Experimental phonon imaging in diamond anvils cell is demonstrated to be an adequate tool to extract the complete set of elastic constants of single-crystalline silicon up to the ZB$\rightarrow β-$Sn transition (10 GPa). Contrary to what was commonly admitted, we demonstrate that the development of the strain-energy density in terms of strains cannot be stopped, for silicon, after the terms containing the third-order elastic constants. Nonlinear elasticity, degree of anisotropy and pressure-induced mechanical stability of the cubic silicon structure are thus revisited and investigated in more detail.
We combine density functional theory within the local density approximation, the quasiharmonic approximation, and vibrational density of states to calculate single crystal elastic constants, and bulk and shear moduli of diamond at simultaneous high pressures and temperatures in the ranges of 0-500 GPa and 0-4800 K. Comparison with experimental values at ambient pressure and high temperature shows an excellent agreement for the first time with our first-principles results validating our method. We show that the anisotropy factor of diamond increases to 40% at high pressures and becomes temperat…
The main aim of the present work is to estimate the effective elastic stiffnesses of a two-phase diamond/$β$-SiC composite thin film that is fabricated by chemical vapor deposition. The parameters of linear elasticity are determined by numerical homogenization. The database is sparse since for the 3D volume of interest only two micrographs displaying the phase distributions in perpendicular planes are available; micrographs each of a cross-section and the surface of the thin film. A representative volume element (RVE) is reconstructed by an optimization software and by means of identified mate…
We extend the results of our previous papers in order to prove the diamond like crystal structure of the deposited from laser plasma doped by manganese silicon diluted magnetic semiconductor.
Chemical vapour deposition (CVD) grown nanocrystalline diamond is an attractive material for the fabrication of devices. For some device architectures, optimisation of its growth on silicon nitride is essential. Here, the effects of three pre-growth surface treatments, often employed as cleaning methods of silicon nitride, were investigated. Such treatments provide control over the surface charge of the substrate through modification of the surface functionality, allowing for the optimisation of electrostatic diamond seeding densities. Zeta potential measurements and X-ray photoelectron spectr…
Renormalization of the electronic band gap due to electron-phonon coupling in the tetrahedral semiconductors diamond, silicon and cubic silicon carbide is studied from first principles. There is a marked difference between the coupling of the vibrational state to the valence band maximum and to the conduction band minimum. The strength of phonon coupling to the valence band maximum is similar between the three systems and is dominated by vibrations that change the bond length. The coupling strength to the conduction band minimum differs significantly in diamond, silicon carbide and silicon. In…
We report the first experimental observation of a doubly-charged defect in diamond, SiV2-, in silicon and nitrogen co-doped samples. We measure spectroscopic signatures we attribute to substitutional silicon in diamond, and identify a silicon-vacancy complex decorated with a nearest-neighbor nitrogen, SiVN, supported by theoretical calculations. Samples containing silicon and nitrogen are shown to be heavily photochromic, with the dominant visible changes due to the loss of SiV0/- and gain in the optically-inactive SiV2-.
The ability to inject dopant atoms with high spatial resolution, flexibility in dopant species and high single ion detection fidelity opens opportunities for the study of dopant fluctuation effects and the development of devices in which function is based on the manipulation of quantum states in single atoms, such as proposed quantum computers. We describe a single atom injector, in which the imaging and alignment capabilities of a scanning force microscope (SFM) are integrated with ion beams from a series of ion sources and with sensitive detection of current transients induced by incident io…
Optical coupling of an ensemble of silicon-vacancy (SiV) centers to single-crystal diamond microdisk cavities is demonstrated. The cavities are fabricated from a single-crystal diamond membrane generated by ion implantation and, electrochemical liftoff followed by homo-epitaxial overgrowth. Whispering gallery modes which spectrally overlap with the zero-phonon line (ZPL) of the SiV centers and exhibit quality factors ~2200 are measured. Lifetime reduction from 1.8 ns to 1.48 ns is observed from SiV centers in the cavity compared to those in the membrane outside the cavity. These results are pi…
45-degree rotated epitaxial diamond nucleation on both (001) and {111} planes of a silicon substrate was observed using chemical vapor deposition with nucleation enhancement by electron emission. The epitaxial relationship between diamond and Si is D(001)//Si(001) and D<100>//Si<110> in both cases. While the case of diamond nucleation on Si(001) may be explained in Verwoerd's model, the other case has no theoretical model as yet. The as-grown diamond was characterized by scanning electron microscopy and Raman spectroscopy. It is speculated that a suitable combination of low temperature and low…
An ensemble of silicon vacancy centers in diamond (\ce{SiV-}) is probed using two coherent spectroscopy techniques. Two main distinct families of \ce{SiV-} centers are identified using multidimensional coherent spectroscopy, and these families are paired with two orientation groups by comparing spectra from different linear polarizations of the incident laser. By tracking the peak centers in the measured spectra, the full diamond strain tensor is calculated local to the laser spot. Such measurements are made at multiple points on the sample surface and variations in the strain tensor are obser…
The negatively-charged silicon-vacancy (SiV$^-$) center in diamond is a promising single photon source for quantum communications and information processing. However, the center's implementation in such quantum technologies is hindered by contention surrounding its fundamental properties. Here we present optical polarization measurements of single centers in bulk diamond that resolve this state of contention and establish that the center has a $\langle111\rangle$ aligned split-vacancy structure with $D_{3d}$ symmetry. Furthermore, we identify an additional electronic level and evidence for the…
Some of the stable isotopes of silicon and carbon have zero nuclear spin, whereas many of the other elements that constitute semiconductors consist entirely of stable isotopes that have nuclear spins. Silicon and diamond crystals composed of nuclear-spin-free stable isotopes (Si-28, Si-30, or C-12) are considered to be ideal host matrixes to place spin quantum bits (qubits) for quntum computing and sensing applications because their coherent properties are not disrupted thanks to the absence of host nuclear spins. The present article describes the state-of-the-art and future perspective of sil…
We report the observation and the theoretical explanation of the parametric down-conversion nonlinear susceptibility at the $K$-absorption edge of diamond and at the $L_{23}$-absorption edge of a silicon crystal. Using arguments similar to those invoked to successfully predict resonant inelastic x-ray spectra, we derive an expression for the renormalization term of the non-linear susceptibility at the x-ray edges, which can be evaluated by using first-principles calculations of the atomic scattering factor $f_1$. Our model is shown to reproduce the observed enhancement of the parametric down-c…
Electrically driven emission from negatively charged silicon-vacancy, (SiV)- centres in single crystal diamond is demonstrated. The SiV centres were generated using ion implantation into an intrinsic (i) region of a p-i-n single crystal diamond diode. Both electroluminescence and the photoluminescence signals exhibit the typical emission that is attributed to the (SiV)- centres. Under forward and reversed biased PL measurements, no signal from the neutral (SiV)0 defect could be observed. The realization of electrically driven (SiV)- emission is promising for scalable nanophotonics devices empl…
We have developed an effective model to investigate the energetic stability of hydrogenated group-IV nanostructures, followed by validations from first-principles calculations. It is found that the Hamiltonian of X$_{m}$H$_{n}$ (X=C, Si, Ge and Sn) can be expressed analytically by a linear combination of the atom numbers ($m$, $n$), indicating a dominating contribution of X$-$X and X$-$H local interactions. As a result, we explain the stable nanostructures observed experimentally, and provide a reliable and efficient technique of searching the magic structures of diamond nanocrystals(Dia-NCs) …
The excellent material properties of diamond make it highly desirable for many extreme electronic applications that are out of reach of conventional electronic materials. For commercial diamond devices to become a reality, it is necessary to have an effective surface passivation since the passivation determines the ability of the device to withstand high surface electric fields. In this paper we present data from lateral Time-of-Flight studies on SiO2-passivated intrinsic single-crystalline CVD diamond. The SiO2 films were deposited using three different techniques. The influence of the passiv…
The silicon-vacancy centre (SiV) in diamond has interesting vibronic features. We demonstrate that the zero phonon line position can be used to reliably identify the silicon isotope present in a single centre. This is of interest for quantum information applications since only the silicon 29 isotope has nuclear spin. In addition, we demonstrate that the 64 meV line is due to a local vibrational mode of the silicon atom. The presence of a local mode suggests a plausible origin of the isotopic shift of the zero phonon line.
The split silicon-vacancy defect (SiV) in diamond is an electrically and optically active color center. Recently, it has been shown that this color center is bright and can be detected at the single defect level. In addition, the SiV defect shows a non-zero electronic spin ground state that potentially makes this defect an alternative candidate for quantum optics and metrology applications beside the well-known nitrogen-vacancy color center in diamond. However, the electronic structure of the defect, the nature of optical excitations and other related properties are not well-understood. Here w…
We introduce a process for the fabrication of high quality, spatially isolated nano-diamonds on iridium via microwave plasma assisted CVD-growth. We perform spectroscopy of single silicon-vacancy (SiV)-centres produced during the growth of the nano-diamonds. The colour centres exhibit extraordinary narrow zero-phonon-lines down to 0.7 nm at room temperature. Single photon count rates up to 4.8 Mcps at saturation make these SiV-centres the brightest diamond based single photon sources to date. We measure for the first time the fine structure of a single SiV-centre thus confirming the atomic com…
Silicon is an important material and many empirical interatomic potentials have been developed for atomistic simulations of it. Among them, the Tersoff potential and its variants are the most popular ones. However, all the existing Tersoff-like potentials fail to reproduce the experimentally measured thermal conductivity of diamond silicon. Here we propose a modified Tersoff potential and develop an efficient open source code called GPUGA (graphics processing units genetic algorithm) based on the genetic algorithm and use it to fit the potential parameters against energy, virial and force data…
The controlled creation of color centers in phosphorus-doped (n-type) diamond can facilitate the electronics integration of quantum photonics devices, such as single-photon sources operating upon electrical injection. Silicon vacancy (SiV) color centers are promising candidates, but so far the conditions for single-photon emission in phosphorus-doped diamond have not been investigated. In this study, we create SiV color centers in diamond samples with different phosphorus concentrations and show that the fluorescence background due to doping, nitrogen-impurities and ion implantation induced de…
We demonstrate that silicon-vacancy (SiV) centers in diamond can be used to efficiently generate coherent optical photons with excellent spectral properties. We show that these features are due to the inversion symmetry associated with SiV centers, and demonstrate generation of indistinguishable single photons from separate emitters in a Hong-Ou-Mandel (HOM) interference experiment.Prospects for realizing efficient quantum network nodes using SiV centers are discussed.
To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at given temperature and pressure was derived, hence the full minimization of the Gibbs free energy with respect to temperature and lattice parameters can be put into effective operation by using first principles. Therefore, with this new theory, anisotropic thermal expansion and temperature dependent elastic constants can be obtained for crystals with arbitrary …
The silicon-vacancy center in diamond offers attractive opportunities in quantum photonics due to its favorable optical properties and optically addressable electronic spin. Here, we combine both to achieve all-optical coherent control of its spin states. We utilize this method to explore spin dephasing effects in an impurity-rich sample beyond the limit of phonon-induced decoherence: Employing Ramsey and Hahn-echo techniques at 12mK base temperature we identify resonant coupling to a substitutional nitrogen spin bath as the limiting decoherence source for the electron spin.
Novel extended networks of C8, Si8 and silicon carbide Si4C4 are proposed based on crystal chemistry rationale and optimized structures to ground state energies and derived physical properties within the density functional theory (DFT). The two carbon and silicon allotropes and the silicon carbide belong to primitive tetragonal space group P-4m2 Number 115. C8 allotrope structure made of corner sharing C4 and Si4 tetrahedra is illustrated by charge density projections exhibiting sp3 like carbon hybridization. From careful symmetry analysis, Symmetry analysis of C8 indicated that it is another …
We characterize a high-density sample of negatively charged silicon-vacancy (SiV$^-$) centers in diamond using collinear optical multidimensional coherent spectroscopy. By comparing the results of complementary signal detection schemes, we identify a hidden population of \ce{SiV^-} centers that is not typically observed in photoluminescence, and which exhibits significant spectral inhomogeneity and extended electronic $T_2$ times. The phenomenon is likely caused by strain, indicating a potential mechanism for controlling electric coherence in color-center-based quantum devices.
The negatively charged silicon vacancy (SiV) color center in diamond has recently proven its suitability for bright and stable single photon emission. However, its electronic structure so far has remained elusive. We here explore the electronic structure by exposing single SiV defects to a magnetic field where the Zeeman effect lifts the degeneracy of magnetic sublevels. The similar response of single centers and a SiV ensemble in a low strain reference sample proves our ability to fabricate almost perfect single SiVs, revealing the true nature of the defect's electronic properties. We model t…
The possibility of propagation of second sound waves in diamond single crystals depending on their dimensions, concentrations of isotopes and temperature is studied. At this correct account of phonon scattering on boundaries is important. The calculation of phonon collision frequencies is carried out in the reduced isotropic crystal model using second and third modules of elasticity and in Callaway model on the basis of experimental data on diamond thermal conductivity. Both models give us the consistent values of parameters under which the propagation of SSW is possible. It is discovered that…
We demonstrate a new approach for engineering group IV semiconductor-based quantum photonic structures containing negatively charged silicon-vacancy (SiV$^-$) color centers in diamond as quantum emitters. Hybrid SiC/diamond structures are realized by combining the growth of nanoand micro-diamonds on silicon carbide (3C or 4H polytype) substrates, with the subsequent use of these diamond crystals as a hard mask for pattern transfer. SiV$^-$ color centers are incorporated in diamond during its synthesis from molecular diamond seeds (diamondoids), with no need for ionimplantation or annealing. We…
We performed high-temperature luminescence studies of silicon-vacancy color centers obtained by ion implantation in single crystal diamond. We observed reduction of the integrated fluorescence upon increasing temperature, ascribable to a transition channel with an activation energy of 180 meV that populates a shelving state. Nonetheless, the signal decreased only 50% and 75% with respect to room temperature at 500 K and 700 K, respectively. In addition, the color center is found highly photostable at temperatures exceeding 800 K. The luminescence of this color center is thus extremely robust e…
The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters, (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, and anisotropic elastic constants of the chosen crystal. Diamond, due to its unique elastic properties, can provide notably higher resolution than silicon. The results allow to optimize the parameters of bent crystal spectrometers for the h…
Diamond and Silicon Carbide (SiC) are promising wide band-gap semiconductors for power electronics, SiC being more mature especially in term of large wafer size (that has reached 200 mm quite recently). Nitrogen impurities are often used in both materials for different purpose: increase the diamond growth rate or induce n-type conductivity in SiC. The determination of the nitrogen content by secondary ion mass spectrometry (SIMS) is a difficult task mainly because nitrogen is an atmospheric element for which direct monitoring of N$^\pm$ ions give no or a weak signal. With our standard diamond …
In our present work, five previously proposed sp$^3$ carbon crystals were suggested as silicon allotropes and their stabilities, electronic and optical properties were investigated by first-principles method. We find that these allotropes with direct or quasi-direct band gaps in range of 1.2-1.6 eV are very suitable for applications in thin-film solar cells. They display strong adsorption coefficients in the visible range of the sunlight in comparison with diamond silicon. These five silicon allotropes are confirmed possessing positive dynamical stability and remarkable themodynamical stabilit…
Force-constant and positional disorder have been introduced into diamond lattice models in an attempt to mimic the vibrational properties of a realistic amorphous silicon model. Neither type of disorder is sufficient on its own to mimic the realistic model. By comparing the spectral densities of these models, it is shown that a combination of both disorders is a better representation, but still not completely satisfactory. Topological disorder in these models was investigated by renumbering the atoms and examining the dynamical matrix graphically. The dynamical matrix of the realistic model is…
The silicon-vacancy (SiV) and nitrogen-vacancy (NV) centers in diamond are commonly regarded as prototypical defects for solid-state quantum information processing. Here we show that when silicon and nitrogen are simultaneously introduced into the diamond lattice these defects can strongly interact and form larger complexes. Nitrogen atoms strongly bind to Si and SiV centers and complex formation can occur. Using a combination of hybrid density functional theory (DFT) and group theory, we analyze the electronic structure and provide various useful physical properties, such as hyperfine structu…
Vacancy centers in diamond have proven to be a viable solid-state platform for quantum coherent opto-electronic applications. Among the variety of vacancy centers, silicon-vacancy (SiV) centers have recently attracted much attention as an inversion-symmetric system that is less susceptible to electron-phonon interactions. Nevertheless, phonon-mediated processes still degrade the coherent properties of SiV centers, however characterizing their electron-phonon coupling is extremely challenging due to their weak spectroscopic signatures and remains an open experimental problem. In this paper we t…
We investigate the pressure-induced metal-insulator transition from diamond to beta-tin in bulk Silicon, using quantum Monte Carlo (QMC) and density functional theory (DFT) approaches. We show that it is possible to efficiently describe many-body effects, using a variational wave function with an optimized Jastrow factor and a Slater determinant. Variational results are obtained with a small computational cost and are further improved by performing diffusion Monte Carlo calculations and an explicit optimization of molecular orbitals in the determinant. Finite temperature corrections and zero p…
Color centers in diamond are a promising platform for quantum technologies, and understanding their interactions with the environment is crucial for these applications. We report a study of spin- lattice relaxation (T1) of the neutral charge state of the silicon vacancy center in diamond. Above 20 K, T1 decreases rapidly with a temperature dependence characteristic of an Orbach process, and is strongly anisotropic with respect to magnetic field orientation. As the angle of the magnetic field is rotated relative to the symmetry axis of the defect, T1 is reduced by over three orders of magnitude…
The neutrally-charged silicon vacancy in diamond is a promising system for quantum technologies that combines high-efficiency, broadband optical spin polarization with long spin lifetimes (T2 ~ 1 ms at 4 K) and up to 90% of optical emission into its 946 nm zero-phonon line. However, the electronic structure of SiV0 is poorly understood, making further exploitation difficult. Performing photoluminescence spectroscopy of SiV0 under uniaxial stress, we find the previous excited electronic structure of a single 3A1u state is incorrect, and identify instead a coupled 3Eu - 3A2u system, the lower st…
We study single silicon vacancy (SiV) centres in chemical vapour deposition (CVD) nanodiamonds on iridium as well as an ensemble of SiV centres in a high quality, low stress CVD diamond film by using temperature dependent luminescence spectroscopy in the temperature range 5-295 K. We investigate in detail the temperature dependent fine structure of the zero-phonon-line (ZPL) of the SiV centres. The ZPL transition is affected by inhomogeneous as well as temperature dependent homogeneous broadening and blue shifts by about 20 cm-1 upon cooling from room temperature to 5 K. We employ excitation p…
Triboemission is a phenomenon associated with the sliding of variety of materials. The phenomenon is thought to be related to wear of diamond tools used in precision machining of semiconductors. As such, the physics of emission has recently acquired importance. Many researchers studied emission during scratching of solid surfaces. They observed that the intensity of tribo-induced emission of the electrons, ions, and photons decrease in the order: insulator>semiconductor> conductor. Many experiments conducted to compare the emission of negatively-charged particles in case of the semiconductors …
Diamond silicon (Si) is the leading material in current solar cell market. However, diamond Si is an indirect band gap semiconductor with a large energy difference (2.4 eV) between the direct gap and the indirect gap, which makes it an inefficient absorber of light. In this work, we develop a novel inverse-band structure design approach based on the particle swarming optimization algorithm to predict the metastable Si phases with better optical properties than diamond Si. Using our new method, we predict a cubic Si20 phase with quasi-direct gaps of 1.55 eV, which is a promising candidate for m…
The silicon-vacancy (SiV) center in diamond is typically found in three stable charge states, SiV0, SiV- and SiV2-, but studying the processes leading to their formation is challenging, especially at room temperature, due to their starkly different photo-luminescence rates. Here, we use confocal fluorescence microscopy to activate and probe charge interconversion between all three charge states under ambient conditions. In particular, we witness the formation of SiV0 via the two-step capture of diffusing, photo-generated holes, a process we expose both through direct SiV0 fluorescence measurem…
A new experimental approach for the characterization of the lateral elastic modulus of individual nanowires is demonstrated by implementing a micro/nano scale diametrical compression test geometry, using a flat punch indenter inside of a scanning electron microscope (SEM). A 250 nm diameter single crystal silicon nanowire is tested. Since silicon is highly anisotropic, the compression axis of the wire was determined by electron backscatter diffraction (EBSD). A two dimensional analytical closed-form solution based on a Hertz model is presented. The results of the analytical model are compared …
We investigate phonon induced electronic dynamics in the ground and excited states of the negatively charged silicon-vacancy ($\mathrm{SiV}^-$) centre in diamond. Optical transition line widths, transition wavelength and excited state lifetimes are measured for the temperature range 4-350 K. The ground state orbital relaxation rates are measured using time-resolved fluorescence techniques. A microscopic model of the thermal broadening in the excited and ground states of the $\mathrm{SiV}^-$ centre is developed. A vibronic process involving single-phonon transitions is found to determine orbita…
CVD diamond is an attractive material option for LHC vertex detectors because of its strong radiation-hardness causal to its large band gap and strong lattice. In particular, pixel detectors operating close to the interaction point profit from tiny leakage currents and small pixel capacitances of diamond resulting in low noise figures when compared to silicon. On the other hand, the charge signal from traversing high energy particles is smaller in diamond than in silicon by a factor of about 2.2. Therefore, a quantitative determination of the signal-to-noise ratio (S/N) of diamond in compariso…
Influence of tip materials on the friction force microscopy of epitaxial graphene on SiC(0001): comparison of diamond and silicon tips in experiments and atomistic simulations
Silicon-vacancy (SiV) centers in diamond are promising systems for quantum information applications due to their bright single photon emission and optically accessible spin states. Furthermore, SiV centers in low-strain diamond are insensitive to pertubations of the dielectric environment, i.e. they show very weak spectral diffusion. This property renders ensembles of SiV centers interesting for sensing applications. We here report on photoluminescence excitation (PLE) spectroscopy on an SiV ensemble in a low strain, CVD-grown high quality diamond layer, where we measure the fine structure wit…
The silicon-vacancy ($\mathrm{SiV}^-$) color center in diamond has attracted attention due to its unique optical properties. It exhibits spectral stability and indistinguishability that facilitate efficient generation of photons capable of demonstrating quantum interference. Here we show high fidelity optical initialization and readout of electronic spin in a single $\mathrm{SiV}^-$ center with a spin relaxation time of $T_1=2.4\pm0.2$ ms. Coherent population trapping (CPT) is used to demonstrate coherent preparation of dark superposition states with a spin coherence time of $T_2^\star=35\pm3$…
We demonstrate optical spin polarization of the neutrally-charged silicon-vacancy defect in diamond ($\mathrm{SiV^{0}}$), an $S=1$ defect which emits with a zero-phonon line at 946 nm. The spin polarization is found to be most efficient under resonant excitation, but non-zero at below-resonant energies. We measure an ensemble spin coherence time $T_2>100~\mathrm{μs}$ at low-temperature, and a spin relaxation limit of $T_1>25~\mathrm{s}$. Optical spin state initialization around 946 nm allows independent initialization of $\mathrm{SiV^{0}}$ and $\mathrm{NV^{-}}$ within the same optically-addres…
The electron-phonon interaction contribution to the electronic energies is included in density functional total energy calculations with ab initio pseudopotentials via the Allen formalism [Phys. Rev. B 18, 5217 (1978)] to obtain temperature dependent electronic structure of diamond and silicon. This method allows us to obtain the thermally-averaged ab initio electronic structure in a straightforward and computationally inexpensive way. Our investigations on the finite temperature electronic structure of diamond and silicon lead to a new criterion, temperature transferability, which is required…
Point defects are responsible for a wide range of optoelectronic properties in materials, making it crucial to engineer their concentrations for novel materials design. However, considering the plethora of defects in co-doped semiconducting and dielectric materials and the dependence of defect formation energies on heat treatment parameters, process design based on an experimental trial and error approach is not an efficient strategy. This makes it necessary to explore computational pathways for predicting defect equilibria during heat treatments. The accumulated experimental knowledge on defe…
The utilisation of crystalline semiconductor materials as detectors and devices operating in high radiation environments, at the future particle colliders, in space applications, in medicine and industry, makes necessary to obtain radiation harder materials. Diamond, SiC and different AIIIBV compounds (GaAs, GaP, InP, InAs, InSb) are possible competitors for silicon to different electronic devices for the up-mentioned applications. The main goal of this paper is to give theoretical predictions about the behaviour of these semiconductors in hadron fields (pions, protons). The effects of the int…
It was previously believed that the Bloch electronic states of non-magnetic materials with inversion symmetry cannot have finite spin polarizations. However, since the seminal work by Zhang et al. [Nat. Phys. 10, 387-393 (2014)] on local spin polarizations of Bloch states in non-magnetic, centrosymmetric materials, the scope of spintronics has been significantly broadened. Here, we show, using a framework that is universally applicable independent of whether hidden spin polarizations are small (e.g., diamond, Si, Ge, and GaAs) or large (e.g., MoS2 and WSe2), that the corresponding quantity ari…
