Two-electron absorption in a biased quantum well

Linear light absorption of 2D electrons confined within a biased quantum well is studied theoretically. We demonstrate that for light polarization perpendicular to the 2D plane, in addition to conventional absorption peak at frequency ω≈Δ, where Δ is the intersubband energy distance, there exists a peak around a double frequency ω≈2Δ. This additional peak is entirely due to electron–electron interactions, and corresponds to excitation of two electrons by one photon. The magnitude of two-electron absorption is proportional to U², where U is the applied bias.     

Electron drag in intermediate magnetic fields with low electron density

Electron drag between two two-dimensional electron systems has been measured in intermediate magnetic fields (/τ<ω_ck_BT) with a relatively low electron density. We explore, in this sample, the unusual increase of drag in intermediate magnetic fields which was well characterized by a nearly temperature independent B³ dependence. The anomalous behavior of electron drag observed in higher density samples is found to persist for low sample density.     

Single InAs/GaAs quantum dots: Photocurrent and cross-sectional AFM analysis

Photocurrent (PC) spectroscopy is employed to study the carrier escape from self-assembled InAs/GaAs quantum dots (QDs) embedded in a Schottky photodiode structure. As a function of the applied field, we detect a shift of the exciton ground-state transition due to the quantum-confined Stark effect (). The tunneling time, which is directly related to the observed photocurrent linewidth due to τ/(2Γ), changes by a factor of five in the photocurrent regime. The measured linewidth dependency on the electric field is modeled by a simple 1D WKB approximation for the tunneling process, which shows that the energetic position of the wetting layer is important for the measured tunneling time out of the dot. In addition to that we present cross-sectional atomic force measurements (AFM) of the investigated photodiode structure. The method needs a minimum of time and sample preparation (cleaving and etching) to obtain the dot density, dot distribution, and give an estimate of the dot dimensions. Etching only the cleaved surface of the sample opens up the opportunity to determine the properties of a buried dot layer before or even after device fabrication.     

Dynamics of the collective excitations of the quantum Hall system

Using the non linear optical technique of 3-pulse 4-wave mixing, we study the dynamics of the collective excitations of the quantum Hall system. We excite the system with 100 fs pulses propagating in directions k₁ and k₃ and then probe its time evolution with a delayed pulse k₂. We measure the non-linear optical response from the lowest Landau level along the direction k₁+k₂−k₃. As function of the time delay of pulse k₂, this signal shows striking beats for short time delays (500 fs), followed by a rise (20 ps) and then a decay (100 ps). We identify the microscopic origin of this dynamics by extending the standard theory of ultra fast nonlinear optics to include the effects of the correlations.     

Quantum Hall ferromagnetism in a two-valley strained Si quantum well

Tilted field magnetotransport study was performed in a two-valley strained Si quantum well and hysteretic diagonal resistance spikes were observed near the coincidence angles. The spike around filling factor ν=3 develops into a giant feature when it moves to the high-field edge of the quantum Hall (QH) state and quenches for higher tilt angles. When the spike is most prominent, its peak resistance is temperature independent from T20 mK up to 0.3 K, which is different from the critical behavior previously reported near the Curie temperature of the QH ferromagnet in AlAs quantum wells. Our data suggest a strong interplay between spins and valleys near the coincidence.     

Stability of soliton lattice phase in the bilayer quantum Hall state under tilted magnetic fields

The bilayer quantum Hall (QH) state at the filling factor ν=1 shows various fascinating quantum phenomena due to the layer degree of freedom called ‘pseudospin’. We report an experimental evidence of the soliton lattice (SL) phase, which is a domain structure of pseudospin, by the appearance of a local maximum of magnetoresistance near the ν=1 QH state. We investigate the stability of the SL phase by changing B and the total electron density n_T. Detailed magnetotransport measurements under tilted magnetic fields were carried out to obtain a B–n_T plane phase diagram containing the C, IC and SL phases. We found the SL phase is only stable at low n_T region. Namely, the C–SL–IC phase transition occurs only at low n_T region as B increases. On the contrary, the C–IC phase transition directly occurs without passing through the SL phase at high n_T region.     

Magnetotunneling spectroscopy of ring-shaped (InGa)As quantum dots: Evidence of excited states with 2pz character

We study the effect of a high magnetic field (B) on the current–voltage characteristics, I(V), of a GaAs/(AlGa)As resonant tunneling diode incorporating a layer of ring-shaped quantum dots (QDs) in the quantum well (QW). The dots give rise to a series of four unusual resonances in I(V) which show a high degree of reproducibility across the epitaxial wafer. By combining data for B parallel and perpendicular to the growth axis z, we identify that the unusual resonances arise from resonant tunneling into QD excited states with 2p_z-like symmetry. The two series of magneto-oscillations in I for Bz allow us to determine the resonant charging and discharging of the QW with varying bias.     

Superconductivity as a Kosterlitz–Thouless transition in the two-dimensional Hubbard model

We investigate a superconducting Kosterlitz–Thouless transition in the two-dimensional (2D) Hubbard model using auxiliary quantum Monte Carlo method for the ground state. The pair susceptibility is computed for both the attractive and repulsive Hubbard model. The numerical results show that the s-wave pair susceptibility scales as χ  L² for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ  L² also holds for the d-wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t′.     

Comparison of quasilinear and WKB approximations

It is shown that the quasilinearization method (QLM) sums the WKB series. The method approaches solution of the Riccati equation (obtained by casting the Schrödinger equation in a nonlinear form) by approximating the nonlinear terms by a sequence of the linear ones, and is not based on the existence of a smallness parameter. Each pth QLM iterate is expressible in a closed integral form. Its expansion in powers of reproduces the structure of the WKB series generating an infinite number of the WKB terms. Coefficients of the first 2^p terms of the expansion are exact while coefficients of a similar number of the next terms are approximate. The quantization condition in any QLM iteration, including the first, leads to exact energies for many well known physical potentials such as the Coulomb, harmonic oscillator, Pöschl–Teller, Hulthen, Hyleraas, Morse, Eckart, etc.     

Center-of-mass problem in truncated configuration interaction and coupled-cluster calculations

The problem of center-of-mass (CM) contaminations in ab initio nuclear structure calculations using configuration interaction (CI) and coupled-cluster (CC) approaches is analyzed. A rigorous and quantitative scheme for diagnosing the CM contamination of intrinsic observables is proposed and applied to ground-state calculations for ⁴He and ¹⁶O. The CI and CC calculations for ¹⁶O based on model spaces defined via a truncation of the single-particle basis lead to sizable CM contaminations, while the importance-truncated no-core shell model based on the N_maxΩ space is virtually free of CM contaminations.     

Interband absorption and luminescence in small quantum dots under strong magnetic fields

Interband absorption and luminescence of quasi-two-dimensional, circularly symmetric, N_e-electron quantum dots are studied at high magnetic fields, 8B60 T, and low temperatures, T2 K. In the N_e=0 and 1 dots, the initial and final states of such processes are fixed, and thus the dependence on B of peak intensities is monotonic. For larger systems, ground state rearrangements with varying magnetic field lead to substantial modifications of the absorption and luminescence spectra. Collective effects are seen in the N_e=2 and 3 dots at “filling fractions” and .     

Two sub-band conductivity of Si quantum well

We report on two sub-band/bi-layer transport in double gate SiO₂–Si–SiO₂ quantum well with 14 nm thick Si layer at 270 mK. At symmetric well potential the experimental sub-band spacing changes monotonically from 2.3 to 0.3 meV when the total electron density is adjusted by gate voltages between 0.7×10¹⁶–. The conductivity is mapped in large gate bias window and it shows strong non-monotonic features. At symmetric well potential and high density these features are addressed to sub-band wave function delocalization in the quantization direction and to different disorder of the top and bottom interfaces of the Si well. In the gate bias regimes close to second sub-band/bi-layer threshold the non-monotonic behavior is interpreted to arise from scattering from the other electron sub-system with localized or low mobility states.     

1.3 μm range effectively cylindrical In0.53Ga0.47As/In0.52Al0.48As quantum wires grown on (2 2 1)A InP substrates by molecular beam epitaxy

Vertically coupled quantum wires (QWRs) have been made by alternately stacking nominally 3.6 nm thick In_0.53Ga_0.47As self-organized QWR layers and 1 nm thick In_0.52Al_0.48As barrier layers on (2 2 1)A-oriented InP substrates by molecular beam epitaxy. The surface of In_0.53Ga_0.47As QWR layers was corrugated at an amplitude of 1.1 nm and period of 27 nm, and lateral confinement potential is induced by their thickness modulation. The wavelength of photoluminescence (PL) from the stacked QWRs at 15 K becomes longer from 1220 to 1327 nm with increasing total number of stacked QWR layers, N_SL, from 1 to 9, while PL full-width at half-maximum is reduced from 22 to 8.6 meV. The PL intensity with the polarization parallel to the wire direction, I, is 1.30 times larger than that with the normal polarization, I, when N_SL=1. The PL intensity ratio, I/I, reaches as large as 4 when N_SL=9, indicating successful control of relative strength between vertical confinement and lateral confinement of carriers. The value of I/I obtained for the stacked QWRs with N_SL=9 is the same value as cylindrical QWRs have. The results indicate that effectively cylindrical QWRs with the best uniformity and 1.3 μm range emission were realized by stacking of self-organized QWR layers.     

A Positive Conservative Method for Magnetohydrodynamics Based on HLL and Roe Methods

The exact Riemann problem solutions of the usual equations of ideal magnetohydrodynamics (MHD) can have negative pressures, if the initial data has ·B0. This creates a problem for numerical solving because in a first-order finite-volume conservative Godunov-type method one cannot avoid jumps in the normal magnetic field component even if the magnetic field was divergenceless in the three-dimensional sense. We show that by allowing magnetic monopoles in MHD equations and properly taking into account the magnetostatic contribution to the Lorentz force, an additional source term appears in Faraday's law only. Using the Harten–Lax–vanLeer (HLL) Riemann solver and discretizing the source term in a specific manner, we obtain a method which is positive and conservative. We show positivity by extensive numerical experimentation. This MHD-HLL method is positive and conservative but rather diffusive; thus we show how to hybridize this method with the Roe method to obtain a much higher accuracy while still retaining positivity. The result is a fully robust positive conservative scheme for ideal MHD, whose accuracy and efficiency properties are similar to the first order Roe method and which keeps ·B small in the same sense as Powell's method. As a special case, a method with similar characteristics for accuracy and robustness is obtained for the Euler equations as well.     

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. , in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as  = _r + i_i and μ = μ_r + iμ_i. The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability _i > 0 and μ_i > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability _i < 0 and μ_i < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters _r, μ_r, _i, and μ_i, in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re{Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously  < 0 and μ < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for _r < 0, μ_r > 0, _i > 0, and μ_i > 0, the refractive index is negative n < 0 provided μ_i/_i > μ_r/_r.     

Entanglement evolution of a two-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a two-qubit system under a quantum spin environment at finite temperature in the thermodynamics limit. For the case under study, we find different initial states will result in different entanglement evolution, what deserves mentioning here is that the state |Ψ=cosα|01+sinα|10 is most robust than other states when π/2<α<π, since the entanglement remains unchanged or increased under the spin environment. In addition, we also find the anisotropy parameter Δ can suppress the destruction of decoherence induced by the environment, and the undesirable entanglement sudden death arising from the process of entanglement evolution can be efficiently controlled by the inhomogeneous magnetic field ζ.     

Temperature scaling of quantum Hall plateau transition in bilayer systems

We have investigated the scaling behavior of the quantum Hall plateau transition in double quantum well systems with different interlayer tunneling strengths. The scaling behavior of the localization property is found to be similar between the case when the relevant Landau level (LL) is non-degenerate and the case when two LLs associated with the two layers are accidentally degenerate. In both cases, the scaling exponent κ0.4 close to the canonical value is obtained, and it is unaffected by the in-plane magnetic field which changes the interlayer tunneling strength.     

Multiplication for solutions of the equation

Linear first-order systems of partial differential equations (PDEs) of the form f=Mg, where M is a constant matrix, are studied on vector spaces over the fields of real and complex numbers. The Cauchy–Riemann equations belong to this class. We introduce on the solution space a bilinear *-multiplication, playing the role of a nonlinear superposition principle, that allows for algebraic construction of new solutions from known solutions. The gradient equation f=Mg is a simple special case of a large class of systems of PDEs, admitting a *-multiplication of solutions. We prove that any gradient equation has the exceptional property that the general analytic solution can be expressed as *-power series of certain simple solutions.     

Electron transport and shell structures of single InAs quantum dots probed by nanogap electrodes

We have investigated electron transport and electron filling in single InAs quantum dots (QDs) using nanogap electrodes. Elliptic InAs QDs with diameter of 60/80 nm exhibited clear shell filling up to 12 electrons. Shell-dependent charging energies and level quantization energies for the s, p, and d states were determined from the addition energy spectra. Furthermore, it is found that the charging energies and the tunneling conductances strongly depend on the shell, reflecting that the electron wave functions for higher shells are more extended in space.     

Concavity for nuclear bindings, thermodynamical functions and density functionals

Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential Ω(β,μ) for a mixture of nuclei at low or moderate temperatures T=β⁻¹ and at many chemical potentials μ. The average nucleon number A(β,μ) then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to the drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of A. Concavity, which always occurs for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.