Wannier-Stark states of a quantum particle in 2D lattices

A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a nonseparable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.     

Raman spectroscopy of resonance exciton tunneling in GaAs/AlAs superlattices in electric fields

Optical-resonance-Raman scattering by acoustic phonons is used to study the effect of an electric field on the state of excitons in GaAs/AlAs superlattices. When the energy of the exciting photon coincides with the energy of an exciton bound to Wannier-Stark states of a heavy hole and electron with Δn=0,±1, the acoustic Raman scattering is enhanced. Oscillations in the intensity of the Raman spectrum in the electric field are explained by resonance delocalization of the exciton ground state as it interacts with Wannier-Stark states of neighboring quantum wells or with Wannier-Stark states of a higher electron miniband. Fiz. Tverd. Tela (St. Petersburg) 40, 827–829 (May 1998)     

Oscillations of light absorption in 2D macroporous silicon structures with surface nanocoatings

We investigated the near-IR light absorption oscillations in 2D macroporous silicon structures with microporous silicon layers and CdTe, ZnO surface nanocrystals. The electro-optical effect was taken into account within the strong electric field approximation. Well-separated oscillations were observed in the spectral ranges of the surface bonds of macroporous silicon structures with surface nanocrystals. The model of the resonant electron scattering on impurity states in electric field of heterojunction “silicon-nanocoating” on macropore surface as well as realization of Wannier-Stark effect on the randomly distributed surface bonds were considered. The Wannier-Stark ladders are not broken by impurities because of the longer scattering lifetime as compared with the period of electron oscillations in an external electric field, in all spectral regions considered for macroporous silicon structures with CdTe and ZnO surface nanocrystals.     

Wannier-Stark effect and electron-phonon interaction in macroporous silicon structures with SiO2 nanocoatings

We investigated the contribution of electron-phonon interaction to the broadening parameter Γ of the Wannier-Stark ladder levels in oxidized macroporous silicon structures with different concentration of Si-O-Si states (TO and LO phonons). The obtained value of the Wannier-Stark ladder parameter Γ is much less than the djacent level energy evaluated from giant oscillations of resonance electron scattering on the surface states. We determined the influence of broadening on the oscillation amplitude in IR absorption spectra as interaction of the surface multi-phonon polaritons with scattered electrons. This interaction transforms the resonance electron scattering in samples with low concentration of Si-O-Si states into ordinary scattering on ionized impurities for samples with high concentration of Si-O-Si states. The transformation takes place at the scattering lifetime coinciding with the period of electron oscillations in the surface electric field.     

Density of states in an electrically biased quantum well

Density of states in a quantum well has been studied in the presence of an electric field applied perpendicular to the growth direction. We have shown that an extra quantization is introduced to the motion of the electron due to the discrete energy levels known as Wannier-Stark ladder states and the nature of density of electronic states changes from quasi two-dimensional to quasi one-dimensional.      

Wannier-Stark resonances under strong localization conditions in natural silicon-carbide superlattices

A detailed experimental investigation is made of the electronic transport under conditions of Wannier-Stark localization of carriers in a natural superlattice of hexagonal polytypes of silicon carbide. The 4H and 6H polytypes, which possess different superlattice and miniband spectrum parameters, are employed. Direct measurements of the electronic current versus the average electric field in the active region of the sample revealed a series of regions of negative differential conductivity in fields ranging from 500 to 2100 kV/cm. Analysis of the results shows that the observed current resonances are associated with the development of the Wannier-Stark quantization process and are due to conduction mechanisms such as hopping conduction, induced between the levels of a Wannier-Stark ladder by a resonant electron-phonon interaction, and the resonant interminiband tunneling from the first into the second miniband. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 105–109 (25 July 1996)     

Bloch oscillations and Wannier-Stark ladder in the coupled LC circuits

We present a new scheme for realizing Bloch oscillations and Wannier-Stark ladder based on a lattice of coupled LC circuits. By converting the second order dynamical ODEs of the system into a first order Schrödinger-like equation, we propose an equivalent tight binding Hamiltonian to describe the circuit. We show that a synthesized electric field is produced by introducing a frequency mismatch into the resonant frequency of the adjacent LC resonators. The Wannier-Stark modes are the normal modes of the circuit and the Bloch oscillations can be observed in a coupled LC lattice. By addition of coupling capacitors between nodes of the circuit, we study the Bloch oscillation in the presence of long-range couplings. We also show that the circuit converts to a transmission line simulating synthetic electric fields in the continuum limit. The coupled LC circuit is, in some sense, amongst the simplest physical systems exhibiting Bloch oscillation and Wannier-Stark Ladder.     

Optical Bloch oscillations in waveguide arrays

We show that optical Bloch oscillations can emerge in waveguide arrays with linearly varying propagation constants. The existence of localized modes (Wannier-Stark states) with equidistant wave-number spacing (Wannier-Stark ladder) that do not undergo diffraction is analytically proved. The evolution of arbitrary initial excitations is described, and potential applications are suggested.     

Effects of magnetic field on photon-induced quantum transport in a single dot-cavity system

In this study,we show how a static magnetic field can control photon-induced electron transport through a quantum dot system coupled to a photon cavity.The quantum dot system is connected to two electron reservoirs and exposed to an external perpendicular static magnetic field.The propagation of electrons through the system is thus influenced by the static magnetic and the dynamic photon fields.It is observed that the photon cavity forms photon replica states controlling electron transport in the system.If the photon field has more energy than the cyclotron energy,then the photon field is dominant in the electron transport.Consequently,the electron transport is enhanced due to activation of photon replica states.By contrast,the electron transport is suppressed in the system when the photon energy is smaller than the cyclotron energy.     

Lifetime of the Wannier-Stark Resonances and Perturbation Theory

We consider the small field asymptotics of the lifetime of metastable states in Wannier-Stark problems. Assuming that at zero field we have Bloch operators with only the first gap open and using the regular perturbation theory, we prove that the behavior of the lifetime computed by means of the Fermi Golden Rule is proportional to the correct one with the factor . The connection with adiabatic problems is briefly discussed. Received: 4 March 1996 / Accepted: 24 September 1996     

Calculation of Wannier-Bloch and Wannier-Stark states

The paper discusses the metastable states of a quantum particle in a periodic potential under a constant force (the model of a crystal electron in a homogeneous electric field), which are known as the Wannier-Stark ladder of resonances. An efficient procedure to find the positions and widths of resonances is suggested and illustrated by numerical calculations for a cosine potential, which are in excellent agreement with complex scaling resonance energies. Received: 27 April 1998 / Revised: 21 July 1998 / Accepted: 3 August 1998     

Photocurrent resonances in short-period AlAs/GaAs superlattices in an electric field

The photocurrent was measured as a function of the external electric field in short-period AlAs/GaAs superlattices for various photon energies. Transport resonances, whose positions do not depend on the photon energy, were observed in these dependences together with optical resonances due to interband transitions in Wannier-Stark levels. It is shown that the transport resonances are due to tunneling of photoelectrons from the p-GaAs contact region into the first level in GaAs wells located 2–5 lattice periods from the contact layer. Fiz. Tverd. Tela (St. Petersburg) 41, 159–164 (January 1999)     

Magnetic Bloch oscillations in nanowire superlattice rings

The recent growth of semiconductor nanowire superlattices encourages hope that Bloch-like oscillations in such structures formed into rings may soon be observed in the presence of a time-dependent magnetic flux threading the ring. These magnetic Bloch oscillations are a consequence of Faraday's law; the time-dependent flux produces an electromotive force around the ring, thus leading to the Bloch-like oscillations. In the spectroscopic domain, generalized Wannier-Stark states are found that are manifestations of the emf-induced localization of the states.     

On the one-electron theory of crystalline solids in a homogeneous electric field

Assuming that the one-electron states of a perfect crystalline solid are known, an approach for the calculation of the one-electron states in the presence of external fields and/or other deviations from the periodic potential of the perfect crystal is suggested. The treatment is based on the Wannier representation and the use of a method for solving some operator non-polynomial differential equations. In the approximation of the one-band Wannier equation an exact solution of the problem for electron states of the crystals in a homogeneous external electric field is given. The results obtained in the tight binding approximation for cubic crystals show that the electron motion along the field is finite and the degree of its finiteness for a given electric field strength is greater, the smaller the width of the initial energy band considered. In the one-band approximation Considered the electron energy spectrum has the character of the Wannier-Stark ladder. It is also shown that an influence of transverse motion on the character of the finite motion along the field appears when a non-additivity in the initial energy band function with respect to the energies of motions parallel and perpendicular to the field direction is present.     

Influence of above-barrier and edge states on absorption spectra of shallow GaAs/AlGaAs superlattices of finite length in strong electric fields

An investigation is made of the absorption spectra of a GaAs(82 Å)/Al_0.07Ga_0.93As(37 Å) superlattice at 10 K in electric fields between 0 and 60 kV/cm. By comparing the experimental absorption spectra with calculations of the energies and oscillator strengths of transitions between states of the Wannier-Stark ladder it is established that in strong electric fields above-barrier states do not form a structureless continuum but a fan of states. Intersection of electric-field-localized electron states with the fan of above-barrier states leads to broadening, splitting, and nonmonotonic changes in the intensity of an intrawell transition band. The additional absorption band observed can be attributed to intrawell transitions between states in the left and right quantum wells of the superlattice.     

New Wannier-Stark localization effects in natural 6H-SiC superlattice

A premature electric breakdown caused by the formation of a strong-field domain under conditions of negative differential conductivity in the 6H-SiC n⁺-n^?-n⁺ structure optimized for ultrahigh-frequency measurements was observed in the range of electric fields corresponding to the Bloch oscillation regime in a natural 6H-SiC superlattice. The experimental results and ensuing estimates indicate that this domain is mobile and, hence, oscillating, allowing the microwave oscillations that are rapidly damped under conditions of avalanche break-down in a natural 6H-SiC superlattice to be forecasted. Crystal perfectness of a natural 6H-SiC superlattice made it possible to directly observe the Wannier-Stark localization up to electric breakdown, i.e., during the natural crystal lifetime. This was accomplished by the optical photoelectric transformation method in the multiplication regime for a photocurrent created by photons with above-bandgap energy. It was shown that the Wannier-Stark localization, which involves only electrons, occurs in natural 6H-SiC superlattice up to fields that are almost equal to the breakdown field in 6H-SiC, unresponsively to band mixing, i.e., to the fundamental destroyer of the Wannier-Stark localization.     

Bloch oscillations of an acoustic field in a layered structure

This study is devoted to experimentally achieving the phenomenon of periodic modulation of the acoustic-wave intensity, which is observed upon passage of an acoustic signal through a quasi-periodic structure and is the acoustic analog of the effect of Bloch oscillations (BO). Ultrasound at a frequency of 1 MHz is used, and a layered structure that consists of alternate plane-parallel glass and water layers serves as a super-lattice. In order to create an analog of the external electric field, the thickness of the water layers was changed inversely with respect to their ordinals. It is shown that the transmission spectrum of such a structure has the form of narrow equidistant peaks (an analog of the Wannier-Stark ladder), and the envelope of a transmitted signal undergoes periodic oscillations (analogous to BO). The experimental results are in good agreement with theoretical calculations performed by the transfer-matrix method.     

Excitonic transitions in GaAs---GaAlAs superlattices under a weak electric field

We report a study of the photoluminescence spectra of GaAs---Ga_0.65Al_0.35As superlattice under an electric field of about 10 kVcm⁻¹, from 9 K up to 80 K; the ratio of the intensities of the −1 and 0 peaks of the Wannier-Stark ladder varies with the temperature T. To fit these variations, we assume for both transitions, a trapped exciton density of states with a gaussian distribution of eigenenergies, and a two dimensional density of states for free excitons. We show that above about 50 K there is a thermal equilibrium between direct and crossed free excitons whereas at low temperatures, the equilibrium statistics are not respected: the excitons trap into the direct state rather than to the crossed one.     

Determination of the roughness of heteroboundaries from photocurrent spectra of short-period AlAs/GaAs superlattices

Photocurrent spectroscopy is used to study the nature of the roughness of heteroboundaries in (AlAs)_m/(GaAs)_n short-period superlattices (m=3−5, n=10−13) grown by molecularbeam epitaxy. The formation of minibands broadens the optical spectra of superlattices in comparison with isolated quantum wells; therefore to analyze the degree of perfection of the boundaries we used the decay of the minibands into a series of discrete Wannier-Stark levels in an electric field parallel to the superlattice axis. Exciton lines were observed in the photocurrent spectra in an electric field corresponding to direct and indirect (in space) transitions between the Wannier-Stark levels. Comparison of experimental data with calculation indicates that even in the better structures, in addition to monotonic variation of the thickness of the layers over area, roughnesses in the heteroboundaries one monolayer in height are present with characteristic lateral dimension not exceeding 10 nm. Fiz. Tverd. Tela (St. Petersburg) 39, 2085–2089 (November 1997)     

Coherent delocalization of atomic wave packets in driven lattice potentials

Atomic wave packets loaded into a phase-modulated vertical optical-lattice potential exhibit a coherent delocalization dynamics arising from intraband transitions among Wannier-Stark levels. Wannier-Stark intraband transitions are here observed by monitoring the in situ wave-packet extent. By varying the modulation frequency, we find resonances at integer multiples of the Bloch frequency. The resonances show a Fourier-limited width for interrogation times up to 2 s. This can also be used to determine the gravity acceleration with ppm resolution.