Higher Landau Levels Research Articles

Hall conductivity in n-type silicon inversion layers under strong magnetic fields

Abstract Quantitative results of the Hall conductivity σ xy as well as the transverse conductivity σ xx in silicon MOS inversion layers have been obtained successfully by use of the Hall current method. Experimental electron mobility dependence of the Landau level width in higher Landau levels are in good agreement with theoretical predictions. The electron localization in strong magnetic fields has been investigated by utilizing σ xy as well as σ xx .

Friedel sum rule in a static magnetic field

The Friedel sum rule in a static magnetic field is derived. The theory is applicable to arbitrary magnetic field strengths. No specific assumptions are imposed on the form of the impurity potential. The impurity-induced mixing between Landau levels is taken into account exactly. The increase in the number of states below the Fermi energy is obtained by considering the boundary-value problem of the one-electron wave function. It is shown that the sum rule is written in terms of the phase shifts derived by diagonalizing the 2 N F-dimensional S matrix ( N F is the quantum number specifying the highest Landau level below the Fermi energy). The sum rule, however, is shown to contain important E-independent terms which arise due to the one-dimensionality of the problem.

Quantum galvanomagnetic properties of n-type inversion layers on Si(100) MOSFET

Transverse magnetoconductivity σ xx and Hall effect in n-type inversion layers of Si(100) MOSFET are measured for various source-drain fields between 0.08 and 40 V/cm under magnetic fields up to 150 kOe at 1.4 K. Conductivity peaks in low Landau levels are in good agreement with theory. Effect of the source-drain field in the magnetoconductivity is found to be very important in higher Landau levels as well as in the appearance of the lowest Landau level peak. Immobile electrons are clearly observed in conductivity bottoms. Electrode geometry effect for Hall effect measurement under strong magnetic fields is discussed.

Temperature dependence of far-infrared cyclotron resonance of n-type germanium

Cyclotron resonance has been observed on n-Ge samples of varying doping concentrations with the radiation of an HCN laser. A shift of the transverse-mass resonance with increasing temperature has been found. This is explained by the increasing population of higher Landau levels which are not equally spaced due to the nonparabolicity of the conduction band. It seems that the use of a value of 2.2 eV for the direct gap epsilon G(L1,L3') at the L-point of the Brillouin zone underestimates the nonparabolicity as already observed in magnetopiezotransmission experiments.

Magnetophonon Resonance of Hot Electrons in n-InSb at 77 K

Magnetophonon resonances, which were first predicted by Gurevich and Firsov, have been observed in the hot electron mobility in pure n -InSb. The resonance experiment was carried out at 77 K in transverse magnetic field up to 22 kG with application of sufficiently small electric field to produce a slight change in the electron mobility. The quantity β in the formula µ=µ 0 (1-β E 2 ) was measured with extremely good accuracy ( Δ µ/µ 0 ∼10 -7 ) by adopting a bridge circuit. The minima in the quantity |β| were observed at magnetic fields, B =17.5, 11.3, 8.53, 6.89, 5.72, 4.83, 4.12, 3.68, 3.72, and 2.93 kG. These resonance extrema are attributed to resonant cooling of hot electrons due to optical phonon induced transitions from the high energy tail of the electron distribution near k z =0 at higher Landau levels to lower Landau levels. The extremal positions are well explained by taking the non-parabolicity of the conduction band of InSb into account.

Magneto-absorption in CdS

We have investigated the 2°K absorption spectra of CdS between 4700 Å and 4860 Å for magnetic fields up to 100 kG. We find that excitonic effects are important for the two lowest Landau levels but not for the third or higher Landau levels. The most interesting feature of the data is that the higher excited states ( n ⩾ 3) of the exciton are associated with the two lowest Landau levels. These results are discussed and compared with those in other materials. A reduced effective mass of 0.18m 0 has been deduced.

Shubnikov-de Haas Measurements in Bismuth

The oscillatory transverse magnetoresistance (Shubnikov---de Haas effect) has been measured for the magnetic field in the binary and trigonal planes of single-crystal bismuth at liquid-helium temperatures, using a technique which permits accurate identification and determination of the periods and measurement of the amplitudes. Periods observed in high-purity samples [resistivity ratios $(\frac{{R}_{300 ^{\ensuremath{\circ}}\mathrm{K}}}{{R}_{4.2 ^{\ensuremath{\circ}}\mathrm{K}}})\ensuremath{\gtrsim}400$] can be fit to the generally accepted Fermisurface model of one hole ellipsoid and three tilted electron ellipsoids. For resistivity ratios $\ensuremath{\lesssim}300$, additional periods are observed which recently have been shown to be caused by twinning. The effects of twinning, together with the difficulty in interpreting oscillatory resistivity data taken by traditional techniques, are suggested as explanations for the many spurious periods reported in the literature and used as arguments for additional pieces of the Fermi surface. By fitting the amplitudes of the oscillations to the theory for the magnetoresistance of an electron gas with level (Dingle) broadening, the Dingle temperatures of holes and electrons were found to be (0.7\ifmmode\pm\else\textpm\fi{}0.2) and (0.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode^\circ\else\textdegree\fi{}K, respectively. These values are comparable with earlier results of Bhargava from de Haas-van Alphen (thermodynamic as opposed to transport) measurements, but are 50 times larger than the values estimated from zero-field conductivity. Agreement within a factor of 2 is obtained when the increased scattering of carriers in the highest Landau level, due to their low velocities along the magnetic field, is considered.

Photoreflectance from Landau Levels in InSb

We report the first observation of photoreflectance in an applied magnetic field. Oscillatory structure shown to be due to Landau levels is observed in InSb at photon energies up to 150 meV above the band gap. The observation of this structure demonstrates clearly that the dominant physical mechanism in the photoreflectance effect is not band filling, as proposed recently by several authors, since the higher Landau levels have no significant population.