MoS2 encapsulated by hexagonal boron nitride. At low magnetic fields (|B|<0.5T), we observe a negative magnetoresistance, which we identify as the weak localization effect. We determine both the phase coherence length and mean free path as a function of electron density and displacement field. Both characteristic lengths show a similar monotonic increase with electron density, while they are not affected by the displacement field. We further investigate the dephasing mechanism by measuring the temperature dependence of the phase coherence length. Our results suggest that when only the lower spin-orbit split bands (K↑, K′↓) contribute to transport is Coulomb scattering the dominant source of decoherence, while intervalley scattering seems not to play a relevant role in this regime. This observation is consistent with the picture of spin-polarized valleys (spin-valley locking), where the intrinsic spin-orbit coupling protects the spin states, rather than introducing an additional dephasing mechanism as in other materials. Published by the American Physical Society 2024

Measurement of the conduction band spin-orbit splitting in WSe2 and WS2 monolayers

The conduction band spin-orbit splitting ∆${}_{c}$ has a strong impact on optical, transport, and spin-valley properties of 2D materials based on transition metal dichalcogenide monolayers. Here, the authors study charge tunable devices based on WSe${}_{2}$ and WS${}_{2}$ monolayers. In addition to the well-known radiative recombination of neutral and charged excitons, photoluminescence measurements highlight a weaker intensity optical transition. This line is interpreted as an impurity-assisted recombination of the negatively charged exciton (triplet trion), whose radiative recombination energy differs by ∆${}_{c}$ from that of the trion's direct optically active recombination.

Two-bands Ising superconductivity from Coulomb interactions in monolayer

The nature of superconductivity in monolayer transition metal dichalcogenides is still under debate. It has already been argued that repulsive Coulomb interactions, combined with the disjoint Fermi surfaces around the K, Kʹ valleys and at the Γ point, can lead to superconducting instabilities in monolayer . Here, we demonstrate the two-bands nature of superconductivity in . It arises from the competition of repulsive long range intravalley and short range intervalley interactions together with Ising spin–orbit coupling. The two distinct superconducting gaps, one for each spin-orbit split band, consist of a mixture of s-wave and f-wave components. Their different amplitudes are due to the difference between the normal densities of states of the two bands at the Fermi level. Using a microscopic multiband BCS approach, we derive and self-consistently solve the gap equation, demonstrating the stability of nontrivial solutions in a realistic parameter range. We find a universal behavior of the temperature dependence of the gaps and of the critical in-plane field which is consistent with various sets of existing experimental data.

POLARIZATION AND FREQUENCY-POLARIZATION DEPENDENCES OF THREE-PHOTON INTERBAND LINEAR-CIRCULAR DICHROISM IN SEMICONDUCTORS OF CUBIC SYMMETRY

The polarization and frequency-polarization dependences of the linear-circular dichroism and light absorption coefficients in semiconductors of cubic symmetry, caused by vertical three-photon optical transitions between the states of the spin-orbit splitting and conduction bands, are calculated. KEY WORDS: three-photon optical transitions, spin-orbit splitting band, conduction band, linear-circular dichroism, light absorption, semiconductor.

Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe2

Strong Coulomb correlations together with multi-valley electronic bands in the presence of spin-orbit interaction are at the heart of studies of the rich physics of excitons in monolayers of transition metal dichalcogenides (TMD). Those archetypes of two-dimensional systems promise a design of new optoelectronic devices. In intrinsic TMD monolayers the basic, intravalley excitons, are formed by a hole from the top of the valence band and an electron either from the lower or upper spin-orbit-split conduction band subbands: one of these excitons is optically active, the second one is dark, although possibly observed under special conditions. Here we demonstrate the s-series of Rydberg dark exciton states in tungsten diselenide monolayer, which appears in addition to a conventional bright exciton series in photoluminescence spectra measured in high in-plane magnetic fields. The comparison of energy ladders of bright and dark Rydberg excitons is shown to be a method to experimentally evaluate one of the missing band parameters in TMD monolayers: the amplitude of the spin-orbit splitting of the conduction band.

Level attraction and exceptional points in a resonant spin-orbit torque system

Level attraction can appear in driven systems where instead of repulsion two modes coalesce in a region separated by two exceptional points. This behavior was proposed for optomechanical and optomagnonic systems, and recently observed for dissipative cavity magnon-polaritons. We demonstrate that such a regime exists in a spin-orbit torque system where a magnetic oscillator is resonantly coupled to an electron reservoir. An instability mechanism necessary for mode attraction can be provided by applying an electric field. The field excites interband transitions between spin-orbit split bands leading to an instability of the magnetic oscillator. Two exceptional points then appear in the oscillator energy spectrum and the region of instability. We discuss conditions under which this can occur and estimate the electric field strength necessary for reaching the attraction region for a spin-orbit torque oscillator with Rashba coupling. A proposal for experimental detection is made using magnetic susceptibility measurements.

Hall Coefficient of Semimetals.

A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 066601 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.066601] is applied to nodal line and Weyl semimetals (including graphene) and to spin-orbit split semiconductor bands in two and three dimensions. The calculation reduces to a ratio of two equilibrium susceptibilities, where corrections are negligible at weak disorder. Deviations from Drude's inverse carrier density are associated with band degeneracies, Fermi surface topology, and interband currents. Experiments which can measure these deviations are proposed.

Low-energy excitations in type-II Weyl semimetal Td−MoTe2 evidenced through optical conductivity

Molybdenum ditelluride, MoTe2, is a versatile material where the topological phase can be readily tuned by manipulating the associated structural phase transition. The fine details of the band structure of MoTe2, key to understanding its topological properties, have proven difficult to disentangle experientially due to the multi-band character of the material. Through experimental optical conductivity spectra, we detect two strong low-energy interband transitions. Both are linked to excitations between spin-orbit split bands. The lowest interband transition shows a strong thermal shift, pointing to a chemical potential that dramatically decreases with temperature. With the help of ab initio calculations and a simple two-band model, we give qualitative and quantitative explanation of the main features in the temperature-dependent optical spectra up to 400 meV.

Giant bowing of the band gap and spin-orbit splitting energy in GaP1\u2212xBix dilute bismide alloys

Using spectroscopic ellipsometry measurements on GaP1−xBix/GaP epitaxial layers up to x = 3.7% we observe a giant bowing of the direct band gap ({E}_{g}^{{rm{Gamma }}}) and valence band spin-orbit splitting energy (ΔSO). {E}_{g}^{{rm{Gamma }}} (ΔSO) is measured to decrease (increase) by approximately 200 meV (240 meV) with the incorporation of 1% Bi, corresponding to a greater than fourfold increase in ΔSO in going from GaP to GaP0.99Bi0.01. The evolution of {E}_{g}^{{rm{Gamma }}} and ΔSO with x is characterised by strong, composition-dependent bowing. We demonstrate that a simple valence band-anticrossing model, parametrised directly from atomistic supercell calculations, quantitatively describes the measured evolution of {E}_{g}^{{rm{Gamma }}} and ΔSO with x. In contrast to the well-studied GaAs1−xBix alloy, in GaP1−xBix substitutional Bi creates localised impurity states lying energetically within the GaP host matrix band gap. This leads to the emergence of an optically active band of Bi-hybridised states, accounting for the overall large bowing of {E}_{g}^{{rm{Gamma }}} and ΔSO and in particular for the giant bowing observed for x ≲ 1%. Our analysis provides insight into the action of Bi as an isovalent impurity, and constitutes the first detailed experimental and theoretical analysis of the GaP1−xBix alloy band structure.

Infrared photoreflectance of InSb-based two-dimensional nanostructures

An IR photoreflectance (PR) study of two-dimensional nanoheterostructures based on InSb was performed by using Fourier-transform IR photomodulation spectroscopy. The studied structures, including InSb/AlxIn1−xSb quantum wells (QWs) and type-II nanostructures with monolayer-thick InSb insertions within bulk InAs layers, were grown via molecular beam epitaxy on GaAs (001) and InAs (001) substrates, respectively. The PR spectra of the InSb/AlxIn1−xSb heterostructures exhibited a series of signals from the QWs, including the spin-orbit split band, as well as the AlxIn1−xSb layers, which enabled control of the barrier height and composition. A comparison of the experimental results with calculations made by the effective mass approximation technique was used to identify several optical transitions observed within the QWs, including those related to the excited states not visible in the photoluminescence spectra. For the InSb/InAs monolayer nanostructures, an analysis of the PR spectra features allowed for determination of their energy spectrum, internal electric field value, and localization energy of holes up to room temperature.

Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer MoS_{2}.

The strong spin-orbit coupling and the broken inversion symmetry in monolayer transition metal dichalcogenides results in spin-valley coupled band structures. Such a band structure leads to novel applications in the fields of electronics and optoelectronics. Density functional theory calculations as well as optical experiments have focused on spin-valley coupling in the valence band. Here we present magnetotransport experiments on high-quality n-type monolayer molybdenum disulphide (MoS_{2}) samples, displaying highly resolved Shubnikov-de Haas oscillations at magnetic fields as low as 2T. We find the effective mass 0.7m_{e}, about twice as large as theoretically predicted and almost independent of magnetic field and carrier density. We further detect the occupation of the second spin-orbit split band at an energy of about 15meV, i.e., about a factor of 5 larger than predicted. In addition, we demonstrate an intricate Landau level spectrum arising from a complex interplay between a density-dependent Zeeman splitting and spin- and valley-split Landau levels. These observations, enabled by the high electronic quality of our samples, testify to the importance of interaction effects in the conduction band of monolayer MoS_{2}.

A- and B-exciton photoluminescence intensity ratio as a measure of sample quality for transition metal dichalcogenide monolayers

The photoluminescence (PL) in monolayer transition metal dichalcogenides (TMDs) is dominated by the recombination of electrons in the conduction band with holes in the spin-orbit split valence bands, and there are two distinct emission features referred to as the A-peak (ground state exciton) and B-peak (higher spin-orbit split state). The intensity ratio of these two features varies widely, and several contradictory interpretations have been reported. In this work, we analyze the room temperature PL from MoS2, MoSe2, WS2, and WSe2 monolayers and identify the underlying cause of observed variations in emission profile. We determine that PL variations arise from differences in the non-radiative recombination associated with defect densities. Therefore, the relative intensities of the A- and B-emission features can be used to qualitatively assess the non-radiative recombination and a low B/A ratio is indicative of low defect density and high sample quality. We also performed polarization-resolved PL measurements. Emission from TMD monolayers is governed by unique optical selection rules which make them promising materials for valleytronic operations. We observe a notably higher valley polarization in the B-exciton relative to the A-exciton. The high polarization is a consequence of the shorter B-exciton lifetime resulting from rapid relaxation of excitons from the B-exciton to the A-exciton of the valence band. Our work clarifies disparities reported in the literature relating to the emission profile and provides a straightforward means to assess sample quality.

Revealing Optical Transitions and Carrier Recombination Dynamics within the Bulk Band Structure of Bi2Se3.

Bismuth selenide (Bi2Se3) is a prototypical 3D topological insulator whose Dirac surface states have been extensively studied theoretically and experimentally. Surprisingly little, however, is known about the energetics and dynamics of electrons and holes within the bulk band structure of the semiconductor. We use mid-infrared femtosecond transient reflectance measurements on a single nanoflake to study the ultrafast thermalization and recombination dynamics of photoexcited electrons and holes within the extended bulk band structure over a wide energy range (0.3 to 1.2 eV). Theoretical modeling of the reflectivity spectral line shapes at 10 K demonstrates that the electrons and holes are photoexcited within a dense and cold electron gas with a Fermi level positioned well above the bottom of the lowest conduction band. Direct optical transitions from the first and the second spin-orbit split valence bands to the Fermi level above the lowest conduction band minimum are identified. The photoexcited carriers thermalize rapidly to the lattice temperature within a couple of picoseconds due to optical phonon emission and scattering with the cold electron gas. The minority carrier holes recombine with the dense electron gas within 150 ps at 10 K and 50 ps at 300 K. Such knowledge of interaction of electrons and holes within the bulk band structure provides a foundation for understanding how such states interact dynamically with the topologically protected Dirac surface states.

Semiclassical theory of anisotropic transport at LaAlO3/SrTiO3 interfaces under an in-plane magnetic field

The unconventional magnetotransport at the interface between transition-metal oxides $LaAlO_3$ (LAO) and $SrTiO_3$ (STO) is frequently related to mobile electrons interacting with localized magnetic moments. However nature and properties of magnetism at this interface are not well understood so far. In this paper, we focus on transport effects driven by spin-orbit coupling and intentionally neglect possible strong correlations. The electrical resistivity tensor is calculated as a function of the magnitude and orientation of an external magnetic field parallel to the interface. The semiclassical Boltzmann equation is solved numerically for the two-dimensional system of spin-orbit coupled electrons accelerated by an electric field and scattered by spatially-correlated impurities. At temperatures of a few Kelvin and densities such that the chemical potential crosses the second pair of spin-orbit split bands, we find a strongly anisotropic modulation of the (negative) magnetoresistance above 10 T, characterized by multiple maxima and minima away from the crystalline axes. Along with the drop of the magnetoresistance, an abrupt enhancement of the transverse resistivity occurs. The angular modulation of the latter considerably deviates from a (low-field) sinusoidal dependence to a (high-field) step-like behaviour. These peculiar features are the consequences of the anisotropy of both (intra-band and inter-band ) scattering-amplitudes in the Brillouin zone when the relevant energy scales in the system - chemical potential, spin-orbit interaction and Zeeman energy - are all comparable to each other. The theory provides good qualitative agreement with experimental data in the literature.

Electroluminescence of InAs/InAs(Sb)/InAsSbP LED heterostructures in the temperature range 4.2–300 K

The electroluminescence of InAs/InAsSbP and InAsSb/InAsSbP LED heterostructures grown on InAs substrates is studied in the temperature range T = 4.2–300 K. At low temperatures (T = 4.2–100 K), stimulated emission is observed for the InAs/InAsSbP and InAsSb/InAsSbP heterostructures with an optical cavity formed normal to the growth plane at wavelengths of, respectively, 3.03 and 3.55 μm. The emission becomes spontaneous at T > 70 K due to the resonant “switch-on” of the CHHS Auger recombination process in which the energy of a recombining electron–hole pair is transferred to a hole, with hole transition to the spin–orbit-split band. It remains spontaneous up to room temperature because of the influence exerted by other Auger processes. The results obtained show that InAs/InAs(Sb)/InAsSbP structures are promising for the fabrication of vertically emitting mid-IR lasers.

Fermi surface and band structure of BiPd from ARPES studies

We present a detailed electronic structure study of the non-centrosymmetric superconductor BiPd based on our angle resolved photoemission spectroscopy (ARPES) measurements and Density Functional Theory (DFT) based calculations. We observe a high intensity distribution on the Fermi surface (FS) of this compound resulting from various electron and hole like bands which are present in the vicinity of the Fermi energy (Ef). The near Ef states are primarily composed of Bi-6p with a little admixture of Pd-4dx2−y2/zy orbitals. There are various spin-orbit split bands involved in the crossing of Ef making a complex FS. The FS mainly consists of multi sheets of three dimensions which disfavor the nesting between different sheets of the FS. Our comprehensive study elucidates that BiPd could be a s-wave multiband superconductor.

Control of the electron spin relaxation by the built-in piezoelectric field in InGaAs quantum wells

The electron spin dynamics is studied by time-resolved optical orientation experiments in strained InGaAs/GaAs quantum wells (QWs) grown on (111) or (001) substrates. For a given well width, the electron spin relaxation time in (111) InGaAs QWs decreases by an order of magnitude when the indium fraction in the well varies only from 4% to 12%. In contrast, the electron spin relaxation time depends weakly on the indium fraction in similar InGaAs quantum wells grown on (001) substrates. The strong variation of the electron spin relaxation time in (111) strained quantum well can be well interpreted by the Dyakonov-Perel spin relaxation mechanism where the conduction band spin-orbit splitting is dominated by the structural inversion asymmetry (Rashba term) induced by the piezoelectric field. In (001) QWs, due to the absence of piezoelectric field, the electron spin relaxation time is solely controlled by the Dresselhaus term. These results demonstrate the possibility to engineer the electron spin relaxation time in (111)-oriented quantum wells by the piezoelectric field induced by the built-in strain.

Band renormalization and spin polarization of MoS2 in graphene/MoS2 heterostructures

Transition metal dichalcogenides exhibit spin–orbit split bands at the K-point that become spin polarized for broken crystal inversion symmetry. This enables simultaneous manipulation of valley and spin degrees of freedom. While the inversion symmetry is broken for monolayers, we show here that spin polarization of the MoS2 surface may also be obtained by interfacing it with graphene, which induces a space charge region in the surface of MoS2. Polarization induced symmetry breaking in the potential gradient of the space charge is considered to be responsible for the observed spin polarization. In addition to spin polarization we also observe a renormalization of the valence band maximum (VBM) upon interfacing of MoS2 with graphene. The energy difference between the VBM at the Γ-point and K-point shifts by ∼150 meV between the clean and graphene covered surface. (© 2015 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim)

Different spin textures in one-dimensional electronic bands on Si(5 5 3)-Au surface

A doublet of one-dimensional metallic bands on Au-stabilized Si(553) surface features different splitting due to the spin–orbit interaction. Density functional theory calculations reveal the origin of unequal magnitude of the splitting. Furthermore, different orientations of spin polarizations, almost perpendicular to each other, in both spin–orbit split bands are discovered. These observations are consistent with the Rashba effect and induced electric field in the system with out-of-plane and in-plane components. The results of calculations are confirmed by spin- and angle-resolved photoelectron spectroscopy measurements. The Si(553)-Au surface appears as a unique 1D Rashba system.