Averages of static electric and magnetic fields over a spherical region: a derivation based on the mean-value theorem
Submitted to "Notes and Discussions" in American Journal of Physics.
physics.ed-ph↗
arXiv subjects
Ben Yu-Kuang Hu
Publications and source records attributed to Ben Yu-Kuang Hu.
Theory of Transmission through disordered superlattices
We derive a theory for transmission through disordered finite superlattices in which the interface roughness scattering is treated by disorder averaging. This procedure permits efficient calculation of the transmission thr ough samples with large cross-sections. These calculations can be performed utilizing either the Keldysh or the Landauer-Büttiker transmission formalisms, both of which yield identical equations. For energies close to the lowest miniband, we demonstrate the accuracy of the computationally efficient Wannier-function approximation. Our calculations indicate that the transmission is strongly affected by interface roughness and that information about scale and size of the imperfections can be obtained from transmission data.
cond-mat.mes-hall↗
Prospecting for the superfluid transition in electron-hole coupled quantum wells using Coulomb drag
I investigate the possibility of using Coulomb drag to detect a precursor of the predicted (but as yet not definitively observed) superfluid transition in electron-hole coupled quantum wells. The drag transresisitivity $ρ_{21}$ is shown to be significantly enhanced above the transition temperature $T_c$ and to diverge logarithmically as $T\to T_c^+$, due to electron-hole pairing fluctuations which are somewhat analogous to the Maki-Thompson contribution to conductivity in metals above the superconducting $T_c$. The enhancement in $ρ_{21}$ is estimated to be detectable at temperatures much higher than $T_c$.
cond-mat.mes-hall↗
First principles theory of inelastic currents in a scanning tunneling microscope
A first principles theory of inelastic tunneling between a model probe tip and an atom adsorbed on a surface is presented, extending the elastic tunneling theory of Tersoff and Hamann. The inelastic current is proportional to the change in the local density of states at the center of the tip due to the addition of the adsorbate. We use the theory to investigate the vibrational heating of an adsorbate below an STM tip. We calculate the desorption rate of H from Si(100)-H(2$\times$1) as function of the sample bias and tunnel current, and find excellent agreement with recent experimental data.
cond-mat.mtrl-sci↗
STM induced hydrogen desorption via a hole resonance
We report STM-induced desorption of H from Si(100)-H(2$\times1$) at negative sample bias. The desorption rate exhibits a power-law dependence on current and a maximum desorption rate at -7 V. The desorption is explained by vibrational heating of H due to inelastic scattering of tunneling holes with the Si-H 5$σ$ hole resonance. The dependence of desorption rate on current and bias is analyzed using a novel approach for calculating inelastic scattering, which includes the effect of the electric field between tip and sample. We show that the maximum desorption rate at -7 V is due to a maximum fraction of inelastically scattered electrons at the onset of the field emission regime.
cond-mat.mtrl-sci↗
Optical phonon induced frictional drag in coupled two-dimensional electron gases
The role of optical-phonons in frictional drag between two adjacent but electrically isolated two-dimensional electron gases is investigated. Since the optical-phonons in III-V materials have a considerably larger coupling to electrons than acoustic phonons (which are the dominant drag mechanism at low T and large separations) it might be expected that the optical phonons will give a large effect high temperatures. The two key differences between optical and acoustic phonon mediated drag are: (1) the optical phonon mediated interlayer interaction is short-ranged due to their negligible group velocity at the Brillouin zone center; and (2) the typical momentum transfer for an optical phonon mediated scattering is relatively large. These considerations make optical phonon mediated drag difficult to see in single subband GaAs systems, but it may be possible to see the effect in double subband GaAs systems or single subband quantum wells in a material with a lower effective mass and lower optical phonon energy such as InSb.
cond-mat.mes-hall↗
Frictional drag between quantum wells mediated by phonon exchange
We use the Kubo formalism to evaluate the contribution of acoustic phonon exchange to the frictional drag between nearby two-dimensional electron systems. In the case of free phonons, we find a divergent drag rate ($τ_{D}^{-1}$). However, $τ_{D}^{-1}$ becomes finite when phonon scattering from either lattice imperfections or electronic excitations is accounted for. In the case of GaAs quantum wells, we find that for a phonon mean free path $\ell_{ph}$ smaller than a critical value, imperfection scattering dominates and the drag rate varies as $ln (\ell_{ph}/d)$ over many orders of magnitude of the layer separation $d$. When $\ell_{ph}$ exceeds the critical value, the drag rate is dominated by coupling through an electron-phonon collective mode localized in the vicinity of the electron layers. We argue that the coupled electron-phonon mode may be observable for realistic parameters. Our theory is in good agreement with experimental results for the temperature, density, and $d$-dependence of the drag rate.
cond-mat↗
Correlation Effects on the Coupled Plasmon Modes of a Double Quantum Well
At temperatures comparable to the Fermi temperature, we have measured a plasmon enhanced Coulomb drag in a GaAs/AlGaAs double quantum well electron system. This measurement provides a probe of the many-body corrections to the coupled plasmon modes, and we present a detailed comparison between experiment and theory testing the validity of local field theories. Using a perpendicular magnetic field to raise the magnetoplasmon energy we can induce a crossover to single-particle Coulomb scattering.
cond-mat.mes-hall↗
Can Hall drag be observed in Coulomb coupled quantum wells in a magnetic field?
We study the transresistivity $\tensorρ_{21}$ (or equivalently, the drag rate) of two Coulomb-coupled quantum wells in the presence of a perpendicular magnetic field, using semi-classical transport theory. Elementary arguments seem to preclude any possibility of observation of ``Hall drag'' (i.e., a non-zero off-diagonal component in $\tensorρ_{21}$). We show that these arguments are specious, and in fact Hall drag can be observed at sufficiently high temperatures when the {\sl intra}layer transport time $τ$ has significant energy-dependence around the Fermi energy $\varepsilon_F$. The ratio of the Hall to longitudinal transresistivities goes as $T^2 B s$, where $T$ is the temperature, $B$ is the magnetic field, and $s = [\partialτ/ \partial\varepsilon] (\varepsilon_F)$.
cond-mat↗
Quasiparticle properties of a coupled quantum wire electron-phonon system
We study leading-order many-body effects of longitudinal optical (LO) phonons on electronic properties of one-dimensional quantum wire systems. We calculate the quasiparticle properties of a weakly polar one dimensional electron gas in the presence of both electron-phonon and electron-electron interactions. The leading-order dynamical screening approximation (GW approximation) is used to obtain the electron self-energy, the quasiparticle spectral function, and the quasiparticle damping rate in our calculation by treating electrons and phonons on an equal footing. Our theory includes effects (within the random phase approximation) of Fermi statistics, Landau damping, plasmon-phonon mode coupling, phonon renormalization, dynamical screening, and impurity scattering. In general, electron-electron and electron-phonon many-body renormalization effects are found to be nonmultiplicative and nonadditive in our theoretical results for quasiparticle properties.
cond-mat↗
Electron--electron scattering in linear transport in two-dimensional systems
We describe a method for numerically incorporating electron--electron scattering in quantum wells for small deviations of the distribution function from equilibrium, within the framework of the Boltzmann equation. For a given temperature $T$ and density $n$, a symmetric matrix needs to be evaluated only once, and henceforth it can be used to describe electron--electron scattering in any Boltzmann equation linear-response calculation for that particular $T$ and $n$. Using this method, we calculate the distribution function and mobility for electrons in a quantum-well, including full finite-temperature dynamic screening effects. We find that at some parameters which we investigated, electron--electron scattering reduces mobility by approximately 40\%.
cond-mat↗
Plasmon enhancement of Coulomb drag in double quantum well systems
We derive an expression for the drag rate (i.e., interlayer momentum transfer rate) for carriers in two coupled two-dimensional gases to lowest nonvanishing order in the screened interlayer electron--electron interaction, valid for {\sl arbitrary} intralayer scattering mechanisms, using the Boltzmann transport equation. We calculate the drag rate for experimentally relevant parameters, and show that for moderately high temperatures ($T\gtrsim 0.2 T_F$, where $T_F$ is the Fermi temperature) the dynamical screening of the interlayer results in a large enhancement of the drag rate due to the presence of coupled plasmon modes. This plasmon enhancement causes the scaled drag rate to have a peak (i) as a function of temperature at $T \approx 0.5 T_F$, and (ii) as a function of the ratio of densities of the carriers in the two layers when their Fermi velocities are equal. We also show that the drag rate can be significantly affected by the {\sl intralayer} scattering mechanisms; in particular, the drag rate changes approximately by a factor of 2 when the dopant layer modulation doped structures are moved in from 400~Åto 100~Å.
cond-mat↗
Linear response theory of Coulomb drag in coupled electron systems
We report a fully microscopic theory for transconductivity, or, equivalently, momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear response formalism, and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which are topologically related, but not equivalent to, the Aslamazov-Larkin diagrams known for superconductivity. Previously reported results are shown to be special cases of our general expression; specifically, for constant impurity scattering rates, we recover the Boltzmann equation results in the semiclassical clean limit, and the memory function results in dirty systems. Furthermore, we show that for energy dependent relaxation times, the final result is not expressible in terms of standard density-response functions. Other new results include: (i) at T=0, the frequency dependence of the transfer rate is found to be proportional to $Ω$ and $Ω^2$ for frequencies below and above the impurity scattering rate, respectively and (ii) the weak localization correction to the transconductivity is given by $δσ^{WL}_{21} \propto δσ^{WL}_{11} +δσ^{WL}_{22}$.
cond-mat↗
Coulomb Drag as a Probe of Coupled Plasmon Modes in Parallel Quantum Wells
We show theoretically that the Coulomb drag rate between two parallel quasi-two-dimensional electron gases is substantially enhanced by the coupled acoustic and optic plasmon modes of the system at temperatures $T \gtrsim 0.2T_F$ (where $T_F$ is the Fermi temperature) for experimentally relevant parameters. The acoustic mode causes a sharp upturn in the scaled drag rate as a function of temperature at $T \approx 0.2 T_F$. Other experimental signatures of plasmon-dominated drag are a $d^{-3}$ dependence on the well separation $d$, and a peak in the drag rate as a function of relative carrier densities at matched Fermi velocities.
cond-mat↗
Dynamic Magneto-Conductance Fluctuations and Oscillations in Mesoscopic Wires and Rings
Using a finite-frequency recursive Green's function technique, we calculate the dynamic magneto-conductance fluctuations and oscillations in disordered mesoscopic normal metal systems, incorporating inter-particle Coulomb interactions within a self-consistent potential method. In a disordered metal wire, we observe ergodic behavior in the dynamic conductance fluctuations. At low $ω$, the real part of the conductance fluctuations is essentially given by the dc universal conductance fluctuations while the imaginary part increases linearly from zero, but for $ω$ greater than the Thouless energy and temperature, the fluctuations decrease as $ω^{-1/2}$. Similar frequency-dependent behavior is found for the Aharonov-Bohm oscillations in a metal ring. However, the Al'tshuler-Aronov-Spivak oscillations, which predominate at high temperatures or in rings with many channels, are strongly suppressed at high frequencies, leading to interesting crossover effects in the $ω$-dependence of the magneto-conductance oscillations.
cond-mat↗
Self-consistent calculation of ionized impurity scattering in semiconductor quantum wires
We calculate the electron elastic mean free path due to ionized impurity scattering in semiconductor quantum wires, using a scheme in which the screened ionized impurity potential and the electron screening self-consistently determine each other. By using a short-range scattering potential model, we obtain an {\sl exact} solution of the self-energy within the self-consistent Born and ``noncrossing" approximations. We find that, compared to the mean free path for the bare unscreened potential $\ell_{\rm bare}$, the calculated mean free path including self-consistent screening $\ell_{\rm sc}$ is {\sl substantially larger}, going as $\ell_{\rm sc} \sim \ell_{\rm bare}[\ln(\ell_{\rm bare})]^2$ for large $\ell_{\rm bare}$.
cond-mat↗
Enhancement of the decay rate of nonequilibrium carrier distributions due to scattering-in processes
We show that, for some semiconductor devices and physical experiments, processes which scatter electrons {\em into} a state $|{\bf k}\rangle$ can contribute strongly to the decay of a nonequilibrium electron occupation of $|{\bf k}\rangle$. For electrons, the decay rate $γ({\bf k})$ is given by the sum of the total scattering-out {\em and scattering-in} rates of state $|{\bf k}\rangle$. The scattering-in term, which is often neglected in calculations, increases $γ({\bf k})$ of low energy electrons injected into semidegenerate systems, which includes many doped semiconductor structures at nonzero temperatures, particularly those of reduced dimensions.
cond-mat↗
Many-body exchange-correlation effects in the lowest subband of semiconductor quantum wires
We consider theoretically the electron--electron interaction induced exchange-correlation effects in the lowest subband of a quasi-one-dimensional GaAs quantum wire structures. We calculate, within the leading order dynamical screening approximation ({\em i.e.} the so-called $GW$ approximation of the electron gas theory), the electron self-energy, spectral function, momentum distribution function, inelastic scattering rate, band gap renormalization, and, the many-body renormalization factor both at zero and finite temperatures, and, both with and without impurity scattering effects. We also calculate the effects of finite temperatures and finite impurity scattering on the many-body properties. We propose the possibility of a hot-electron transistor device with a large negative differential resistance which is based on the sudden onset of plasmon emission by energetic ballistic electrons in one dimension. The issue of the existence or non-existence of the Fermi surface among the interacting one-dimensional quantum wire electrons is critically discussed based on our numerical results.
cond-mat↗