Quantum resonances in the valence bands of zinc-blende semiconductors. I. Theoretical aspects

Trebin, Hans‐Rainer; Rößler, U.; Ranvaud, R.

doi:10.1103/physrevb.20.686

Cited by 226 publications

(138 citation statements)

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“…This assumption is based on our sample parameters; we note, however, that the deduced spin splitting is insensitive to the exact value of the background doping. Using V H we obtain the Landau fan chart for B > 0 from an 8 × 8 k · p Hamiltonian that fully takes into account the spin-orbit coupling due to both SIA and BIA [5,16]. From this fan chart we then determine the magneto-oscillations by evaluating the density of states at the Fermi energy as a function of B.…”

mentioning

confidence: 99%

Negative differential Rashba effect in two-dimensional hole systems

Habib

Tutuc

Melinte

et al. 2004

Applied Physics Letters

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We demonstrate experimentally and theoretically that two-dimensional (2D) heavy hole systems in single heterostructures exhibit a decrease in spin-orbit interaction-induced spin splitting with an increase in perpendicular electric field. Using front and back gates, we measure the spin splitting as a function of applied electric field while keeping the density constant. Our results are in contrast to the more familiar case of 2D electrons where spin splitting increases with electric field.In a solid that lacks inversion symmetry, the spin-orbit interaction leads to a lifting of the spin degeneracy of the energy bands, even in the absence of an applied magnetic field, B. In such a solid, the energy bands at finite wave vectors are split into two spin subbands with different energy surfaces, populations, and effective masses. The problem of inversion asymmetry-induced spin splitting in two-dimensional (2D) carrier systems in semiconductor heterojunctions and quantum wells [1,2,3,4] has become of renewed interest recently [5] because of their possible use in realizing spintronic devices such as a spin field-effect transistor [6,7], and for studying fundamental phenomena such as the spin Berry phase [8,9].In 2D carrier systems confined to GaAs/AlGaAs heterostructures, the bulk inversion asymmetry (BIA) of the zinc blende structure and the structure inversion asymmetry (SIA) of the confining potential contribute to the B = 0 spin splitting [4,5]. While BIA is fixed, the so called Rashba spin splitting [10] due to SIA can be tuned by means of external gates that change the perpendicular electric field (E ⊥ ) in the sample. For many years it has been assumed that the Rashba spin splitting in 2D carrier systems is proportional to E ⊥ that characterizes the inversion asymmetry of the confining potential [4]. 2D holes contained in a GaAs square quantum well provide an example [11]. On the contrary, in the present work we show both experimentally and theoretically that for heavy holes confined to a triangular well at the GaAs/AlGaAs interface, spin splitting decreases with an increase in E ⊥ . We demonstrate this negative differential Rashba effect by analyzing the Shubnikov-de Haas oscillations in this system at a constant density. We note that hole systems have recently gained great attention for spintronics applications [12] because ferromagnetic (III,Mn)V compounds are intrinsically p type. A detailed understanding of the B = 0 spin splitting in hole systems is thus of great importance.The sample used in our study was grown on a GaAs (001) substrate by molecular beam epitaxy and contains a modulation-doped 2D hole system confined to a GaAs/AlGaAs heterostructure [ Fig. 1(a)]. The Al 0.3 Ga 0.7 As/GaAs interface is separated from a 16 nm thick Be-doped Al 0.3 Ga 0.7 As layer (Be concentration of 3.5 × 10 18 cm −3 ) by a 25 nm Al 0.3 Ga 0.7 As spacer layer. We fabricated Hall bar samples via lithography and used In/Zn alloyed at 440 • C for the ohmic contacts. Metal gates were deposited on the sample's front and back to c...

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confidence: 99%

Negative differential Rashba effect in two-dimensional hole systems

Habib

Tutuc

Melinte

et al. 2004

Applied Physics Letters

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“…At larger magnetic fields pairs of strong lines dominate the spectra. They shift with increasing magnetic field to higher energies similar to the light hole Landau levels [12]. A careful analysis of the spectra shows that each strong line is connected with a series of weaker lines at higher energies (Fig.…”

Section: [8]mentioning

confidence: 99%

“…2 are connected by bars and labelled by (N,., t;). N = na + M i +3/2 is the usual notation of Landau levels in spherical approximation which combines the oscillator quantum number na with the Bloch state angular momentum M i [5,12]. t; numbers the Coulomb states by counting the nodes of the envelope wave function on an axis parallel to the magnetic field [2].…”

Section: [8]mentioning

confidence: 99%

Magnetic field dependence of quasi-bound Coulomb states of light holes in germanium

Jungwirt¹,

Kropf²,

Roessler³

et al. 1989

Solid State Communications

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The photothermal spectra of the shallow acceptor boron in high purity p-Ge has been investigated for various magnetic field strengths at low temperatures. A large number of lines observed at frequencies above the binding energy of boron are attributed to optical excitation of quasi-bound Coulomb states, which arise in a magnetic field below each Landau level. By comparison with calculated Landau level energies the final states of the observed transitions can be unambigously identified.Shallow impurities in semiconductors represent hydrogen-like systems for which the high magnetic field case can be exprimentally realized by standard laboratory magnets due to the large effective Bohr radius. Therefore the optical excitation spectra of shallow impurities in a uniform magnetic field have been extensively studied by far-infrared (FIR) photothermal ionization and photoionization spectroscopy [1]. The hydrogen atom in a magnetic field is a fundamental problem of quantum theory, which cannot be solved in closed form because of different symmetries of the Coulomb potential and the uniform magnetic field. The energy spectrum of this system consists besides of continuum states, corresponding to Landau levels with quantum number n, of bound (stable) or quasi-bound (metastable) Coulomb states depending on their angular momentum quantum number m [2,3]. Due to the relation m < n, the Coulomb states connected with the higher Landau levels n > 1 and m < n -1 are degenerate with the continuum of lower Landau levels with the same m quantum number, to which they are coupled by the Coulomb potential. Thus autoionization transitions may occur and, therefore, these states are called quasi-bound or metastable. In contrast, the Coulomb states connected with the lowest Landau level n = 0 and m < 0 and those with n = m, which are not degenerate with a continuum, are bound or stable.In a previous investigation of shallow donors in nGaAs several structures in FIR photoconductivity spectra could be attributed to optical transitions from the donor ground state to those metastable states [4]. The identification of the final states was based on the fact that pairs of states with m = 4-1 separated by the cyclotron resonance energy hwc are optically accessible in Faraday configuration from the donor ground state using unpolarized light. In the fourfold degenerate valence band of tetrahedrally coordinated semiconductors the situation is more complex because the Landau levels are irregularly spaced [5]. Zverev et al. analyzed p-Ge in detail by investigating magneto-photoconductivity upon monochromatic irradiation [6] and optical phonon emission induced resonant recombination of holes excited by broad band infrared illumination [7]. For each degenerate Landau level they observed a single resonance attributed to quasi-bound acceptor states.In the present paper we report on FIR photoconductivity measurements on boron doped p-Ge carried out by Fourier-spectroscopy. In high purity samples a whole series of spectral lines has been observed and identified...

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“…Both KIKI* and X/' 1 are constructed with group theoretical methods (see refs. [2][3][4]). The parameters aK are the specific material constants (e.g.…”

Section: Physical Problemmentioning

confidence: 99%

“…To this end we change to a new set of canonical variables [3] and choose the direction of magnetic field and stress to be parallel to the [001] direction. Then the eigenstates are expanded into the elements of the orthonormal basis { I r; n (/aM)} for fixed r.…”

Section: Physical Problemmentioning

confidence: 99%

TRS: a program to calculate Landau levels and direct dipole transitions in uniaxially stressed semiconductors

Schmitz

Trebin

Rößler

1991

Computer Physics Communications

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Quantum resonances in the valence bands of semiconductors under uniaxial stress provide very detailed information on the band parameters if the experimental data can be analyzed on the basis of an adequate theoretical model. Trebin and R6ssler developed such a model for narrow-gap semiconductors with a zincblende lattice and applied it to lnSb. Using their theoretical results they wrote a program for the numerical evaluation of energy eigenvalues. wave functions and oscillator strengths for direct inter-and intraband dipole transitions. It is based on an effective Hamiltonian constructed by invariant expansion and describes the Landau levels in an eightfold space of valence and conduction bands when uniaxial stress and magnetic field are applied along the [001] direction. All eigenstates are evaluated for any three values of wave vector. magnetic field and stress. Recently. Schmitz made several improvements and additions to this program including a complete user interface making the program easy to use. adaptable to a wide variety of computers. and allowing calculations done systematically.

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Quantum resonances in the valence bands of zinc-blende semiconductors. I. Theoretical aspects

Cited by 226 publications

References 21 publications

Negative differential Rashba effect in two-dimensional hole systems

Negative differential Rashba effect in two-dimensional hole systems

Magnetic field dependence of quasi-bound Coulomb states of light holes in germanium

TRS: a program to calculate Landau levels and direct dipole transitions in uniaxially stressed semiconductors

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