Magnetophonon Resonance Research Articles

Landau level transition and magnetophonon resonance in a twisted bilayer graphene

We perform resonant Raman spectroscopy on 8° twisted bilayer graphene placed in an out-of-plane magnetic field. The high-quality device has narrow Landau level linewidth of less than 5 meV that enables detection of features from both electronic Raman scattering and magnetophonon resonance involving electronic transitions between the low energy Landau levels. Two magnetophonon resonances are observed, one at 4.6T in the strong coupling regime, and the other at 2.6T in the weak coupling regime. Using the measured Landau level transition energy, we analyze the renormalization of effective band velocity, whose dependence on magnetic field points to a 20% enhancement of dielectric constant due to the presence of an adjacent graphene layer, a quite prominent screening effect from a monolayer of carbon atoms in proximity. Both the Landau level transition electronic Raman and the magnetophonon resonance are gate tunable. Harnessing angular momentum conservation, we demonstrate charge tuning of electron phonon coupling strength for left and right circularly polarized G band phonons separately.

Absorption and emission of longitudinal optical phonons by confined electrons in Pöschl–Teller quantum wells under the effects of the aluminum concentration, temperature, and hydrostatic pressure

In this study, we investigated the simultaneous effects of the alloy concentration, electron temperature, and hydrostatic pressure on the magneto-optical transport properties (MOTPs) of GaAs/AlηGa1−ηAs Pöschl–Teller quantum wells (QW) by using the operator projection method and profile technique. The optical absorption power and full width at half maximum were calculated and compared for the optically detected magneto-phonon resonance peaks with phonon absorption and emission. In addition, the main results were compared with those for the rectangular potential QW. The results showed that the alloy concentration, electron temperature, and hydrostatic pressure greatly influenced the MOTPs of the GaAs/AlηGa1−ηAs Pöschl–Teller QW in both cases with the absorption and emission of phonons. In addition, these effects were greater when the degree of asymmetry was stronger for the Pöschl-Teller QW. Our results also demonstrated that the combined effects of the alloy concentration, electron temperature, and hydrostatic pressure on the MOTPs of the GaAs/AlηGa1−ηAs Pöschl-Teller QW were always greater in the phonon absorption case than the phonon emission case. Furthermore, the combined effects of these three parameters on the MOTPs of the Pöschl-Teller potential QW were greater than those on the rectangular potential QW in both the phonon emission and absorption processes.

Magneto-transport properties of monolayer borophene in perpendicular magnetic field: influence of electron-phonon interaction

The magneto-transport properties of a borophene monolayer in a perpendicular magnetic field B are studied via calculating the conductivity tensor and resistance under electron-optical phonon interaction by using the linear response theory. Numerical results are obtained and discussed for some specific parameters. The magnetic field-dependent longitudinal conductivity shows the magneto-phonon resonance effect that describes the transition of electrons between Landau levels by absorbing/emitting an optical phonon. The Hall conductivity increases first and then decreases with the magnetic field strength. Also, the longitudinal resistance increases significantly with increasing temperature, which shows the metal behaviour of the material. Practically, the observed magneto-phonon resonance can be applied to experimentally determine some material parameters, such as the distance between Landau levels and the optical phonon energy.

Combined influences of temperature, pressure, and alloy-composition on magneto-optical properties of the semi-parabolic well under all four different phonon models

In this study, combined influences of the pressure, alloy composition, and temperature on the magneto-optical properties of the semiparabolic well under all four different phonon models, including three confining phonon models are considered in detail through the magneto-phonon resonance oscillation (MPRO). The magneto-optical transport absorption power (MOTAP) and MO-conductivity tensor (MOCT) expressions are obtained utilizing the method of operator projection. Simultaneously the profile method also is used in order to measure the inter-subband absorption linewidth. Our calculated result shows that (i) the aluminum composition y has significant effect on the position of the resonant peak; (ii) the absorption line-width as a function of the Al-composition, temperature of electron, and hydrostatic pressure for all four models of phonons; (iii) the influence of the Al-composition, temperature of electron, and pressure on the intersubband absorption line-width is different for each of phonon model; (iv) our present result is fairly consistent with experimental measurement; (v) combined effects of the aluminum composition, the temperature of electron, and the hydrostatic pressure on the intersubband absorption line-width of the semiparabolic QWs are important when the phonon confinement is taken into consideration.

Intersubband absorption linewidth in a semi-parabolic quantum well: Comparison among three different phonon models

In this article, effects of different confined phonon models on intersubband absorption linewidth in semiparabolic quantum well (SPQW) is studied in detail through considering the optically detected magneto-confined phonon resonance (ODMCPR) effect. The projection operator and profile methods are utilized in order to calculate the linear conductivity tensor as well as magneto-phonon resonance absorption power (MPRAP) and measure the absorption linewidth or the full width at half maximum (FWHM) at the ODMCPR peak, respectively. We find that (i) the FWHM (absorption linewidth) as functions of the temperature, Landau level, and confining potential frequency; (ii) there is a different dependence in slab and guided phonon modes, as well as Huang–Zhu (HZ) phonon mode model on the FWHM; (iii) the confined phonon modes have great influence on the intersubband absorption linewidth in semiparabolic quantum well; (iv) the present calculations accord well with previous experimental studies.

One-dimensional cylindrical quantum wire: The theoretical study of photo-stimulated Ettingshausen effect

Based on the quantum kinetic equation (QKE) for electron, we have theoretically studied the theory of photo-stimulated Ettingshausen effect in a one-dimensional cylindrical quantum wire (CQW). The strong electromagnetic wave (EMW) [Formula: see text] plays a role as photo-stimulation source. We obtain the analytic expressions for the kinetic tensors [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the Ettingshausen coefficient (EC) in the CQW with the dependence on the amplitude and the energy of EMW, the CQW radius, the magnetic field and the temperature for two cases: optical phonon and acoustic phonon. The results are numerically evaluated and graphed for GaAs/AlGaAs CQW model. It is shown that we observe the cyclotron resonance and magneto-phonon resonance effect while surveying EC in terms of magnetic field (with and without EMW) and EMW energy, considered the electron-optical phonon scattering. In case of electron-acoustic phonon scattering, the oscillation of EC is obtained with the transition between low Landau levels (LLs). We also clarify the impact of quantum size effect (QSE) on EC by surveying the influence of EC on the radius of CQW.

Graphene\u2019s non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.

Comparison of the magneto-optical properties of the semi-parabolic well with those of the parabolic and rectangular wells under the combined influences of aluminum concentration and hydrostatic pressure

In this paper, we report the comparison of the magneto-optical transport properties of the semi-parabolic potential quantum well with those of the parabolic and rectangular potential quantum wells under the combined influences of the aluminum concentration, the temperature, the hydrostatic pressure, and the Landau levels by using the methods of the quantum field theory for many-particle systems in statistical physics and the profile to calculate analytically the conductivity tensor expression, the magneto-optical absorption power expression of the optically detected magneto-phonon resonance (ODMPR) oscillation, and the full width at half maximum (FWHM) of the ODMPR peak, respectively, in quantum wells with three above different confining potential shapes for typical GaAs/AlxGa1−xAs material. The results obtained from the present study show that (i) the ODMPR peak position undergoes a red-shift as the aluminum concentration and the hydrostatic pressure increase while it experiences a blue-shift as the temperature augments for all three above confining potential shapes; (ii) the FWHM as functions of the barrier's Al-concentration, the system's temperature, and the hydrostatic pressure for all three confining potential shapes is presented to compare; (iii) the dependence of the FWHM on the barrier's Al-concentration and the hydrostatic pressure for the Landau levels for three confining potential shapes also is taken into account in detail; (iv) our present theoretical calculations are found to be consistent with previous experimental calculations.

Comparison of the contribution of different types of interface-optical phonon modes to electron–phonon scattering in a quasi-two-dimensional system

Utilizing the operator projection technique, we theoretically study the contribution of different types of optical phonon modes to electron–phonon scattering in a quasi-two-dimensional system through calculating the expression for the magnetophonon resonance absorption power (MPR-AP) caused by scattering between the electrons with interface-optical phonons in parabolic quantum wells (PQWs). Electron interactions with different modes of interface-optical-phonons include the symmetric and antisymmetric modes in both the barrier and well layers together are considered in detail. The full width at half maximum (FWHM) of the resonant peaks due to different interface-optical-phonon modes was measured by using the profile method. Numerical results show that the strength of electron–interface-phonon interaction increases with confining frequency of parabolic confinement potential, temperature, and magnetic field under all antisymmetric- and symmetric-modes in both well and barrier layers. The electron-interaction with symmetric-interface-phonon has stronger strength compared to antisymmetric-interface-phonon in all well and barrier layers. The strongest-electron-scattering for symmetric phonon in well layer, meanwhile weakest that for antisymmetric phonon in barrier layer. At higher value of the photon frequency, the contributions of interface-optical-phonons is not significant. Our present calculations well accord with previous experimental and theoretical studies.

Electrical Control over Phonon Polarization in Strained Graphene.

We explore the tunability of the phonon polarization in suspended uniaxially strained graphene by magneto-phonon resonances. The uniaxial strain lifts the degeneracy of the LO and TO phonons, yielding two cross-linearly polarized phonon modes and a splitting of the Raman G peak. We utilize the strong electron-phonon coupling in graphene and the off-resonant coupling to a magneto-phonon resonance to induce a gate-tunable circular phonon dichroism. This, together with the strain-induced splitting of the G peak, allows us to controllably tune the two linearly polarized G mode phonons into circular phonon modes. We are able to achieve a circular phonon polarization of up to 40% purely by electrostatic fields and can reverse its sign by tuning from electron to hole doping. This provides unprecedented electrostatic control over the angular momentum of phonons, which paves the way toward phononic applications.

Magnetophonon resonance on the phonon frequency difference in quasi-free-standing graphene

The structure of magnetoresistance curves as a function of magnetic field from 0 to 14 T at temperatures from 0.4 to 6.0 K for macroscopic samples of the quasi-free-standing (QFS) graphene monolayer on SiC substrate, are observed and analyzed, and also the spatial and depth frequency distribution of phonons have been measured using the micro-Raman spectroscopy (MRS). That one enables us to interpret the obtained resonance magnetoresistance curves based on the electron-phonon (e-p) interaction taking into account the actually observed phonon spectrum in researched samples: in the case of a linear e-p interaction the observation of the corresponding peaks on the ${R}_{xx}(B)$ curves is difficult because an uninterrupted background is created. While nonlinear MPR with simultaneous G-phonon emission and D-phonon absorption occur in magnetic fields below 5 T against the background of MPR due to linear e-p interaction as well as Shubnikov--de Haas oscillations.

Magneto-optical transport properties of parabolic potential GaAs/Ga1−Al As wells under the influence of Al concentration and hydrostatic pressure

Abstract Magneto-optical transport properties of GaAs/Ga1−κAlκAs parabolic potential quantum-wells (PQWs) under the effects of Al-contents, hydrostatic pressure, and temperature is examined by studying their effects on the absorption power (AP) for magnetophonon resonance (MPR) and on the full width at half maximum (FWHM) of the optically-detected-MPR (ODMPR) peak due to modes confinement represented by slab-mode model, Huang-Zhu (HZ) model, guided-mode model. The numerical results indicate the Al-contents, pressure, as well as temperature which have great effect on the AP and FWHM in PQWs. Moreover, the results are also compared to bulk phonon modes for both two processes of phonons (emission and absorption). The results denote that phonon absorption process is always much more dominant compared to phonon emission process for four types of above phonons. In particular, the influences of pressure, Al-concentration in Ga1−κAlκAs barriers on the magneto-phonon resonance AP and FWHM in PQWs are more pronounced as confined modes are taken into account.

Many‐Body Effects in Suspended Graphene Probed through Magneto‐Phonon Resonances

Micro‐magneto‐Raman scattering spectroscopy is made use of to probe magneto‐phonon resonances (MPR) in suspended mono‐ to pentalayer graphene. MPR correspond to avoided crossings between zone‐center optical phonons (G‐mode) and optically active inter‐Landau level (LL) transitions and provide a tool to perform LL spectroscopy at a fixed energy (≈197 meV) set by the G‐mode phonon. Using a single‐particle effective bilayer model, the velocity parameter associated with each MPR is readily extracted. A single velocity parameter slightly above the bulk graphite value suffices to fit all MPR for N ≥ 2 layer systems. In contrast, in monolayer graphene, it is found that the velocity parameter increases significantly from (1.23 ± 0.01) × 106 m s−1 up to (1.45 ± 0.02) × 106 m s−1 as the first to third optically active inter‐LL transitions couple to the G‐mode phonon. This result is understood as a signature of enhanced many‐body effects in unscreened graphene.

Combined effects of temperature, hydrostatic pressure, and aluminum concentration on the magneto-optical properties of GaAs/Al Ga1−μAs quantum wells when phonons are confined

Abstract The combined influence of temperature, hydrostatic pressure, and applied aluminum concentration on the magneto-optical properties of GaAs/AlμGa1−μAs quantum wells (QWs) is presented by considering the combined influences of them on the magnetophonon resonance absorption power (AP) and the full width at half maximum (FWHM) of the optically detected magneto-phonon resonance (ODMPR) peaks for both phonon absorption and emission processes when phonons are confined to describe by Huang and Zhu. The numerical results denote that the AP and the FWHM have great influence (strong dependence) on the applied aluminum concentration, the temperature, and hydrostatic pressure. Moreover, the results also indicate the value and variation of the FWHM with applied aluminum concentration, hydrostatic pressure, as well as temperature of the ODMPR peak for phonon absorption processes is always larger and faster in comparison with that phonon emission process for both the confined and bulk phonons. Especially, when the phonons are confined, the more pronounced these properties are.

Study of the Quantum Magneto-Thermoelectric Effect in the Two-Dimensional Compositional Superlattice GaAs/AlGaAs under the influence of an Electromagnetic Wave by Using the Quantum Kinetic Equation

The quantum magneto-thermoelectric effect in a two-dimensional compositional superlattice under the influence of an electromagnetic wave (EMW) in two cases is investigated. Two cases of the electron scattering mechanism are considered: the electron-acoustic phonon scattering and electron-optical phonon scattering. Analytical expressions for the quantum Ettingshausen coefficient (EC), the thermopower tensor, the thermoelectric tensor and the kinetic tensor are obtained by using a quantum kinetic equation. These expressions are numerically solved for the two-dimensional compositional superlattice GaAs/AlGaAs and the results are discussed. The results show that in the case of electron-acoustic phonon scattering, the Shubnikov-de Haas oscillations appear when we examine the dependences of the quantum EC, the thermopower tensor and the thermoelectric tensor on the magnetic field. In the case of electron-optical phonon scattering, resonance peaks that satisfy the condition of the inter-subband magneto-phonon resonance appear. In the two cases, the superlattice period (a parameter specific to the material) strongly affects the quantum magneto-thermoelectric effect. When the superlattice period is small, quantum EC oscillations (in the case of electron-acoustic phonon interaction) and quantum EC resonance peaks (in the case of electron-optical phonon interaction) appear. However, when the superlattice period is large, these oscillations and resonance peaks are not observed. Especially, the influence of electromagnetic waves on the quantum magneto-thermoelectric effect is also clarified. The quantum theory of the magneto-thermoelectric effect has been studied from low temperature to high temperature. This overcomes the limitations of the Boltzmann kinetic equation which was studied at high temperature. The results are new and can serve as a basis for further development of the theory of quantum magneto-thermoelectric effects in low-dimensional semiconductor systems.

Magnetophonon spectroscopy of Dirac fermion scattering by transverse and longitudinal acoustic phonons in graphene

Recently observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the experimental data over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements also provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4-150 K. A semiclassical description of magnetophonon resonance in graphene is shown to provide a simple physical explanation for the dependence of the magneto-oscillation period on carrier density. The correspondence between the quantum calculation and the semiclassical model is discussed.

Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.

Intervalley polaron in atomically thin transition metal dichalcogenides

We study theoretically intervalley coupling in transition-metal dichalcogenide monolayers due to electron interaction with short-wavelength phonons. We demonstrate that this intervalley polaron coupling results in (i) a renormalization of the conduction band spin splitting and (ii) an increase of the electron effective masses. We also calculate the renormalization of the cyclotron energy and the Landau level splitting in the presence of an external magnetic field. An inter-valley magneto-phonon resonance is uncovered. Similar, but much weaker effects are also expected for the valence band holes. These results might help to resolve the discrepancy between ab initio values of the electron effective masses and the ones deduced from magneto-transport measurements.

Magnetophonon resonance in quantum wells due to absorption and emission of confined phonon

In this paper, the effect of confined phonons described by the Huang-Zhu model, Ridley's guided mode model, and Fuchs-Kliewer slab mode model on the full-width at half-maximum (FWHM) of the optically detected magnetophonon resonance (ODMPR) peak for the inter-subband transitions (1–2) with the absorption/emission of phonon in GaAs quantum wells is investigated by using the projection operator method. The ODMPR conditions depend on the photon energy and well width are presented. Our numerical results show that the FWHM of the ODMPR peak for the inter-subband transitions with the absorption/emission of phonon increases with the growing temperature and decreases with the rise of well width for all models of phonons. Besides, the FWHM of the above ODMPR peaks for the bulk phonons has a smaller value and changes slower than it does for the confined phonons. The FWHM for the Huang-Zhu model is largest among three models of confined phonons (Huang-Zhu model, Ridley's guided mode model, and Fuchs-Kliewer slab mode model), while it for Ridley's guided mode model is smallest. This result is in good agreement with the theoretical results in Refs. [1–3]. In addition, the FWHM of the ODMPR peak for the inter-subband transitions with the emission of phonon has a smaller value than that for absorption of phonon for both the bulk and confined phonons. This result is in good agreement with the theoretical results in Ref. [4] but very different from that the theoretical results in Refs. [5,6].

Comparison of magneto-resonance absorption FWHM for the intrasubband/intersubband transition in quantum wells

We compare magneto-resonance absorption FWHM (full-width at half-maximum) for the intrasubband transition (1→1) to that for the intersubband transition (1→2) in a square GaAs quantum well by using the projection operator method due to confined LO-phonon delineated by the model of Fuchs-Kliewer, Ridley, and Huang-Zhu. The numerical results show that the FWHM of the optically detected magnetophonon resonance (ODMPR) peak for the intrasubband/intersubband transition decreases with the rise of the width of well and increases with the growing temperature for all models of phonon. This is in accordance with the result has been investigated in the theory and experimental [1,2]. Furthermore, the FWHM of the above ODMPR peaks for the bulk phonon has a smaller and changes slower than it does for the confined phonon. The FWHM for the Huang-Zhu model is largest among three models of confined phonon (Fuchs-Kliewer, Ridley, and Huang-Zhu model), while it for Ridley model is smallest. This result is in accordance with the results have been investigated in the theory [3,4]. In addition, the FWHM of the ODMPR peak for the intrasubband transition has larger value than that for intersubband transition for both the bulk and confined phonon, this is in accordance with the result has been investigated in the theory and experimental [5].