Phonon-induced Relaxation Research Articles

(η8-Cyclooctatetraene)(η5-fluorenyl)titanium: a processable molecular spin qubit with optimized control of the molecule-substrate interface.

Depositing single paramagnetic molecules on surfaces for sensing and quantum computing applications requires subtle topological control. To overcome issues that are often encountered with sandwich metal complexes, we exploit here the low symmetry architecture and suitable vaporability of mixed-sandwich [FluTi(cot)], Flu = fluorenyl, cot = cyclooctatetraene, to drive submonolayer coverage and select an adsorption configuration that preserves the spin of molecules deposited on Au(111). Electron paramagnetic resonance spectroscopy and ab initio quantum computation evidence a d z 2 ground state that protects the spin from phonon-induced relaxation. Additionally, computed and measured spin coherence times exceed 10 μs despite the molecules being rich in hydrogen. A thorough submonolayer investigation by scanning tunneling microscopy, X-ray photoelectron and absorption spectrocopies and X-ray magnetic circular dichroism measurements supported by DFT calculations reveals that the most stable configuration, with the fluorenyl in contact with the metal surface, prevents titanium(iii) oxidation and spin delocalization to the surface. This is a necessary condition for single molecular spin qubit addressing on surfaces.

Confining single Er3+ ions in sub-3 nm NaYF4 nanoparticles to induce slow relaxation of the magnetisation

Molecular systems known as single-molecule magnets (SMMs) exhibit magnet-like behaviour of slow relaxation of the magnetisation and magnetic hysteresis and have potential application in high-density memory storage or quantum computing. Often, their intrinsic magnetic properties are plagued by low-energy molecular vibrations that lead to phonon-induced relaxation processes, however, there is no straightforward synthetic approach for molecular systems that would lead to a small amount of low-energy vibrations and low phonon density of states at the spin-resonance energies. In this work, we apply knowledge accumulated over the last decade in molecular magnetism to nanoparticles, incorporating Er3+ ions in an ultrasmall sub-3 nm diamagnetic NaYF4 nanoparticle (NP) and probing the slow relaxation dynamics intrinsic to the Er3+ ion. Furthermore, by increasing the doping concentration, we also investigate the role of intraparticle interactions within the NP. The knowledge gained from this study is anticipated to enable better design of magnetically high-performance molecular and bulk magnets for a wide variety of applications, such as molecular electronics.

Transform-Limited Photon Emission from a Lead-Vacancy Center in Diamond above 10K.

Transform-limited photon emission from quantum emitters is essential for high-fidelity entanglement generation. In this Letter, we report the coherent optical property of a single negatively charged lead-vacancy (PbV) center in diamond. Photoluminescence excitation measurements reveal stable fluorescence with a linewidth of 39MHz at 6K, close to the transform limit estimated from the lifetime measurement. We observe 4 orders of magnitude different linewidths of the two zero-phonon lines, and find that the phonon-induced relaxation in the ground state contributes to this huge difference in the linewidth. Because of the suppressed phonon absorption in the PbV center, we observe nearly transform-limited photon emission up to 16K, demonstrating its high temperature robustness compared to other color centers in diamond.

Pseudo-gap in RuGa3: A microscopic point of view

We report a detailed study of the nature of the RuGa3in-gap states by means of precision microscopic methods: nuclear quadrupole resonance (NQR), nuclear magnetic resonance (NMR), and pump-probe spectroscopy. We observe a pronounced splitting of 69Ga nuclear spin-lattice relaxation curves below ∼40 K and between 70 and 145 K, although the corresponding NQR lines remain narrow over the entire temperature range under study. The slow relaxing component behaves like a typical phonon-induced relaxation way, while the fast relaxing one demonstrates signatures of paramagnetic (below ∼40 K) and activation (between 70 and 145 K) mechanisms. Moreover, additional Ga’ and Ga’’ positions with anomalously low electric field gradient were revealed for the first time for IrIn3-type structure gallides, which stay almost unchanged, at least up to 77 K. The observed microscopic features are accompanied with in-gap states saturation or depleting, which is seen as the resistivity mechanism crossover at ∼180 K and electron localization below 145 K evidenced by pump-probe spectroscopy. Based on our experimental results, we associate this pseudo-gap like behavior with inhomogeneously distributed electronic density defects, which manifest at both micro- (nuclear spin and phonon dynamics) and macroscale (bulk transport properties such as resistivity).

Investigation of plasmon relaxation mechanisms using nonadiabatic molecular dynamics.

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au20 beyond the Born-Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ∼10.4fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process.

Many-body theory of phonon-induced spin relaxation and decoherence

First-principles calculations enable accurate predictions of electronic interactions and dynamics. However, computing the electron spin dynamics remains challenging. The spin-orbit interaction causes various dynamical phenomena that couple with phonons, such as spin precession and spin-flip e-ph scattering, which are difficult to describe with current first-principles calculations. In this work, we show a rigorous framework to study phonon-induced spin relaxation and decoherence, by computing the spin-spin correlation function and its vertex corrections due to e-ph interactions. We apply this approach to a model system and develop corresponding first-principles calculations of spin relaxation in GaAs. Our vertex-correction formalism is shown to capture the Elliott-Yafet, Dyakonov-Perel, and strong-precession mechanisms - three independent spin decoherence regimes with distinct physical origins - thereby unifying their theoretical treatment and calculation. Our method is general and enables quantitative studies of spin relaxation, decoherence, and transport in a wide range of materials and devices.

Finite-Size Effect in Phonon-Induced Elliott-Yafet Spin Relaxation in Al.

The Elliott-Yafet theory of spin relaxation in nonmagnetic metals predicts proportionality between spin and momentum relaxation times for scattering centers such as phonons. Here, we test this theory in Al nanowires over a very large thickness range (8.5-300nm), finding that the Elliott-Yafet proportionality "constant" for phonon scattering in fact exhibits a large, unanticipated finite-size effect. Supported by analytical and numerical modeling, we explain this via strong phonon-induced spin relaxation at surfaces and interfaces, driven in particular by enhanced spin-orbit coupling.

Photoluminescence of Cis-Polyacetylene Semiconductor Material

Photoluminescence (PL) is one of the key experimental characterizations of optoelectronic materials, including conjugated polymers (CPs). In this study, a simplified model of an undoped cis-polyacetylene (cis-PA) oligomer was selected and used to explain the mechanism of photoluminescence (PL) of the CPs. Using a combination of the ab initio electronic structure and a time-dependent density matrix methodology, the photo-induced time-dependent excited state dynamics were computed. We explored the phonon-induced relaxation of the photoexcited state for a single oligomer of cis-PA. Here, the dissipative Redfield equation of the motion was used to compute the dissipative excited state dynamics of electronic degrees of freedom. This equation used the nonadiabatic couplings as parameters. The computed excited state dynamics showed that the relaxation rate of the electron is faster than the relaxation rate of the hole. The dissipative excited-state dynamics were combined with radiative recombination channels to predict the PL spectrum. The simulated results showed that the absorption and emission spectra both have a similar transition. The main result is that the computed PL spectrum demonstrates two mechanisms of light emission originating from (i) the inter-band transitions, corresponding to the same range of transition energies as the absorption spectrum and (ii) intra-band transitions not available in the absorption spectra. However, the dissipative Redfield equation of the motion was used to compute the electronic degrees of freedom of the nonadiabatic couplings, which helped to process the time propagation of the excited dynamic state. This excited dynamic state shows that the relaxation rate of the electron is faster than the relaxation rate of the hole, which can be used for improving organic semiconductor materials for photovoltaic and LED applications.

Phonon-induced relaxation mechanisms are changed by a chelating effect in a CoII single-ion magnet.

It is well known that phonon-induced relaxation processes play a significant role in accelerating magnetization relaxation in the low-temperature regime. Unfortunately, many SIMs (single-ion magnets) suffer from being quenched by these mechanisms such that neither out-of-phase signals nor magnetization hysteresis can be readily observed. Nevertheless, because it involves molecular motions at low-frequency (low-energy) levels, methods for synthetically controlling this factor have not yet been addressed by chemists. In this study, we prepared a series of three compounds in which one contains a rigid chelating ligand, and the other two contain analogous ligands that can coordinate more liberally. To our surprise, compound 1, with a rigid chelating ligand, displayed promising SIM behavior with out-of-phase signals up to 11 K in a zero d.c. magnetic field at an a.c. frequency of 1000 Hz. The other two (2 and 3) with dangling ligands failed to show significant out-of-phase signals until an extra d.c. field was applied. The results of magnetization relaxation studies suggest that the phonon-induced relaxation processes play an essential role in 2 and 3, even at very low temperatures. Nevertheless, the rigid chelating ligand in 1 prevents the molecule from being involved in phonon-induced relaxation processes that seriously interfere with the magnetization relaxation up to 5.6 K. Therefore, we concluded that the presence of a rigid chelating ligand can efficiently change the phonon-induced relaxation processes at low temperatures.

From carriers and virtual excitons to exciton populations: Insights into time-resolved ARPES spectra from an exactly solvable model

We calculate the {\em exact} time-resolved ARPES spectrum of a two-band model semiconductor driven out of equilibrium by resonant and nonresonant laser pulses, highlighting the effects of phonon-induced decoherence and relaxation. {\em Resonant} excitations initially yield a replica of the {\em valence} band shifted upward by the energy of the exciton peak in photoabsorption. This phase is eventually destroyed by phonon-induced decoherence: the valence-band replica lowers in energy by the Stokes shift, locating at the energy of the exciton peak in photoluminescence, and its width grows due to phonon dressing. {\em Nonresonant} excitations initially yield a map of the conduction band. Then electrons transfer their excess energy to the lattice and bind with the holes left behind to form excitons. In this relaxed regime a replica of the {\em conduction} band appears inside the gap. At fixed momentum the lineshape of the conduction-band replica versus the photoelectron energy is proportional to the exciton wavefunction in "energy space" and it is highly asymmetric. Although the two-band model represents an oversimplified description of real materials the highlighted features are qualitative in nature; hence they provide useful insights into time-resolved ARPES spectra and their physical interpretation.

Exciton-exciton interaction and cascade relaxation of excitons in colloidal CdSe nanoplatelets

The exciton-exciton interaction and phonon-induced cascade relaxation of free electrons and holes determine the dynamic of stationary resonantly excited excitons in CdSe/CdS nanoplatelets. Along with saturation of the heavy-hole and light-hole exciton transitions explained by the phase space filling effect the exciton-exciton interaction increases and starts to play a significant role in excitons dynamic. The lowest four band structure of CdSe/CdS nanoplatelets at the Γ point of Brillouin zone and its modification with CdS shell thickness changing are experimentally investigated for the first time. Bleaching of the two additional to the heavy- and light-hole exciton transitions with the energies higher than the absorbed photons energy can occur at room temperature due to rapid cascade relaxation of free electrons and holes formed as a result of the exciton-exciton interaction. To analyze the recombination and interaction of excitons in the colloidal nanoplatelets under high excitation densities the rate equations describing the exciton-exciton and exciton-electron interactions are applied.

Effect of phonons on the electron spin resonance absorption spectrum

The unavoidable presence of vibrations in solid-state devices can drastically modify the expected electron spin resonance (ESR) absorption spectrum in magnetically active systems. In this work, we model the effect of phonons and temperature on the ESR signal in molecular systems with strong E ⊗ e Jahn–Teller (JT) effect and an electronic spin-1/2. Our microscopic model considers the linear JT interaction with a continuum of phonon modes, the spin–orbit coupling, the Zeeman effect, and the response of the system under a weak oscillating magnetic field. We derive a Lindblad master equation for the orbital and spin degrees of freedom, where one- and two-phonon processes are considered for the phonon-induced relaxation, and the thermal dependence of Ham reduction factors is calculated. We find that the suppression of ESR signals is due to phonon broadening but not based on the common assumption of orbital quenching. Our results can be applied to explain the experimentally observed absence of the ESR signal in color centers in diamond, such as the neutral nitrogen-vacancy and negatively charged silicon-vacancy color centers in diamond.

Phonon-induced electronic relaxation in a strongly correlated system: The Sn/Si(111) (3×3) adlayer revisited

The ordered adsorbate layer Sn/Si(111) ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$) with coverage of one third of a monolayer is considered as a realization of strong electronic correlation in surface physics. Our theoretical analysis shows that electron-hole pair excitations in this system can be long lived, up to several hundred nanoseconds, since the decay into surface phonons is found to be a highly nonlinear process. We combine first-principles calculations with help of a hybrid functional (HSE06) with modeling by a Mott-Hubbard Hamiltonian coupled to phononic degrees of freedom. The calculations show that the Sn/Si(111) ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$) surface is insulating and the two Sn-derived bands inside the substrate band gap can be described as the lower and upper Hubbard band in a Mott-Hubbard model with $U=0.75$ eV. Furthermore, phonon spectra are calculated with particular emphasis on the Sn-related surface phonon modes. The calculations demonstrate that the adequate treatment of electronic correlations leads to a stiffening of the wagging mode of neighboring Sn atoms; thus, we predict that the onset of electronic correlations at low temperature should be observable in the phonon spectrum, too. The deformation potential for electron-phonon coupling is calculated for selected vibrational modes and the decay rate of an electron-hole excitation into multiple phonons is estimated, substantiating the very long lifetime of these excitations.

Phonon-induced relaxation and decoherence times of the hybrid qubit in silicon quantum dots

We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. Hybrid qubit behaves as a charge qubit when the detuning is close to zero and as spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e. the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.

Electron spin relaxation of single phosphorus donors in metal-oxide-semiconductor nanoscale devices

We analyze the electron spin relaxation rate $1/T_1$ of individual ion-implanted $^{31}$P donors, in a large set of metal-oxide-semiconductor (MOS) silicon nanoscale devices, with the aim of identifying spin relaxation mechanisms peculiar to the environment of the spins. The measurements are conducted at low temperatures ($T\approx 100$~mK), as a function of external magnetic field $B_0$ and donor electrochemical potential $\mu_{\rm D}$. We observe a magnetic field dependence of the form $1/T_1\propto B_0^5$ for $B_0\gtrsim 3\,$ T, corresponding to the phonon-induced relaxation typical of donors in the bulk. However, the relaxation rate varies by up to two orders of magnitude between different devices. We attribute these differences to variations in lattice strain at the location of the donor. For $B_0\lesssim 3\,$T, the relaxation rate changes to $1/T_1\propto B_0$ for two devices. This is consistent with relaxation induced by evanescent-wave Johnson noise created by the metal structures fabricated above the donors. At such low fields, where $T_1>1\,$s, we also observe and quantify the spurious increase of $1/T_1$ when the electrochemical potential of the spin excited state $|\uparrow\rangle$ comes in proximity to empty states in the charge reservoir, leading to spin-dependent tunneling that resets the spin to $|\downarrow\rangle$. These results give precious insights into the microscopic phenomena that affect spin relaxation in MOS nanoscale devices, and provide strategies for engineering spin qubits with improved spin lifetimes.

Phonon-induced Majorana qubit relaxation in tunnel-coupled two-island topological superconductors

A Majorana-based qubit can form within the fermion parity subspace of a two-island topological superconductor setup consisting of four Majorana zero modes. We study the relaxation time of this Majorana qubit induced by the intrinsic Majorana-phonon interaction in combination with single electron tunneling between the two islands. The theory is developed for both the spinless p-wave Kitaev chain model and the spin-orbit-coupled semiconductor nanowire with induced superconductivity and Zeeman splitting. We systematically discuss the dependence of the relaxation rate on Majorana charge distribution (varying with the chemical potential, magnetic field, superconducting paring, spin-orbit coupling and island length) as well as on phonon wavelength and the length of the tunnel barrier. Importantly, the accompanied phonon energy can be tuned by the voltage bias over the tunnel barrier, leading to relatively easy manipulation and suppression of the relaxation rate.

Spin-relaxation anisotropy in a nanowire quantum dot with strong spin-orbit coupling

We study the impacts of the magnetic field direction on the spin-manipulation and the spin-relaxation in a one-dimensional quantum dot with strong spin-orbit coupling. The energy spectrum and the corresponding eigenfunctions in the quantum dot are obtained exactly. We find that no matter how large the spin-orbit coupling is, the electric-dipole spin transition rate as a function of the magnetic field direction always has a π periodicity. However, the phonon-induced spin relaxation rate as a function of the magnetic field direction has a π periodicity only in the weak spin-orbit coupling regime, and the periodicity is prolonged to 2π in the strong spin-orbit coupling regime.

Exciton Relaxation Cascade in two-dimensional Transition Metal Dichalcogenides

Monolayers of transition metal dichalcogenides (TMDs) are characterized by an extraordinarily strong Coulomb interaction giving rise to tightly bound excitons with binding energies of hundreds of meV. Excitons dominate the optical response as well as the ultrafast dynamics in TMDs. As a result, a microscopic understanding of exciton dynamics is the key for a technological application of these materials. In spite of this immense importance, elementary processes guiding the formation and relaxation of excitons after optical excitation of an electron-hole plasma has remained unexplored to a large extent. Here, we provide a fully quantum mechanical description of momentum- and energy-resolved exciton dynamics in monolayer molybdenum diselenide (MoSe2) including optical excitation, formation of excitons, radiative recombination as well as phonon-induced cascade-like relaxation down to the excitonic ground state. Based on the gained insights, we reveal experimentally measurable features in pump-probe spectra providing evidence for the exciton relaxation cascade.

Phonon-assisted relaxation and decoherence of singlet-triplet qubits in Si/SiGe quantum dots

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.

Modeling Plasmon-Induced Hot-Carrier Transfer

In this issue of Chem , Zhang et al. use first-principle simulations (i.e., no empirically adjustable parameters) to elucidate the detailed mechanisms of plasmon-induced hot-carrier transfer at a heterojunction interface between a plasmonic gold nanomaterial and a semiconductor. Together with earlier work by Long and Prezhdo, this study shows how the donor-acceptor interaction at the interface determines the mechanism by which plasmonic excitations lead to hot-electron transfer at interfaces.