Small Carrier Density Research Articles

Spectral hole-burning and carrier-heating dynamics in InGaAs quantum-dot amplifiers

The ultrafast gain and index dynamics in a set of InAs-InGaAs-GaAs quantum-dot (QD) amplifiers are measured at room temperature with femtosecond resolution. The role of spectral hole-burning (SHB) and carrier heating (CH) in the recovery of gain compression is investigated in detail. An ultrafast recovery of the spectral hole within /spl sim/100 fs is measured, comparable to bulk and quantum-well amplifiers, which is contradicting a carrier relaxation bottleneck in electrically pumped QD devices. The CH dynamics in the QD is quantitatively compared with results on an InGaAsP bulk amplifier. Reduced CH for both gain and refractive index dynamics of the QD devices is found, which is a promising prerequisite for high-speed applications. This reduction is attributed to reduced free-carrier absorption-induced heating caused by the small carrier density necessary to provide amplification in these low-dimensional systems.

Green function of fermions in 2D superconducting Fröhlich model with inhomogeneous order parameter

The fermion Green function and spectral characteristics for the 2D Frohlich model of superconductivity at static fluctuations in the phase of the order parameter are calculated. The results demonstrate strongly non-Fermi-liquid properties of the system at finite temperatures and relate with the pseudogap behavior of high-$T_{c}$ superconductors at relatively small charge carrier densities.

The physical origin of the electron-phonon vertex correction

The electron-phonon vertex correction has a complex structure both in momentum and frequency. We explain this structure on the basis of physical considerations and we show how the vertex correction can be decomposed into two terms with different physical origins. In particular, the first term describes the lattice polarization induced by the electrons and it is essentially a single-electron process whereas the second term is governed by the particle-hole excitations due to the exchange part of the phonon-mediated electron-electron interaction. We show that by weakening the influence of the exchange interaction the vertex takes mostly positive values giving rise to an enhanced effective coupling in the scattering with phonons. This weakening of the exchange interaction can be obtained by lowering the density of the electrons, or by considering only long-ranged (small q) electron-phonon couplings. These findings permit to understand why in the High-Tc materials the small carrier density and the long ranged electron-phonon interaction may play a positive role in enhancing Tc.

Interfaces involving complex superconductors

The physics of interfaces involving complex superconductors is considerably richer and much less explored than the physics of interfaces and surfaces of conventional superconductors. The startling effects shown by such interfaces are directly caused by basic properties of unconventional superconductors, such as their pairing symmetry, or their small carrier densities and coherence lengths. In this contribution, these unusual interface properties are summarized, with a particular emphasis on effects caused by the unconventional order parameter symmetry and by bending of the electronic band structure.

Semimetallic behavior inFe2VAl:NMR evidence

We report the results of a ${}^{27}\mathrm{Al}$ and ${}^{51}\mathrm{V}$ nuclear magnetic resonance study of ${\mathrm{Fe}}_{2}\mathrm{VAl}$ at temperatures between 4 and 550 K. This material has been a subject of current interest due to indications of possible heavy fermion behavior. The low-temperature NMR relaxation rate follows a Korringa law, indicating a small density of carriers at the Fermi level. At elevated temperatures, the shifts and relaxation rates go over to a thermally activated response, a semiconductorlike behavior, consistent with separate low-lying bands removed from the Fermi-level. These results are consistent with recent electronic structure calculations, and can explain both the reported activated resistivity as well as the Fermi cutoff exhibited in photoemission studies. While we observe nonstoichiometric samples of $({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{V}}_{x}{)}_{3}\mathrm{Al}$ to be magnetic, the $x=0.33$ composition is nonmagnetic, with narrow NMR linewidths.

Observation of charged X−and X+excitons and metal-to-insulator transition in CdTe/CdMgZnTe modulation-doped quantum wells

The positively and negatively charged excitons,X+andX−, respectively, are identified by their magnetic circular dichroism in the absorption spectra of modulation-doped CdTe/Cd0.69Mg0.23Zn0.08Te multiple quantum wells at small carrier densities (≈1010cm−2). In these quantum wells with a width of 8 nm the binding energies of the second electron of theX−exciton and of the second hole of theX+exciton are very similar, 2.9 meV and 2.6 meV, respectively. At larger hole densities a transition to the conducting state is observed. In a sample with intermediate hole density (low 1011cm−2) the insulating phase is restored by application of a magnetic field.

Carrier relaxation and electronic structure in InAs self-assembled quantum dots.

We studied the electronic structure and relaxation processes in InAs quantum dots embedded in GaAs. Using capacitance measurements along with photoluminescence spectroscopy, we estimate the energy splitting between the ground and first excited quantum-dot state in the conduction and valence band, respectively. There are five quantum-dot transitions observable in our photoluminescence (PL) spectra, which we attribute to allowed transitions between electron and hole states of the same quantum number. Phonon-related relaxation processes were studied combining PL, resonant PL (RPL), and photoluminescence excitation (PLE) experiments. In the RPL as well as in the PLE spectra, we observed enhanced signals at twice the phonon energies available in the system. Therefore, a maximum in the intensity of the PLE and RPL signal does not necessarily occur when most of the dots are pumped resonantly into an excited state. The main criterion, however, seems to be that the energy distance between the pumped levels and the levels below matches a multiple of the available phonon energies. Changing the pump power in our resonant PL experiments corroborates that at least in the small carrier density regime phonon-related processes are important for the carrier relaxation in InAs quantum dots embedded in GaAs bulk material. \textcopyright{} 1996 The American Physical Society.

Superconductivity and transport properties of narrow-gap semiconductor Pb(Tl)Te film by HWE growth

The IV–VI semiconductor PbTe doped with a small amount of Tl shows superconductivity of T c max ∼ 1.4 K in spite of the small hole carrier densities of p∼10 20 cm −3. The superconducting generating mechanism has received much attention from the viewpoint of carrier resonance scattering with a Tl quasi-localized state. In order to investigate the superconductivity on well-defined film samples, we prepared high-quality Pb(Tl)Te films by the HWE method, and carried out the observation of superconductivity and electrical-transport properties. Furthermore, in the experiment with the coordinated system of Pb(Tl,Na)Te film, the results show for the first time the possible existence of two quasi-localized states of Tl causing strong scattering of carriers accompanied by reduction in Hall mobility μ, which play an important role in the superconductivity of this Pb(Tl)Te system.

Fractional quantum Hall effect in bilayer two-dimensional hole-gas systems.

We have studied the fractional and integer quantum Hall effect in high-mobility double-layer two-dimensional hole-gas systems. The large hole effective mass inhibits tunneling, allowing us to investigate the regime in which the interlayer and intralayer interactions are comparable without significant interlayer tunneling occurring. As the interlayer separation is reduced we observe the formation of bilayer-correlated quantum Hall states at total filling factor $\ensuremath{\nu}=\frac{3}{2}$ and $\ensuremath{\nu}=1$. We find that the bilayer $\ensuremath{\nu}=\frac{3}{2}$ state is rapidly destroyed by small carrier density imbalances between the layers, whereas the bilayer $\ensuremath{\nu}=1$ state evolves continuously into the single-layer $\ensuremath{\nu}=1$ state.

Expulsion of charge carriers from quasi-two-dimensional antiferromagnetic structures and formation of spin-liquid droplets in them

In antiferromagnetic semiconductors the charge carrier energy decreases, when the long-range magnetic ordering is destroyed. This leads to the fact that in degenerate quasi-two-dimensional semiconductors to which high-TC superconductors belong, both the collinear and canted antiferromagnetic orderings are unstable at arbitrarily small charge carrier density, if the exchange between carriers and localized moments is not very weak. The condition for instability coincides with condition for formation of an electron self-trapped state inside a ferromagnetic region. This means that the antiferromagnetic structure expulses charge carriers into the ferromagnetic phase. An alternative to it is its expulsion into magnetically disordered phase. Then a new type of the carrier self-trapped state realizes when a carrier disorders magnetically a certain region in the antiferromagnet and stabilizes this region by its localization inside it. It corresponds to antiferromagnetic-spinliquid phase separation on the single-electron level. At sufficiently large carrier densities the canted antiferromagnetic structure induced by carriers may be, atleast, relatively stable.

Momentum dependence of the spin and charge excitations in the two dimensional Hubbard model

The low energy spin and charge excitations in the 2D Hubbard model near half filling are analyzed. The RPA spectra derived from inhomoheneous mean field textures are analyzed. Spin excitations show a commensurate peak at half filling, incommensurate peaks near half filling, and a broad background typical of a dilute Fermi liquid away from half filling. Charge excitations, near half filling, are localized near (0,0), and they occupy a small portion of the Brillouin Zone, in a way consistent with the existence of a small density of carriers, and a small Fermi surface. At higher hole densities, they fill the entire BZ, and can be understood in terms of a conventional Fermi liquid picture. The results are consistent with the observed features of the high-T$_c$ superconductors.

Exchange and correlation in the quasi-one-dimensional electron gas: The local-field correction.

The local-field correction for the quasi-one-dimensional electron gas in cylindrical quantum wires with wire radius ${\mathit{R}}_{0}$ is calculated within the sum-rule approach of the self-consistent theory of Singwi, Tosi, Land, and Sj\"olander. The local-field correction is expressed by a generalized Hubbard form with two coefficients, which are determined self-consistently. Numerical results for the exchange energy and the correlation energy are presented for 0${\mathit{r}}_{\mathit{s}}$20, where ${\mathit{r}}_{\mathit{s}}$ is the random-phase-approximation parameter. We find that the exchange energy in the low-density regime is strongly enhanced compared to two and three dimensions: ${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{ex}}$(${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty})\ensuremath{\propto}-ln(${\mathit{r}}_{\mathit{s}}$)/${\mathit{r}}_{\mathit{s}}$. For high density we find ${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{ex}}$(${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0)\ensuremath{\propto}-${\mathit{a}}^{\mathrm{*}}$/${\mathit{R}}_{0}$, where ${\mathit{a}}^{\mathrm{*}}$ is the Bohr radius. For the correlation energy we get ${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{cor}}$(${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0)\ensuremath{\propto}-${\mathit{r}}_{\mathit{s}}^{2}$/${\mathit{R}}_{0}^{2}$. The local-field correction strongly reduces the correlation energy for small carrier density if compared with the random-phase approximation. We study the pair-correlation function, the plasmon dispersion, and the compressibility, and we describe the effects of exchange and correlation on these quantities. The parameter for weak coupling in wire systems is described by ${\mathit{R}}_{\mathit{s}}$=4${\mathit{r}}_{\mathit{s}}$${\mathit{a}}^{\mathrm{*}}$/\ensuremath{\pi}${\mathit{R}}_{0}$1 and strong coupling corresponds to ${\mathit{R}}_{\mathit{s}}$>1.

SUPERCONDUCTIVITY AND SUPERFLUIDITY IN FERMI SYSTEMS WITH REPULSIVE INTERACTIONS

We study the possibility of a pairing instability in Fermi systems with a purely repulsive interaction potential. The effective interaction between particles at the Fermi surface is shown to contain a contribution from the fermionic background. This contribution is attractive and in many cases it overshadows the interactive potential in the pairing channels with nonzero orbital angular momenta. In particular, we show that 3D Fermi gas with repulsive interaction is unstable against p-pairing. Both the value of T c and its field dispersion are consistent with the experimental data for pure 3 He . It is also shown that in a magnetic field and in the two-band model there is the possibility of a significant mcrease of T c . We also consider the situation in two dimensions, where the effect of the fermionic background is much weaker than in the 3D case. Nevertheless, we show that the positive-U Hubbard model may have an intrinsic instability at arbitrarily small carrier densities. In particular, the Hubbard model with hopping between nearest neighbors is unstable against d-wave pairing with dxy symmetry of the gap wave function. The superconducting states we study correspond to the actual minima of the Free energy.

Transport and localization in Nd2-xCexCuO4-y crystals at low doping.

We report in-plane transport properties of ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4\mathrm{\ensuremath{-}}\mathit{y}}$ crystals prepared in low-doped (x\ensuremath{\sim}0.01--0.11), nonsuperconducting compositions. The large negative Hall coefficient ${\mathit{R}}_{\mathit{H}}$ and thermopower S in these samples confirm the presence of a small density of n-type carriers. At low T we find a highly anisotropic negative magnetoresistance which, together with the behavior of \ensuremath{\rho}, S, and ${\mathit{R}}_{\mathit{H}}$, demonstrates two-dimensional weak localization of these carriers occurring as Ce content decreases. Analysis of the magnetoresistance data reveals an anomalously weak T dependence of the electron inelastic-scattering rate 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{i}}$.

17O nuclear-magnetic-resonance evidence for distinct carrier densities in the two types of CuO2 planes of (Bi,Pb)2Sr2Ca2Cu3Oy.

A study of {sup 17}O NMR spectra in the normal phase of {sup 17}O-enriched powder samples of (Bi,Pb){sub 2}Sr{sub 2}Ca{sub 2}Cu{sub 3}O{sub {ital y}} (2:2:2:3 phase) has allowed us to distinguish the NMR lines of the CuO{sub 2} planes having respectively pyramidal and square coordination for copper. The observed differences in the magnitude and temperature dependence of the {sup 17}O Knight shift of the two types of planes are consistent with the occurrence of stronger electron correlations, or smaller carrier density, in the plane-square coordinated planes, in accordance with recent theoretical predictions.

Electron-hole liquid model for high-Tc superconductors.

We show that the hole concentration dependence of ${T}_{c}$ in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathrm{x}}$- and ${\mathrm{Nd}}_{1+\mathrm{x}}$${\mathrm{Ba}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathrm{y}}$-type superconductors can be understood within a model electron-boson hole liquid that possesses a linear sound mode like the one in liquid $^{4}\mathrm{He}$. The electronic specific heat follows a ${T}^{3}$ law near T=0. The metal-insulator transition found in these compounds is proposed to be connected with the vanishing of the sound velocity at small carrier densities.

Ginzburg-Landau-Gorkov theory for high-temperature superconductors.

We use Gorkov's theory to calculate the coefficients of the Ginzburg-Landau theory from a narrow two-dimensional tight-binding band. We consider s-wave, d-wave, and coupled s-d-wave pairing states of square symmetry. The resulting energy gap \ensuremath{\Delta}, the thermodynamic critical field ${H}_{c}$, the coherence length \ensuremath{\xi}, and the magnetic penetration depth ${\ensuremath{\lambda}}_{L}$ depend on band width, band filling, and pairing state. The simple s-wave state yields the highest \ensuremath{\Delta} and the highest ${H}_{c}$ and thus appears to be the most likely candidate. Scattering of carriers by phonons and impurities leads to multiplication of ${\ensuremath{\xi}}^{2}$ and ${\ensuremath{\lambda}}_{L}^{\mathrm{\ensuremath{-}}2}$ by \ensuremath{\chi}(x), where \ensuremath{\chi} is the Gorkov function and x=\ensuremath{\lambda}+(\ensuremath{\Gamma}/\ensuremath{\pi}${k}_{B}$${T}_{c}$) (here \ensuremath{\lambda} is the electron-phonon coupling constant and \ensuremath{\Gamma} the scattering rate due to impurities). For small band widths and low carrier densities, we obtain qualitative agreement with the measured values of the coherence length and penetration depth in the ab plane for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$. .AE

Theory of conductivity in superlattice minibands.

We have calculated the impurity-scattering--limited electrical conductivity for vertical transport in superlattice minibands. For sufficiently small carrier density and/or ``large'' disorder the collisional broadening \ensuremath{\Gamma}(\ensuremath{\mu}) can be larger than the chemical potential \ensuremath{\mu}. In such situations the quasiparticle approximation breaks down, and use of the conventional Bloch-Boltzmann transport theory is unreliable. Also, as the period of the superlattice increases, the ratio \ensuremath{\Gamma}(\ensuremath{\mu})/\ensuremath{\mu} grows, resulting in a reduction of the mobility, leading eventually to Anderson localization. In addition, the carriers in the miniband become nondegenerate already at low temperatures, giving rise to a significant temperature dependence of the mobility. Furthermore, due to the unique shape of the Fermi surface of the superlattice the mobility becomes independent of the carrier density when the chemical potential exceeds the miniband width.

Theoretical calculation of the normal-state resistivity of the high-Tc oxide materials.

We calculate the resistivity of a two-dimensional electron gas, which is relevant to the high-${T}_{c}$ oxide materials, based upon the electron-phonon scattering mechanism and considering temperature effects of the chemical potential due to the small carrier density. The calculated results show that the resistivity $\ensuremath{\rho}$ is nearly linear, and its slope $\frac{d\ensuremath{\rho}}{\mathrm{dT}}$ is a slowly varying function of the temperature rather than a constant. By using sets of parameters extracted from the experimental data for Y-Ba-Cu-O and La-Sr-Cu-O and choosing reasonable electron-phonon coupling parameters ($\ensuremath{\lambda}=0.2 \mathrm{and} 1.3$, respectively, for Y-Ba-Cu-O and La-Sr-Cu-O), the obtained results for $\ensuremath{\rho}$ and $\frac{d\ensuremath{\rho}}{\mathrm{dT}}$ can be quantitatively compared with experimental measurements.

Thermal transport properties of YBa2Cu

We have measured the thermal conductivity, thermopower, Hall constant, and resistivity of a Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ high-${T}_{c}$ superconductor. The thermal conductivity shows a striking increase below the transition temperature ${T}_{c}$, which we ascribe to an increase in lattice conduction due to a reduction in the scattering of phonons by holes as superconducting pairs form. This property, and the others we have measured, are consistent with ordinary metallic conduction mechanisms with short phonon and carrier free paths, and a strong interaction of phonons with a small density of hole carriers.