Deformation Potential Coupling Research Articles

Spin-flip relaxation via optical phonon scattering in quantum dots

Based on the spin-orbit coupling admixture mechanism, we theoretically investigate the spin-flip relaxation via optical phonon scattering in quantum dots by considering the effect of lattice relaxation due to the electron-acoustic phonon deformation potential coupling. The relaxation rate displays a cusp-like structure (or a spin hot spot) that becomes more clearly with increasing temperature. We also calculate the relaxation rate of the spin-conserving process, which follows a Gaussian form and is several orders of magnitude larger than that of spin-flip process. Moreover, we find that the relaxation rate displays the oscillatory behavior due to the interplay effects between the magnetic and spatial confinement for the spin-flip process not for the spin-conserving process. The trends of increasing and decreasing temperature dependence of the relaxation rates for two relaxation processes are obtained in the present model.

Spin-flip phonon-mediated charge relaxation in double quantum dots

We theoretically study the $(1,1)$ triplet to $(0,2)$ singlet relaxation rate in a lateral gate-defined double quantum dot tuned to the regime of Pauli spin blockade. We present a detailed derivation of the effective phonon density of states for this specific charge transition, keeping track of the contribution from piezoelectric as well as deformation potential electron-phonon coupling. We further investigate two different spin-mixing mechanisms which can couple the triplet and singlet states: a magnetic field gradient over the double dot (relevant at low external magnetic field) and spin-orbit interaction (relevant at high field), and we also indicate how the two processes could interfere at intermediate magnetic field. Finally, we show how to combine all results and evaluate the relaxation rate for realistic system parameters.

Structural, electronic, and magnetic behavior of two dimensional epitaxial Fe3O4/TiN/Si(100) system

Epitaxial Fe3O4 thin films are deposited at 400, 500, 600 °C on TiN buffered Si(100) using reactive magnetron sputtering. In-situ reflection high energy electron diffraction confirmed the growth to be two-dimensional (2-D) at 500–600 °C and X-ray reflectivity revealed a sharp interface (∼0.4 nm). Growth temperature effect on structural, electronic, and magnetic behavior was probed by X-ray diffraction, Raman, and magnetization studies. Small value of deformation potential (0.19 eV/Å) and electron phonon coupling constant (0.71), sharp Verwey transition with large jump at 119 K in magnetization during field cooled warming and early saturation at 2.5 kOe affirmed the superior magnetic quality of epitaxial Fe3O4 samples.

Finite temperature inelastic mean free path and quasiparticle lifetime in graphene

We adopt the GW approximation and random phase approximation to study finite temperature effects on the inelastic mean free path and quasiparticle lifetime by directly calculating the imaginary part of the finite temperature self-energy induced by electron-electron interaction in extrinsic and intrinsic graphene. In particular, we provide the density-dependent leading order temperature correction to the inelastic scattering rate for both single-layer and double-layer graphene systems. We find that the inelastic mean free path is strongly influenced by finite-temperature effects. We present the similarity and the difference between graphene with linear chiral band dispersion and conventional two dimensional electron systems with parabolic band dispersion. We also compare the calculated finite temperature inelastic scattering length with the elastic scattering length due to Coulomb disorder, and comment on the prospects for quantum interference effects showing up in low density graphene transport. We also carry out inelastic scattering calculation for electron-phonon interaction, which by itself gives rather long carrier mean free paths and lifetimes since the deformation potential coupling is weak in graphene, and therefore electron-phonon interaction contributes significantly to the inelastic scattering only at relatively high temperatures.

Electron-phonon mediated heat flow in disordered graphene

We calculate the heat flux and electron-phonon thermal conductance in a disordered graphene sheet, going beyond a Fermi's golden rule approach to fully account for the modification of the electron-phonon interaction by disorder. Using the Keldysh technique combined with standard impurity averaging methods in the regime ${k}_{F}l\ensuremath{\gg}1$ (where ${k}_{F}$ is the Fermi wave vector and $l$ is the mean free path), we consider both scalar potential (i.e., deformation potential) and vector-potential couplings between electrons and phonons. We also consider the effects of electronic screening at the Thomas-Fermi level. We find that the temperature dependence of the heat flux and thermal conductance is sensitive to the presence of disorder and screening, and reflects the underlying chiral nature of electrons in graphene and the corresponding modification of their diffusive behavior. In the case of weak screening, disorder enhances the low-temperature heat flux over the clean system (changing the associated power law from ${T}^{4}$ to ${T}^{3}$), and the deformation potential dominates. For strong screening, both the deformation potential and vector-potential couplings make comparable contributions, and the low-temperature heat flux obeys a ${T}^{5}$ power law.

Conductivity of twin-domain-wall/surface junctions in ferroelastics: Interplay of deformation potential, octahedral rotations, improper ferroelectricity, and flexoelectric coupling

Electronic and structural phenomena at the twin domain wall-surface junctions in the ferroelastic materials are analyzed. Carriers accumulation caused by the strain-induced band structure changes originated via the deformation potential mechanism, structural order parameter gradient, rotostriction and flexoelectric coupling is explored. Approximate analytical results show that inhomogeneous elastic strains, which exist in the vicinity of the twin walls - surface junctions due to the rotostriction coupling, decrease the local band gap via the deformation potential and flexoelectric coupling mechanisms. This is the direct mechanism of the twin walls static conductivity in ferroelastics and, by extension, in multiferroics and ferroelectrics. On the other hand, flexoelectric and rotostriction coupling leads to the appearance of the improper polarization and electric fields proportional to the structural order parameter gradient in the vicinity of the twin walls - surface junctions. The "flexo-roto" fields leading to the carrier accumulation are considered as indirect mechanism of the twin walls conductivity. Comparison of the direct and indirect mechanisms illustrates complex range of phenomena directly responsible for domain walls static conductivity in materials with multiple order parameters.

Energy relaxation for hot Dirac fermions in graphene and breakdown of the quantum Hall effect

Energy loss rates for hot carriers in graphene are experimentally investigated by observing the amplitude of Shubnikov-de Haas oscillations as a function of electric field. The carrier energy loss in graphene follows the predictions of deformation potential coupling going as $\ensuremath{\sim}$T${}^{4}$ at carrier temperatures up to $\ensuremath{\sim}$100 K, and that deformation potential theory, when modified with a limiting phonon relaxation time, is valid up to several hundred Kelvin. Additionally we investigate the breakdown of the quantum Hall effect and show that energy loss rates in graphene are around ten times larger than GaAs at low temperatures. This leads to significantly higher breakdown currents per micrometer, and we report a measured breakdown current of 8 $\ensuremath{\mu}$A/$\ensuremath{\mu}$m.

Hot electron energy relaxation in a semiconducting armchair graphene nanoribbon

We calculate the hot electron energy relaxation P due to acoustic–phonon scattering via deformation potential coupling in an armchair graphene nanoribbon (AGNR). Its dependence on electron temperature Te, Fermi energy Ef (linear electron concentration nl) and width W of AGNR is investigated. At low Te, P is found to be exponentially suppressed contrary to the power laws in graphene and conventional semiconductor nanostructures. This gradually changes to sublinear behavior for an about Te>100K contrary to conventional P∼Te. P shows strong dependence on Ef and nl and it decreases with the increasing Ef and nl at low Te. At a constant nl, P varies approximately as W−s with s∼2–3. A weak dependence of s on Te and nl is observed. We point out that the low Te study of P, as it is independent of all non-acoustic phonon scattering mechanisms, could be used to determine the accurate value of acoustic–phonon deformation potential coupling constant in graphene about which there is still uncertainty.

Picosecond strain pulses probed by the photocurrent in semiconductor devices with quantum wells

Ultrafast acoustic wave packets are detected by probing the photocurrent in semiconductor devices containing quantum wells. The strain pulses were generated by thermalization of a femtosecond laser pulse in a thin metal film deposited on the surface of the GaAs substrate opposite to the semiconductor device. The probing was realized by measuring the photocurrent excited by a femtosecond optical pulse with photon energy close to the excitonic resonance of the quantum well. Two types of devices are used: a reverse biased (AlGa)As p-i-n tunneling diode containing a GaAs quantum well in its intrinsic region and a planar device containing an (InGa)As quantum well. The change in photocurrent arises from the strain-induced shift of the quantum well excitonic resonance due to deformation potential electron-phonon coupling. The method has a picosecond temporal resolution, shows a high sensitivity to subterahertz acoustic wave packets and has potential for ultrafast control of electrical conductance in semiconductor devices.

Two-phonon processes of intraband relaxation in the terahertz regime in quantumdots

We theoretically investigate the intraband relaxation of quantum dots in the terahertzregime due to two acoustic phonon scattering by applying a lattice relaxationapproach based on the deformation potential coupling between electrons andacoustic phonons. In particular, we find that the relaxation time depends stronglyon the ratio of two acoustic phonons. The influences of the energy separationbetween the ground and first excited state, the quantum dot height, and the latticetemperature on the relaxation time are also discussed. Our theoretical results not onlygive a reasonable explanation for the current experimental measurement but alsoprovide some insight into two-phonon intraband relaxation in quantum dots.

Singlet–triplet relaxation induced by confined phonons in nanowire-based quantum dots

The singlet–triplet relaxation in nanowire-based quantum dots induced by confined phonons is investigated theoretically. Due to the quasi-one-dimensional nature of the confined phonons, the singlet–triplet relaxation rates exhibit multi-peaks as a function of magnetic field, and the relaxation rate between the singlet and the spin-up triplet state is found to be enhanced in the vicinity of the singlet–triplet anti-crossing. We compare the effect of the deformation-potential coupling and the piezoelectric coupling and find that the deformation-potential coupling dominates the relaxation rates in most cases.

Temperature-dependent resistivity of suspended graphene

In this paper we investigate the electron-phonon contribution to the resistivity of suspended single-layer graphene. In-plane as well as flexural phonons are addressed in different temperature regimes. We focus on the intrinsic electron-phonon coupling due to the interaction of electrons with elastic deformations in the graphene membrane. The competition between screened deformation potential vs fictitious gauge-field coupling is discussed together with the role of tension in the suspended flake. In the absence of tension, flexural phonons dominate the phonon contribution to the resistivity at any temperature $T$ with a ${T}^{5/2}$ and ${T}^{2}$ dependence at low and high temperatures, respectively. Sample-specific tension suppresses the contribution due to flexural phonons, yielding a linear temperature dependence due to in-plane modes. We compare our results with recent experiments.

Enhancement of phonon-drag thermopower in bilayer graphene

Phonon-drag thermopower ${S}^{\text{g}}$ is theoretically studied in a bilayer graphene (BLG). Two-dimensional (2D) electrons with chiral property, finite effective mass, and parabolic dispersion are assumed to interact with the 2D acoustic phonons having a linear dispersion via deformation-potential coupling. A comparison is made with the very recent experimental results of Nam et al. [arXiv:1005.4739 (unpublished)] for $30\ensuremath{\le}T\ensuremath{\le}70\text{ }\text{K}$. Numerically ${S}^{\text{g}}$ is studied as a function of temperature $T$, electron concentration ${n}_{\text{s}}$, and phonon mean-free path. ${T}^{3}$ behavior of ${S}^{\text{g}}$ at very low $T$ changes gradually to sublinear at higher $T$ and the effect of chiral property of the electrons is seen explicitly. We suggest the possibility of significant enhancement of ${S}^{\text{g}}$ at lower carrier concentrations by increasing the linear dimension of the sample and reducing its edge roughness. We find that ${S}^{\text{g}}$ in BLG is enhanced by a factor of 7 compared with the magnitude of ${S}^{\text{g}}$ in monolayer graphene, for ${n}_{\text{s}}=0.5\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }{\text{cm}}^{\ensuremath{-}2}$ in the Bloch-Gr\uneisen (BG) regime. In BG regime ${S}^{\text{g}}\ensuremath{\sim}{T}^{3}$, a manifestation of 2D phonons with linear dispersion and ${S}^{\text{g}}\ensuremath{\sim}{n}_{\text{s}}^{\ensuremath{-}3/2}$, a characteristic of 2D electrons with parabolic dispersion. A comparison is also made with the results in conventional and ideal 2D systems. ${S}^{\text{g}}$ is found to be very significant in comparison with the diffusion thermopower ${S}^{\text{d}}$ and the latter is shown to be $\ensuremath{\sim}T$, ${n}_{\text{s}}^{\ensuremath{-}1}$ at low $T$ and high ${n}_{\text{s}}$. Herring's law, ${S}^{\text{g}}{\ensuremath{\mu}}_{\text{p}}\ensuremath{\sim}{T}^{\ensuremath{-}1}$, relating phonon-limited mobility ${\ensuremath{\mu}}_{\text{p}}$ to ${S}^{\text{g}}$, is found to be valid in BLG.

Phonon-mediated relaxation in doped quantum dot molecules

We study a single quantum dot molecule doped with one electron in the presence of electron-phonon coupling. Both diagonal and off-diagonal interactions representing real and virtual processes with acoustic phonons via deformation potential and piezoelectric coupling are taken into account. We employ a non-perturbative quantum kinetic theory and show that the phonon-mediated relaxation is dominated by an electron tunneling on a picosecond time scale. A dependence of the relaxation on the temperature and the strength of the tunneling coupling is analyzed.

Power loss by a two-dimensional hole gas in a Si/Si0.8Ge0.2 heterostructure over a wide temperature range

The average power loss of two-dimensional hole gas (2DHG) due to acoustic and optical phonons is calculated in a Si/Si0.8Ge0.2 heterostructure over a wide temperature range. The power loss of 2DHG due to acoustic phonons via deformation potential coupling and Pekar mechanism is calculated taking account of temperature dependent screening. The hole-acoustic phonon coupling is found to dominate hole power loss for Tc<70 K. The experimental power loss data for Tc<2 K is accounted for by Pekar mechanism and the data for 2 K<Tc<4.2 K is explained by the total contribution of these two mechanisms. Pekar mechanism is found to be important in these systems at very low Tc. Power loss calculation due to nonpolar optical phonons is carried out taking account of hot phonon effect and it is important and dominant for Tc>70 K. Hot phonon effect is found to reduce the power loss of 2DHG by a factor of about 1.5. The power loss calculations are carried out for different carrier concentrations and compared with those in GaAlAs/GaAs heterostructures.

Spin relaxation due to deflection coupling in nanotube quantum dots

We consider relaxation of a single-electron spin in a nanotube quantum dot due to its coupling to flexural phonon modes, and identify a new spin-orbit-mediated coupling between the nanotube deflection and the electron spin. This mechanism dominates other spin-relaxation mechanisms in the limit of small energy transfers. Due to the quadratic dispersion law of long-wavelength flexons, $\ensuremath{\omega}\ensuremath{\propto}{q}^{2}$, the density of states $dq/d\ensuremath{\omega}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1/2}$ diverges as $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Furthermore, because here the spin couples directly to the nanotube deflection, there is an additional enhancement by a factor of $1/q$ compared to the deformation-potential coupling mechanism. We show that the deflection coupling robustly gives rise to a minimum in the magnetic field dependence of the spin lifetime ${T}_{1}$ near an avoided crossing between spin-orbit split levels in both the high- and low-temperature limits. This provides a mechanism that supports the identification of the observed ${T}_{1}$ minimum with an avoided crossing in the single-particle spectrum by Churchill et al. [Phys. Rev. Lett. 102, 166802 (2009)].

Theory of phonon-mediated relaxation in doped quantum dot molecules

A quantum dot molecule doped with a single electron in the presence of diagonal and off-diagonal carrier-phonon couplings is studied by means of a nonperturbative quantum kinetic theory. The interaction with acoustic phonons by deformation potential and piezoelectric coupling is taken into account. We show that the phonon-mediated relaxation is fast on a picosecond time scale and is dominated by the usually neglected off-diagonal coupling to the lattice degrees of freedom leading to phonon-assisted electron tunneling. We show that in the parameter regime of current electrical and optical experiments, the microscopic non-Markovian theory has to be employed.

Optically pumping hole spins in coupled quantum dot molecules into a steady state of high concurrence entanglement

We present a way to prepare a high concurrence steady state entanglement of two hole spins in a quantum dot molecule. We show that the spontaneous dissipation can be used to induce and stabilize the entanglement with rapid rate. By optical pumping of trion levels, two-qubit singlet state can be automatically generated. We also show that our proposal can synchronously accomplish both initialization and entanglement generation. The effects of acoustic phonons and electron tunneling are also discussed and we find that the main influence is from deformation potential coupling to acoustic phonons in InAs/GaAs quantum dots. At low temperature, we show that concurrence of entanglement can be greater than 0.95 at $T=1\text{ }\text{K}$.

Singlet-Triplet Dephasing in Asymmetric Quantum Dot Molecules

Dephasing of singlet-triplet superpositions in twoelectron quantum dot molecules is important for a possible implementation of quantum information processing in semiconductor systems [1]. In a recent work [2], we showed that elastic phonon scattering via virtual transitions to doubly occupied states, which is only possible in a singlet configuration, induces distinguishability of spin configurations and, therefore, leads to pure dephasing of spin superpositions. In Ref. [2], we studied a system of two identical dots. However, as quantum dots are artificial systems, one has to take into account unavoidable inhomogeneity of dot parameters when modeling the properties of the system. Therefore, in the present contribution, we generalize our previous result and study the phonon-induced dephasing process in an asymmetric QDM. We show that in the asymmetric QDM, an additional dephasing channel appears, as compared to the symmetric one. Nonetheless, the dephasing rate is very weakly affected by the asymmetry unless the latter becomes very strong. The system under consideration is composed of two electrons in an asymmetric quantum dot molecule (QDM) built from two different gate-defined quantum dots [3, 4]. The electrons are coupled to phonons by the usual charge-phonon interactions (deformation potential and piezoelectric couplings). We do not take any spin-environment interactions into account (neither direct, with nuclear spins, nor indirect, via spin-orbit coupling). The Hamiltonian of the system is then

Electron Spin Relaxation Due to Phonon Modulation of the Rashba Interaction in Quantum Dots

In this work we calculate the spin-flip transition rates, considering the phonon modulation of the spin–orbit interaction. For this purpose will use the spin–phonon interaction Hamiltonian proposed by Pavlov and Firsov. We compare the contributions of the electron–phonon deformation potential (DP) and piezoelectric (PE) coupling to the spin relaxation. We reveal the importance of an appropriate description of the electron Lande g-factor in the calculation of the rates. Our results demonstrate that, for narrow-gap materials, the DP interaction becomes the dominant one. This behavior is not observed in wide or intermediate gap semiconductors, where the PE coupling, in general, governs the relaxation processes.