Bare Band Mass Research Articles

Quantum oscillations in the type-II Dirac semi-metal candidate PtSe2

Three-dimensional topological semi-metals carry quasiparticle states that mimic massless relativistic Dirac fermions, elusive particles that have never been observed in nature. As they appear in the solid body, they are not bound to the usual symmetries of space-time and thus new types of fermionic excitations that explicitly violate Lorentz-invariance have been proposed, the so-called type-II Dirac fermions. We investigate the electronic spectrum of the transition-metal dichalcogenide PtSe2 by means of quantum oscillation measurements in fields up to 65 T. The observed Fermi surfaces agree well with the expectations from band structure calculations, that recently predicted a type-II Dirac node to occur in this material. A hole- and an electron-like Fermi surface dominate the semi-metal at the Fermi level. The quasiparticle mass is significantly enhanced over the bare band mass value, likely by phonon renormalization. Our work is consistent with the existence of type-II Dirac nodes in PtSe2, yet the Dirac node is too far below the Fermi level to support free Dirac–fermion excitations.

Observation of microwave induced resistance and photovoltage oscillations in MgZnO/ZnO heterostructures

Microwave induced resistance and photovoltage oscillations were investigated in ${\mathrm{Mg}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}\mathrm{O}/\text{ZnO}$ heterostructures. The physics of these oscillations is controlled significantly by scattering mechanisms, and therefore these experiments were motivated by the recently achieved high quality levels in this material and the apparent dominance of large angle, short-range scattering, which is distinct from the prevailing small angle scattering in state-of-the-art GaAs structures. Within the studied frequency range of 35--120 GHz, up to four oscillations were resolved at 1.4 K temperature, but only in high density samples. This allowed us to extract the value of the effective electron mass ${m}^{*}=(0.35\ifmmode\pm\else\textpm\fi{}0.01){m}_{0}$, which is enhanced over the bare band mass, and estimate a local quantum scattering time of about 5 ps.

2kF-selected conductance oscillations of high-mobility two-dimensional electron gas in Corbino devices

We have observed electrical-field induced magneto-conductivity oscillations measured in Corbino samples made of a GaAs high-mobility two-dimensional electron gas, and found a consistent interpretation based on a semiclassical model of 2kF-selected orbital transitions between N and N + 1, 2, 3,…, Landau levels at respective local potentials, where kF is the Fermi wavevector. From the oscillation period, we deduce an effective mass value, which is consistent with the bare electron band mass of GaAs. In the same devices but with a vanishing electrical field and at elevated temperatures, we observed additional oscillation features, which can be attributed to cyclotron resonance by population of acoustic phonons. We thus demonstrate a method to determine the carrier effective mass and the sound velocity of host crystals by standard electrical transport.

Density-of-state effective mass and non-parabolicity parameter of impurity doped ZnO thin films

The density-of-state effective masses of impurity doped polycrystalline ZnO thin films were measured by the method of four coefficients technique. By applying the first-order non-parabolicity approximation, the polaron effective mass and the bare band mass at the conduction band minimum, together with the corresponding non-parabolicity parameters, were analysed successfully. The determined perpendicular polaron mass of 0.29 me and the bare band mass of 0.247 me at the conduction band minimum corresponded very well to the previous results obtained for ZnO single crystals. The non-parabolicity parameter of 0.457 eV−1 derived for the polaron effective mass was larger than 0.33 eV−1 which was obtained for the bare band mass due to the increasing function of the Fröhlich coupling constant with respect to the bare band mass in polycrystalline ZnO films.

Electron effective mass in ultrathin oxide silicon MOSFET inversion layers

The effective mass (m*) of two-dimensional electrons in silicon metal–oxide–semiconductor field-effect transistors (MOSFETs), obtained from measurements of the thermal damping of Shubnikov–de Haas oscillations, has been studied as a function of electron density (ns) for samples with physical gate oxide thicknesses (dox) of 4.7 nm and 3.1 nm. For the latter at a low electron density, the ratio (aBrs)/dox (where rs is the interaction parameter and aB is the Bohr radius in the semiconductor) exceeded 2 and the modification of the electron–electron interaction potential by the presence of the metallic gate was expected to be manifested as a change in the interaction-driven enhancement of the effective mass with increasing rs. The deduced mass enhancement in both thin-oxide samples is well described by m*/mb = 0.96 + γrs, where mb is the bare band mass within the plane of confinement, and γ is a constant. Although the results from both samples are in good quantitative agreement with previous experiments on thicker-oxide MOSFETs, a small but significant difference in the extracted value of γ between the thin-oxide samples was observed. This difference cannot, however, be unambiguously interpreted as a true renormalization of m* caused by the screening effect of the gate.

Polaron crossover in molecular solids

An analytical variational method is applied to the molecular Holstein Hamiltonianin which the dispersive features of the dimension dependent phonon spectrumare taken into account by a force constant approach. The crossover between alarge and a small size polaron is monitored, in one, two and three dimensionsand for different values of the adiabatic parameter, through the behaviour of theeffective mass as a function of the electron–phonon coupling. By increasing thestrength of the intermolecular forces the crossover becomes smoother and occurs athigher e–ph couplings. These effects are more evident in three dimensions. Weshow that our modified Lang–Firsov method starts to capture the occurrence of apolaron self-trapping transition when the electron energies become of order of thephonon energies. The self-trapping event persists in the fully adiabatic regime. Atthe crossover we estimate polaron effective masses of order times the bare band mass according to the dimensionality and the value of the adiabaticparameter. Modified Lang–Firsov polaron masses are substantially reduced intwo and three dimensions. There is no self-trapping in the antiadiabatic regime.

Polaronself-trapping in a honeycomb net

Small-polaron behaviour in a two-dimensional honeycomb net isstudied by applying the strong-coupling perturbative method to theHolstein molecular crystal model. We find that small opticalpolarons can be mobile also if the electrons are strongly coupled tothe lattice. Before the polarons localize and become very heavy,there is in fact a window of electron-phonon couplings in which thepolarons are small and have masses of order ≃5-50 timesthe bare band mass according to the value of the adiabaticityparameter. The two-dimensional honeycomb net favours the mobilityof small optical polarons, in comparison with the square lattice.

Magneto-Polarons in a Harmonic Quantum Dot11The project supported in part by the Youth Science Foundation of Shanghai Jiao Tong University (China) under Grant No. A2132.

We study cyclotron resonance of magnetopolarons in a harmonic quantum dot. The results show that for weak magnetic field , the cyclotron mass in a harmonic quantum dot is split into two cyclotron masses and . One is larger than the bare band mass for large quantum dots but is lower than the bare band mass for small quantum dots, and with decreasing the effective confinement length of the quantum dot, the negative mass renormalization for the small quantum dots is important. The other is greater than the bare band mass and might be a measurable effect fbr the small quantum dots.

Resonant Magnetic Fields of a Magnetopolaron in a Parabolic Quantum Dot

It is shown that for a resonant magnetic field, the two cyclotron masses in a parabolic quantum dot are split into two cyclotron masses, respectively. The cyclotron mass decreases with decreasing the size of the quantum dot, the stronger the magnetic field strength, the larger the cyclotron mass. The lower branch of the cyclotron mass increases linearly with increasing the magnetic field strength. The upper branch of the cyclotron mass is larger than the bare band mass and enhances as the magnetic field strength increases.

FERMI SURFACES OF ORGANIC SUPERCONDUCTORS

In this review an overview of the present-day knowledge of the Fermi surfaces of organic superconductors obtained by Shubnikov-de Haas (SdH) and de Haas-van Alphen (dHvA) experiments is given. Almost all measurements reported here were made on charge transfer salts of the type (ET)2X where ET stands for bis(ethelenedithio)-tetrathiafulvalene (or BEDT-TTF) and X is a monovalent anion. The ET-salts are characterized by their extremely two-dimensional properties. Some unique features resulting from this two-dimensionality, like gigantic SdH and dHvA oscillations, directly observable spin-splitting far from the quantum limit and a distinctive angular dependence of the dHvA amplitude will be discussed in detail. By comparison of the measured cyclotron effective mass with the bare band mass the electron-phonon coupling constant can be extracted and the validity of the BCS formula for the superconducting transition temperature can be checked.

Cyclotron resonance of magnetopolarons in a parabolic quantum dot in strong magnetic fields.

Cyclotron resonance of magnetopolarons in a parabolic quantum dot with a strong magnetic field normal to the plane of the quantum dot is investigated theoretically. It is shown that for a strong magnetic field (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\gg}${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$), the cyclotron mass in a parabolic quantum dot is split into two cyclotron masses (${\mathit{m}}_{+}^{\mathrm{*}}$ and ${\mathit{m}}_{\mathrm{\ensuremath{-}}}^{\mathrm{*}}$). One (${\mathit{m}}_{+}^{\mathrm{*}}$) is lower than the bare band mass, but increases with increasing effective confinement length of the quantum dot, and approaches that of the two-dimensional case. The other (${\mathit{m}}_{\mathrm{\ensuremath{-}}}^{\mathrm{*}}$) is greater than the bare band mass and might be a measurable effect for small quantum dots.

Cyclotron resonance of magnetopolaron in a parabolic quantum dot in weak magnetic fields

Cyclotron resonance of magnetopolarons in a parabolic quantum dot with weak magnetic field normal to the plame of the quantum dot is investigated theoretically. It is shown that for weak magnetic field (ω c ⪡ ω LO), the cyclotron mass in a parabolic quantum dot is split into two cyclotron masses ( m ∗ + and m ∗ -). One ( m ∗ +) is larger tham the bare band mass for large quantum dots but is lower than the bare band mass for small quantum dots, and with decreasing the effective confinement length of the quantum dot, the negative mass renormalization for the small quantum dots is important. The other ( m ∗ -) is greater than the bare band mass and might be a measurable effect for the small quantum dots.

Cyclotron resonance of a magnetopolaron in a harmonic quantum dot in resonant magnetic fields

Cyclotron resonance of a magnetopolaron in a harmonic quantum dot with the resonant magnetic field normal to the plane of the quantum dot is investigated theoretically. It is shown that for a resonant magnetic field, the two cyclotron masses ( m ∗ + and m ∗ −) in a harmonic quantum dot are each split into two cyclotron masses, respectively. The cyclotron mass ( m ∗ +) decreases with decreasing size of the quantum dot, the stronger the magnetic field strength, the larger the cyclotron mass. The lower branch of the cyclotron mass ( m ∗ −) increases linearly with increasing magnetic field strength. The upper branch of the cyclotron mass ( m ∗ −) is larger than the bare band mass and enhances as the magnetic field strength increases.

Theory of Two-Dimensional Magnetopolarons

Two-dimensional weak-coupling Fr\ohlich polarons are investigated theoretically in the presence of an external magnetic field normal to the two-dimensional plane. For a weak magnetic field (${\ensuremath{\omega}}_{c}\ensuremath{\ll}{\ensuremath{\omega}}_{\mathrm{LO}}$), the cyclotron mass approaches the zero-field polaron effective mass, whereas for large fields (${\ensuremath{\omega}}_{c}\ensuremath{\gg}{\ensuremath{\omega}}_{\mathrm{LO}}$), the cyclotron mass approaches the bare band mass from below. In the resonance situation (${\ensuremath{\omega}}_{c}\ensuremath{\approx}{\ensuremath{\omega}}_{\mathrm{LO}}$), the cyclotron mass shows an enhanced polaronic renormalization effect. Connection is made with recent data on magnetoabsorption in semiconductor space-charge layers, explaining why polaron effects show up only in some experiments.

Theory of Two-Dimensional Magnetopolarons

Two-dimensional weak-coupling Fr\"ohlich polarons are investigated theoretically in the presence of an external magnetic field normal to the two-dimensional plane. For a weak magnetic field (${\ensuremath{\omega}}_{c}\ensuremath{\ll}{\ensuremath{\omega}}_{\mathrm{LO}}$), the cyclotron mass approaches the zero-field polaron effective mass, whereas for large fields (${\ensuremath{\omega}}_{c}\ensuremath{\gg}{\ensuremath{\omega}}_{\mathrm{LO}}$), the cyclotron mass approaches the bare band mass from below. In the resonance situation (${\ensuremath{\omega}}_{c}\ensuremath{\approx}{\ensuremath{\omega}}_{\mathrm{LO}}$), the cyclotron mass shows an enhanced polaronic renormalization effect. Connection is made with recent data on magnetoabsorption in semiconductor space-charge layers, explaining why polaron effects show up only in some experiments.

Effect of the electron-phonon interaction on the subband structure of inversion layers in compound semiconductors

Recently electron inversion layers have been fabricated on a number of compound (principally III–V) semiconductors. Because of the polar nature of these materials, the effect of the electron-optical phonon interaction is expected to be significant. This has certainly been true in recent calculations of the ground state energy and equilibrium density of electron-hole liquids in a number of compound semiconductors [1]. We have calculated the subband structure of inversion layers in polar semiconductors. The starting point of our many-body calculation is the Hartree subband structure determined using a variational method described in ref. [2]. Using the Hartree wavefunctions as basis functions we have calculated the self-energy of the ground and first excited subbands to lowest order in the effective interaction. This interaction is the sum of Coulomb (direct and image) and electron-phonon terms which are screened by a dielectric function that includes both e-e and e-ph effects. The screening by inversion layer electrons has been treated in the plasmon-pole approximation. We have obtained the electron self-energy, the quasi-particle energy, and the subband separations as a function of inversion layer concentration for parameters corresponding to GaAs. The coupling of electrons to bulk phonons is considered. Our results are compared to those obtained using the simpler ϵ 0 ∗ approximation [1]. Here, explicit phonon terms are neglected, but the bare band mass is replaced by the polaron mass, and the high frequency dielectric constant (ϵ ∞) is replaced by the static dielectric constant (ϵ 0). This approximation has been applied to the electron-hole liquid for situations in which the optical phonon frequency is larger than the electron plasma frequency. The idea behind the ϵ 0 ∗ approximation is to account in a very rough way for vertex corrections to the electron-phonon interaction. A principal criticism of our dynamic RPA calculations is the neglect of vertex corrections in the effective interaction. In three-dimensional metallic systems (high density), Migdal's theorem applies and vertex corrections are small. However, it is not clear that we may neglect such corrections in inversion layers. This point will be discussed further.

Piezoelectric polaron and polaron pinning inn−CdS

The cyclotron resonance of the piezoelectric polaron in $n\ensuremath{-}\mathrm{C}\mathrm{d}\mathrm{S}$ has been investigated using far-infrared spectroscopy at magnetic fields to 90 kOe. Both lamellar grating and Michelson Fourier-transform spectrometers were used with a 0.3-K Ge bolometer to study the photon energy region from 10 to 60 ${\mathrm{cm}}^{\ensuremath{-}1}$. The theory of Miyake predicts that the frequency of the polaron's cyclotron resonance is shifted from the bare band electron resonance frequency according to the expression $\frac{\ensuremath{\Delta}{\ensuremath{\omega}}_{c}^{p}}{{\ensuremath{\Omega}}_{c}} \ensuremath{\propto} {H}^{\ensuremath{-}1}{T}^{\frac{2}{3}}$. The magnetic field dependence of the present cyclotron resonance confirms this expression; the cyclotron mass is decreased by piezoelectric polaron effects. The bare band mass in $n\ensuremath{-}\mathrm{C}\mathrm{d}\mathrm{S}$ has also been determined by taking into account the Fr\ohlich polaron interaction in addition to the piezoelectric polaron effects. For $H$ parallel to the $c$ axis this cyclotron mass is $(0.155\ifmmode\pm\else\textpm\fi{}0.005)m$. Finally, the polaron pinning due to the 43-${\mathrm{cm}}^{\ensuremath{-}1}$ optically inactive phonon has been observed.