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We predict "intrinsic" spin relaxation times ($T_{1}$) of graphite due to spin-orbit-phonon interaction, i.e., the combination of spin-orbit coupling and electron-phonon interaction, using our developed first-principles density-matrix approach. We obtain ultralong $T_{1}$, e.g., $\sim$600 ns at 300 K, which leads to ultralong in-plane spin diffusion length $\sim$110 $\mu$m within the drift-diffusion model. Our prediction sets the upper bound of $T_{1}$ of graphite at each given temperature and Fermi level. The anisotropy ratios of $T_{1}$ or values of $T_{1z}/T_{1x}$ are found small and around 0.6. We examine the applicability of the well-known Elliot-Yafet (EY) relation, which declares that spin relaxation rate $T_{1\alpha}^{-1}$ ($\alpha=x,y,z$) is proportional to the product of the ensemble average of spin mixing parameter $\left\langle b_{\alpha}^{2}\right\rangle $ and carrier relaxation rate $\tau_{p}^{-1}$. Our numerical tests suggest that the EY relation works qualitatively if the degeneracy threshold $t^{\mathrm{deg}}$ for evaluating $b_{\alpha}^{2}$ is elatively large (not much smaller than or comparable to $k_{B}T$), e.g., $10^{-3}$ eV or larger, but fails if $t^{\mathrm{deg}}$ is too tiny (much smaller than $k_{B}T$), e.g., $10^{-6}$ eV or smaller., Comment: 9 pages, 4 figures

Understanding spin relaxation in topological systems such as quantum spin-hall (QSH) insulator is critical for realizing coherent transport at high temperature. WTe$_{2}$, known as a QSH insulator with a high transition temperature of 100K, is an important test-bed of unveiling spin relaxation mechanism in topological materials. In this work, we employ our recently-developed \emph{ab initio} density-matrix dynamics approach to investigate spin relaxation mechanism, and calculate spin lifetime and diffusion length of monolayer 1T'-WTe$_{2}$, at finite temperature under an external electric field. We found the spin lifetime of electrons have the largest anisotropy when measuring along the canted-spin-texture direction. Moreover, we found an opposite trend between spin and carrier relaxation against applied electric field. Most importantly, the relaxation mechanism under intermediate electric field around 1V/nm can not be explained by either Eillot-Yafet or Dyakonov-Perel models, which highlights the generality of our \emph{ab initio} density-matrix framework. We then proposed analytical models to explain its mechanism and compare well with \emph{ab initio} results at small and large electric field. We predict that spin lifetime and spin diffusion length of bulk-state electrons are $\sim$1 ps and $\sim$30 nm at room temperature respectively, suggesting its promise for spintronic applications.

We present a general ab initio method based on Wannier functions using the covariant derivative for simulating the photocurrent in solids. The method is widely applicable to charge/spin DC and AC photocurrent at any perturbation levels in both semiconductors and metals for both linearly and circularly polarized light. This is because the method is theoretically complete (within the relaxation time approximation), that is to say, it includes all intraband, interband and their cross terms. It is also free from the degeneracy issue, i.e., applicable to arbitrary band structures with arbitrary numbers of degenerate bands. We apply the method to various semiconductors and metals, including GaAs, graphene-hBN heterostructure, monolayer WS2, a 2D ferroelectric material - monolayer GeS, bilayer anti-ferromagnetic MnBi2Te4 and topological Weyl semimetal RhSi, to simulate their charge and/or spin, DC and/or AC photocurrent. Our theoretical results are in agreement with previous theoretical works. Our numerical tests of GaAs, WS2 and GeS suggest setting the degeneracy threshold in the conventional method as \hbar\Gamma^{2}, with \Gamma^{2} the relaxation rate of the off-diagonal elements of the density matrix between two states with close energies. We find that compared with the conventional Wannier-function-based method using non-dgenerate perturbation theory, the numerical errors of optical susceptibilities of bilayer anti-ferromagnetic MnBi2Te4 with the PT symmetry can be reduced by 1-2 orders of magnitude by our method for circularly polarized light. Our method provides a universal computational tool for reliable and accurate predictions of abundant weak-field photocurrent phenomena in disparate materials., Comment: 22 pages, 9 figures

Spin relaxation, dephasing and diffusion are at the heart of spin-based information technology. Accurate theoretical approaches to simulate spin lifetimes ($\tau_s$), determining how fast the spin polarization and phase information will be lost, are important to the understandings of underlying mechanism of these spin processes, and invaluable to search for promising candidates of spintronic materials. Recently, we develop a first-principles real-time density-matrix (FPDM) approach to simulate spin dynamics for general solid-state systems. Through the complete first-principles' descriptions of light-matter interaction and scattering processes including electron-phonon, electronimpurity and electron-electron scatterings with self-consistent spin-orbit coupling, as well as ab initio Land'e g-factor, our method can predict $\tau_s$ at various conditions as a function of carrier density and temperature, under electric and magnetic fields. By employing this method, we successfully reproduce experimental results of disparate materials and identify the key factors affecting spin relaxation, dephasing, and diffusion in different materials. Specifically, we predict that germanene has long $\tau_s$ (~100 ns at 50 K), a giant spin lifetime anisotropy and spin-valley locking effect under electric fields, making it advantageous for spin-valleytronic applications. Based on our theoretical derivations and ab initio simulations, we propose a new useful electronic quantity, named spin-flip angle $\theta^{\uparrow\downarrow}$, for the understanding of spin relaxation through intervalley spin-flip scattering processes. Our method can be further applied to other emerging materials and extended to simulate exciton spin dynamics and steady-state photocurrents due to photogalvanic effect.

Chiral crystals show promise for spintronic technologies on account of their high spin selectivity, which has led to significant recent interest in quantitative characterization and first-principles prediction of their spin-optoelectronics properties. Here, we outline a computational framework for efficient ab-initio calculations of circular dichroism (CD) in crystalline materials. We leverage direct calculations of orbital angular momentum and quadrupole matrix element calculations in density-functional theory (DFT) and Wannier interpolation to calculate CD in complex materials, removing the need for band convergence and accelerating Brillouin-zone convergence compared to prior approaches. We find strong agreement with measured CD signals in molecules and crystals ranging in complexity from small bulk unit cells to 2D hybrid perovskites, and show the importance of the quadrupole contribution to the anisotropic CD in crystals. Spin-orbit coupling affects the CD of crystals with heavier atoms, as expected, but this is primarily due to changes in the electronic energies, rather than due to direct contributions from the spin matrix elements. We showcase the capability to predict CD for complex structures on a 2D hybrid perovskite, finding strong orientation dependence and identifying the eigen-directions of the unit cell with the strongest CD. We additionally decompose CD into separate contributions from inorganic, organic, and mixed organic-inorganic transitions, finding the chiral molecules to dominate the CD, with the inorganic lattice contributing at higher frequencies in specific directions. This unprecedented level of detail in CD predictions in crystals will facilitate experimental development of complex chiral crystals for spin selectivity., Comment: 12 pages, 6 figures

Spintronics in halide perovskites has drawn significant attention in recent years, due to highly tunable spin-orbit fields and intriguing interplay with lattice symmetry. Spin lifetime -- a key parameter that determines the applicability of materials for spintronics and spin-based quantum information applications -- has been extensively measured in halide perovskites, but not yet assessed from first-principles calculations. Here, we leverage our recently-developed \emph{ab initio} density-matrix dynamics framework to compute the spin relaxation time ($T_{1}$) and ensemble spin dephasing time ($T_{2}^{*}$) in a prototype halide perovskite, namely CsPbBr$_{3}$ with self-consistent spin-orbit coupling (SOC) and quantum descriptions of the electron scattering processes. We also implement the Land\'e $g$-factor for solids from first principles and take it into account in our dynamics, which is required to accurately capture spin dephasing at external magnetic fields. We thereby predict intrinsic spin lifetimes as an upper bound for experiments, identify the dominant spin relaxation pathways, and evaluate the dependence on temperature, external fields, carrier density,and impurities. Importantly, we find that the Fr{\"o}hlich interaction that dominates carrier relaxation contributes negligibly to spin relaxation, consistent with the spin-conserving nature of this interaction. We investigated the effect of spin-orbit field with inversion asymmetry on spin lifetime, and we demonstrated from our calculation, persistent spin helix can enhance spin lifetime when the spin-split is large, but it can not be realized by Rashba SOC. Our theoretical approach may lead to new strategies to optimize spin and carrier transport properties in spintronics and quantum information applications., Comment: 10 pages, 6 figures

Understanding substrate effects on spin dynamics and relaxation in two-dimensional (2D) materials is of key importance for spintronics and quantum information applications. However, the key factors that determine the substrate effect on spin relaxation, in particular for materials with strong spin-orbit coupling, have not been well understood. Here we performed first-principles real-time density-matrix dynamics simulations with spin-orbit coupling (SOC) and quantum descriptions of electron-phonon and electron-impurity scattering for the spin lifetimes of supported/free-standing germanene, a prototypical strong SOC 2D Dirac material. We show that the effects of different substrates on spin lifetime can surprisingly differ by two orders of magnitude. We find that substrate effects on $\tau_s$ are closely related to substrate-induced modifications of the SOC-field anisotropy, which changes the spin-flip scattering matrix elements. We propose a new electronic quantity, named spin-flip angle $\theta^{\uparrow\downarrow}$, to characterize spin relaxation caused by intervalley spin-flip scattering. We find that the spin relaxation rate is approximately proportional to the averaged value of $\mathrm{sin}^{2}\left(\theta^{\uparrow\downarrow}/2\right)$, which can be used as a guiding parameter of controlling spin relaxation.

Through First-Principles real-time Density-Matrix (FPDM) dynamics simulations, we investigate spin relaxation due to electron-phonon and electron-impurity scatterings with spin-orbit coupling in two-dimensional Dirac materials - silicene and germanene, at finite temperatures and under external fields. We discussed the applicability of conventional descriptions of spin relaxation mechanisms by Elliott-Yafet (EY) and D'yakonov-Perel' (DP) compared to our FPDM method, which is determined by a complex interplay of intrinsic spin-orbit coupling, external fields, and electron-phonon coupling strength, beyond crystal symmetry. For example, the electric field dependence of spin relaxation time is close to DP mechanism for silicene at room temperature, but rather similar to EY mechanism for germanene. Due to its stronger spin-orbit coupling strength and buckled structure in sharp contrast to graphene, germanene has a giant spin lifetime anisotropy and spin valley locking effect under nonzero Ez and relatively low temperature. More importantly, germanene has extremely long spin lifetime (~100 ns at 50 K) and ultrahigh carrier mobility, which makes it advantageous for spin-valleytronic applications., Comment: 9 pages, 4 figures

Substrates have strong effects on optoelectronic properties of two-dimensional (2D) materials, which have emerged as promising platforms for exotic physical phenomena and outstanding applications. To reliably interpret experimental results and predict such effects at 2D interfaces, theoretical methods accurately describing electron correlation and electron-hole interaction such as first-principles many-body perturbation theory are necessary. In our previous work [Phys. Rev. B 102, 205113(2020)], we developed the reciprocal-space linear interpolation method that can take into account the effects of substrate screening for arbitrarily lattice-mismatched interfaces at the GW level of approximation. In this work, we apply this method to examine the substrate effect on excitonic excitation and recombination of 2D materials by solving the Bethe-Salpeter equation. We predict the nonrigid shift of 1s and 2s excitonic peaks due to substrate screening, in excellent agreements with experiments. We then reveal its underlying physical mechanism through 2D hydrogen model and the linear relation between quasiparticle gaps and exciton binding energies when varying the substrate screening. At the end, we calculate the exciton radiative lifetime of monolayer hexagonal boron nitride with various substrates at zero and room temperature, as well as the one of WS2 where we obtain good agreement with experimental lifetime. Our work answers important questions of substrate effects on excitonic properties of 2D interfaces., Comment: 8 pages, 5 figures

Electrons in graphene are theoretically expected to retain spin states much longer than most materials, making graphene a promising platform for spintronics and quantum information technologies. Here, we use first-principles density-matrix (FPDM) dynamics simulations to show that interaction with electric fields and substrates strongly enhance spin relaxation through scattering with phonons. Consequently, the relaxation time at room temperature reduces from microseconds in free-standing graphene to nanoseconds in graphene on hexagonal boron nitride (hBN) substrate, the order of magnitude typically measured in experiments. Further, inversion symmetry breaking by hBN introduces a stronger asymmetry in electron and hole spin lifetimes, than predicted by the conventional D'yakonov-Perel' (DP) model for spin relaxation. Deviations from the conventional DP model are stronger for in-plane spin relaxation, resulting in out-of-plane to in-plane lifetime ratios much greater than 1/2 with a maximum close to the Dirac point. These FPDM results, independent of symmetry-specific assumptions or material-dependent parameters, also validate recent modifications of the DP model to explain such deviations. Overall, our results indicate that spin-phonon relaxation in the presence of substrates may be more important in graphene than typically assumed, requiring consideration for graphene-based spin technologies at room temperature., Comment: 9 pages, 6 figures

Spin relaxation and decoherence is at the heart of spintronics and spin-based quantum information science. Currently, theoretical approaches that can accurately predict spin relaxation of general solids including necessary scattering pathways and capable for ns to ms simulation time are urgently needed. We present a first-principles real-time density-matrix approach based on Lindblad dynamics to simulate ultrafast spin dynamics for general solid-state systems. Through the complete first-principles descriptions of pump, probe and scattering processes including electron-phonon, electron-impurity and electron-electron scatterings with self-consistent electronic spin-orbit couplings, our method can directly simulate the ultrafast pump-probe measurements for coupled spin and electron dynamics over ns at any temperatures and doping levels. We first apply this method to a prototypical system GaAs and obtain excellent agreement with experiments. We find that the relative contributions of different scattering mechanisms and phonon modes differ considerably between spin and carrier relaxation processes. In sharp contrast to previous work based on model Hamiltonians, we point out that the electron-electron scattering is negligible at room temperature but becomes dominant at low temperatures for spin relaxation in n-type GaAs. We further examine ultrafast dynamics in novel spin-valleytronic materials - monolayer and bilayer WSe2 with realistic defects. We find that spin relaxation is highly sensitive to local symmetry and chemical bonds around defects. Our work provides a predictive computational platform for spin dynamics in solids, which has unprecedented potentials for designing new materials ideal for spintronics and quantum information technology., Comment: 10 pages, 8 figures

Despite the recognition of two-dimensional (2D) systems as emerging and scalable host materials of single photon emitters or spin qubits, uncontrolled and undetermined chemical nature of these quantum defects has been a roadblock to further development. Leveraging the design of extrinsic defects can circumvent these persistent issues and provide an ultimate solution. Here we established a complete theoretical framework to accurately and systematically design quantum defects in wide-bandgap 2D systems. With this approach, essential static and dynamical properties are equally considered for spin qubit discovery. In particular, many-body interactions such as defect-exciton couplings are vital for describing excited state properties of defects in ultrathin 2D systems. Meanwhile, nonradiative processes such as phonon-assisted decay and intersystem crossing rates require careful evaluation, which compete together with radiative processes. From a thorough screening of defects based on first-principles calculations, we identify promising single photon emitters such as SiVV and spin qubits such as TiVV and MoVV in hexagonal boron nitride. This work provided a complete first-principles theoretical framework for defect design in 2D materials., Comment: 7 figures; 2 tables

Two-dimensional (2D) materials are outstanding platforms for exotic physics and emerging applications by forming interfaces. In order to efficiently take into account the substrate screening in the quasiparticle energies of 2D materials, several theoretical methods have been proposed previously, but only applicable to interfaces of two systems' lattice constants with certain integer proportion. In this work, we analytically showed the equivalence and distinction among different approximate methods for substrate dielectric matrices. We evaluated the accuracy of these methods, by applying them to calculate quasi-particle energies of hexagonal boron nitride interface systems (heterojunctions and bilayers), and compared with explicit interface calculations. Most importantly, we developed an efficient and accurate interpolation technique for dielectric matrices that made quasiparticle energy calculations possible for arbitrarily mismatched interfaces, which is extremely important for practical applications., Comment: 9 pages, 7 figures, one table

Designing new quantum materials with long-lived electron spin states urgently requires a general theoretical formalism and computational technique to reliably predict intrinsic spin relaxation times. We present a new, accurate and universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate spin-phonon relaxation time ($\tau_s$) of solids with arbitrary spin mixing and crystal symmetry. This method describes contributions of Elliott-Yafet (EY) and D'yakonov-Perel' (DP) mechanisms to spin relaxation for systems with and without inversion symmetry on an equal footing. We show that intrinsic spin and momentum relaxation times both decrease with increasing temperature; however, for the DP mechanism, spin relaxation time varies inversely with extrinsic scattering time. We predict large anisotropy of spin lifetime in transition metal dichalcogenides. The excellent agreement with experiments for a broad range of materials underscores the predictive capability of our method for properties critical to quantum information science., Comment: 12 pages, 7 figures

Identification and design of defects in two-dimensional (2D) materials as promising single photon emitters (SPE) requires a deep understanding of underlying carrier recombination mechanisms. Yet, the dominant mechanism of carrier recombination at defects in 2D materials has not been well understood, and some outstanding questions remain: How do recombination processes at defects differ between 2D and 3D systems? What factors determine defects in 2D materials as excellent SPE at room temperature? In order to address these questions, we developed first-principles methods to accurately calculate the radiative and non-radiative recombination rates at defects in 2D materials, using h-BN as a prototypical example. We reveal the carrier recombination mechanism at defects in 2D materials being mostly dominated by defect-defect state recombination in contrast to defect-bulk state recombination in most 3D semiconductors. In particular, we disentangle the non-radiative recombination mechanism into key physical quantities: zero-phonon line (ZPL) and Huang-Rhys factor. At the end, we identified strain can effectively tune the electron-phonon coupling at defect centers and drastically change non-radiative recombination rates. Our theoretical development serves as a general platform for understanding carrier recombination at defects in 2D materials, while providing pathways for engineering of quantum efficiency of SPE., Comment: 5 pages, 4 figures

We compute the thermal conductivity and electrical resistivity of solid hcp Fe to pressures and temperatures of Earth's core. We find significant contributions from electron-electron scattering, usually neglected at high temperatures in transition metals. Our calculations show a quasi-linear relation between electrical resistivity and temperature for hcp Fe at extreme high pressures. We obtain thermal and electrical conductivities that are consistent with experiments considering reasonable error. The predicted thermal conductivity is reduced from previous estimates that neglect electron-electron scattering. Our estimated thermal conductivity for the outer core is 77$\pm$10 W/m/K, and is consistent with a geodynamo driven by thermal convection., Comment: 6 pages, 6 figures (Supplemental material: 7 pages, 4 figures, 6 tables)

We present a numerically efficient and accurate Multiple Scattering formalism, which is a generalization of the Multiple Scattering method with a truncated basis set [X. -G. Zhang and W. H. Butler, Phys. Rev. B 46,7433 (1992)]. Compared to the latter method, we keep the phase shifts of high angular momenta but apply approximations in the elements of the scattering matrix which is the subtraction of the unit matrix and the product of transition operator matrix and structure constant matrix. The detailed behaviour of our formalism for different types of calculations, where not full information of Green's function is needed, are discussed. We apply our formalism to study density of states of fcc Cu and silicon and C K-edge X-ray absorption spectra of graphene, in order to check the efficiency and accuracy of our formalism. We find that compared to Zhang's method, the accuracy is greatly improved by our method., Comment: 14 pages, 7 figures