We re-examine the quantum tau_q and transport tau_t scattering lifetimes due to background impurities in two-dimensional systems. We show that the well-known logarithmic divergence in the quantum lifetime is due to the non-physical assumption of an infinitely thick heterostructure, and demonstrate that the existing non-divergent multiple scattering theory can lead to unphysical quantum scattering lifetimes in high quality heterostructures. We derive a non-divergent scattering lifetime for finite thickness structures, which can be used both with lowest order perturbation theory and the multiple scattering theory. We calculate the quantum and transport lifetimes for electrons in generic GaAs-AlGaAs heterostructures, and find that the correct `rule of thumb' to distinguish the dominant scattering mechanisms in GaAs heterostructures should be tau_t/tau_q < 10 for background impurities and tau_t/tau_q > 10 for remote impurities. Finally we present the first comparison of theoretical results for tau_q and tau_t with experimental data from a GaAs 2DEG in which only background impurity scattering is present. We obtain excellent agreement between the calculations and experimental data, and are able to extract the background impurity density in both the GaAs and AlGaAs regions.
We propose that the observed spin-relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and non-dimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to single-layer graphene, the measured spin-relaxation rate in graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening …
We study the spin relaxation of charge carriers in graphene in the presence of spin-polarized charged impurities by calculating the time evolution of initially polarized state. The spin relaxation time shows completely different energy behaviour for short-ranged and long-ranged spin scatterers and can be used to identify the dominant source of spin scattering. Our results agree well with recent experimental findings and indicate that their spin relaxation is likely caused by long-ranged scatterers.
Monolayer graphene is an example of materials with multi-valley electronic structure. In such materials, the valley index is being considered as an information carrier. Consequently, relaxation mechanisms leading to loss of valley information are of interest. Here, we calculate the rate of valley relaxation induced by charged impurities in graphene. A special model of graphene is applied, where the $p_z$ orbitals are two-dimensional Gaussian functions, with a spatial extension characterised by an effective Bohr radius $a_\textrm{eB}$. We obtain the valley relaxation rate by solving the Boltzma…
We study the surface conductivity of a three dimensional topological insulator doped with magnetic impurities. The spin-momentum locking of surface electrons makes their scattering from magnetic impurities anisotropic and the standard relaxation time approximation is not applicable. Using the semiclassical Boltzmann approach together with a generalized relaxation time scheme, we obtain closed forms for the relaxation times and analytic expressions for the surface conductivities of the system as functions of the bulk magnetization and the orientation of the aligned surface magnetic impurities. …
Electron energy relaxation in the presence of magnetic impurities
研究了电子与磁性杂质交换作用下的电子-电子非弹性散射，得到了相应的两粒子碰撞积分的核。在参数的宽范围内，核K与传递能量的平方倒数$K\propto J^4/E^2$成比例。由于近藤效应，交换常数J被重整化，产生K对碰撞电子能量的额外弱依赖性。在小能量转移时，$1/E^2$发散被切断;切断能量由杂质自旋的动力学决定。所得结果可为Pothier等人的实验提供定量解释[Phys. Rev. Lett. 79，3490（1997）]关于短金属丝中的强能量弛豫的研究。
We study the transport properties of two dimensional electron systems with strong Rashba spin-orbit coupling (SOC) doped with interacting magnetic impurities. Interactions between magnetic impurities cause the formation of magnetic clusters with temperature dependent mean sizes (CMSs) distributed randomly on the surface of the system. Treating magnetic clusters as scattering centers, by employing a generalized relaxation time approximation we obtain the non-equilibrium distribution functions of Rashba electrons in both regimes of above and below the band-crossing point (BCP) and present the ex…
The dependences of the transport scattering time τt, quantum lifetime τq, and their ratio τt/τq on the density ne of the electron gas in modulation-doped single GaAs quantum wells with AlAs/GaAs short-period super-lattice barriers are investigated. The experimental dependences are explained in terms of electron scattering by remote ionized donors with an effective two-dimensional concentration n*R and background impurities with a three-dimensional concentration nB. An expression for n*R(ne) is obtained including the contribution of X-valley electrons localized in AlAs layers to the suppression…
Microscopic description of Raman spectra in nanopowders of nonpolar crystals is accomplished by developing the theory of disorder-induced broadening of optical vibrational eigenmodes. Analytical treatment of this problem is performed, and line shape and width are determined as functions of phonon quantum numbers, nanoparticle shape, size, and the strength of disorder. The results are found to be strongly dependent on either the broadened line is separated or it is overlapped with other lines of the spectrum. Three models of disorder, i.e. weak point-like impurities, weak smooth random potentia…
Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an $s$-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities---the Hebel-Slichter effect---and decreases when impurities have spin-orbit coupling. This distinct temperature~dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that th…
Spin relaxation was studied in a two-dimensional electron gas confined in a wide GaAs quantum well. Recently, the control of the spin relaxation anisotropy by diffusive motion was first shown in D. Iizasa et al., arXiv:2006.08253 (2020). Here, we demonstrate electrical control by drift transport in a system with two-subbands occupied. The combined effect of in-plane and gate voltages was investigated using time-resolved Kerr rotation. The measured relaxation time present strong anisotropy with respect to the transport direction. For an in-plane accelerating electric field along $\left[110\righ…
We investigate the magnetic field and temperature dependence of the single-electron spin lifetime in silicon quantum dots and find a lifetime of 2.8 ms at a temperature of 1.1 K. We develop a model based on spin-valley mixing and find that Johnson noise and two-phonon processes limit relaxation at low and high temperature respectively. We also investigate the effect of temperature on charge noise and find a linear dependence up to 4 K. These results contribute to the understanding of relaxation in silicon quantum dots and are promising for qubit operation at elevated temperatures.
We measure singlet-triplet mixing in a precision fabricated double donor dot comprising of 2 and 1 phosphorus atoms separated by $16{\pm}1$ nm. We identify singlet and triplet-minus states by performing sequential independent spin readout of the two electron system and probe its dependence on magnetic field strength. The relaxation of singlet and triplet states are measured to be $12.4{\pm}1.0$ s and $22.1{\pm}1.0$ s respectively at $B_z{=}2.5$ T.
We theoretically investigate the D'yakonov-Perel' spin relaxation properties in diffusive wurtzite semiconductor nanowires and their impact on the quantum correction to the conductivity. Although the lifetime of the long-lived spin states is limited by the dominant $k$-linear spin-orbit contributions in the bulk, these terms show almost no effect in the finite-size nanowires. Here, the spin lifetime is essentially determined by the small $k$-cubic spin-orbit terms and nearly independent of the wire radius. At the same time, these states possess in general a complex helical structure in real sp…
We report the experimental study of the temperature-dependence of the longitudinal spin relaxation time $T_1$ of single Nitrogen-Vacancy (NV) centers hosted in nanodiamonds. To determine the relaxation mechanisms at stake, measurements of the $T_1$ relaxation time are performed for a set of individual NV centers both at room and cryogenic temperatures. The results are consistant with a temperature-dependent relaxation process which is attributed to a thermally-activated magnetic noise produced by paramagnetic impurities lying on the nanodiamond surface. These results confirm the existence of s…
The understanding of spin dynamics and relaxation mechanisms in clean graphene and the upper time and length scales on which spin devices can operate are prerequisites to realizing graphene spintronic technologies. Here we theoretically reveal the nature of fundamental spin relaxation mechanisms in clean graphene on different substrates with spin-orbit Rashba fields as low as a few tens of micron eV. Spin lifetimes ranging from 50 picoseconds up to several nanoseconds are found to be dictated by substrate-induced electron-hole characteristics. A crossover in the spin relaxation mechanism from …
We investigate the spin relaxation and Kondo resistivity caused by magnetic impurities in doped transition metal dichalcogenides monolayers. We show that momentum and spin relaxation times due to the exchange interaction by magnetic impurities, are much longer when the Fermi level is inside the spin split region of the valence band. In contrast to the spin relaxation, we find that the dependence of Kondo temperature $T_K$ on the doping is not strongly affected by the spin-orbit induced splitting, although only one of the spin species are present at each valley. This result, which is obtained u…
Millisecond-long electron spin lifetime in CsPbI$_3$ perovskite nanocrystals revealed by optically detected magnetic resonance
Technische Universität Dortmund（多特蒙德工业大学）；Ioffe Institute, Russian Academy of Sciences（俄罗斯科学院伊俄费研究所）；P.N. Lebedev Physical Institute of the Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Spin Optics Laboratory, St. Petersburg State University（圣彼得堡大学旋光实验室）；ITMO University（ITMO大学）；St. Petersburg State Institute of Technology（圣彼得堡国立理工学院）
Disorder-induced broadening of optical vibrational eigenmodes in nanoparticles of nonpolar crystals is studied numerically. The methods previously used to treat phonons in defectless particles are adjusted for numerical evaluation of the disordered problem. Imperfections in the form of Gaussian and binary disorders as well as surface irregularities are investigated thoroughly in a wide range of impurity concentrations and disorder strengths. For dilute and weak point-like impurities the regimes of separated and overlapped phonon levels are obtained and the behavior of the linewidth predicted t…
Spin Relaxation in Single Layer Graphene with Tunable Mobility
石墨烯是自旋电子学的一种有吸引力的材料，这是由于低自旋轨道和超精细耦合产生的长自旋寿命的理论预测。然而，在实验中，通过Hanle效应测量的单层石墨烯（SLG）的自旋寿命比理论上预期的要短得多。因此，SLG中自旋弛豫的起源是石墨烯自旋电子学的主要问题。尽管有大量的理论和实验工作来解决这个问题，但自旋弛豫的微观起源仍然很不清楚。通过使用有机配体结合的纳米粒子作为电荷库，调整迁移率在2700和12000 cm 2/Vs之间，我们成功地隔离了SLG中带电杂质散射对自旋弛豫的影响。我们的结果表明，虽然带电杂质可以大大影响迁移率，自旋寿命不受带电杂质散射。
Longitudinal relaxation is the process by which an excited spin ensemble decays into its thermal equilibrium with the environment. In solid-state spin systems relaxation into the phonon bath usually dominates over the coupling to the electromagnetic vacuum. In the quantum limit the spin lifetime is determined by phononic vacuum fluctuations. However, this limit was not observed in previous studies due to thermal phonon contributions or phonon-bottleneck processes. Here we use a dispersive detection scheme based on cavity quantum electrodynamics (cQED) to observe this quantum limit of spin rela…
Complementing STM/S, U/XPS, and APECS, BOLS-NEP theory enabled ZPS (USA patent) distils atomistic, dynamic, local, and quantitative information of bond relaxation and associated energetics, localization, quantum entrapment, and polarization of electrons associated with adatoms, point defects, terrace edges, monolayer skins, nanocrystals, impurities, and interfaces. Distilled entitles dominate ubiquitously and will propel the ill-coordination Chemistry and Physics.
We experimentally demonstrate ultralong spin lifetimes of electrons in the one-dimensional (1D) quantum limit of semiconductor nanowires. Optically probing single wires of different diameters reveals an increase in the spin relaxation time by orders of magnitude as the electrons become increasingly confined until only a single 1D subband is populated. We find the observed spin lifetimes of more than $200\,\textrm{ns}$ to result from the robustness of 1D electrons against major spin relaxation mechanisms, highlighting the promising potential of these wires for long-range transport of coherent s…
Disorder such as impurities and dislocations in Weyl semimetals (SMs) drives a quantum critical point (QCP) where the density of states at the Weyl point gains a non-zero value. Near the QCP, the asymptotic low energy singularities of physical quantities are controlled by the critical exponents $ν$ and $z$. The nuclear spin-lattice relaxation rate, which originates from the hyperfine coupling between a nuclear spin and long-range orbital currents in Weyl fermion systems, shows intriguing critical behavior. Based on the self-consistent Born approximation for impurities, we study the nuclear spi…
Unprecedented Spin-Lifetime of Itinerant Electrons in Natural Graphite Crystals
University of Notre Dame（圣母大学）；HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳物理研究中心）；Óbuda University（欧拜伊大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
A theory is developed for the density and temperature dependent carrier conductivity in doped three-dimensional (3D) Dirac materials focusing on resistive scattering from screened Coulomb disorder due to random charged impurities (e.g., dopant ions and unintentional background impurities). The theory applies both in the undoped intrinsic ("high-temperature", $T \gg T_F$) and the doped extrinsic ("low-temperature", $T \ll T_F$) limit with analytical scaling properties for the carrier conductivity obtained in both regimes, where $T_F$ is the Fermi temperature corresponding to the doped free carr…
Thermoelectric effects in graphene are considered theoretically with particular attention paid to the role of impurities. Using the T -matrix method we calculate the impurity resonant states and the momentum relaxation time due to scattering on impurities. The Boltzmann kinetic equation is used to determine the thermoelectric coefficients. It is shown that the resonant impurity states near the Fermi level give rise to a resonant enhancement of the Seebeck coefficient and of the figure of merit $ZT$ . The Wiedemann-Franz ratio deviates from that known for ordinary metals, where this ratio is co…
