The torsional vibration of atomic force microscope (AFM) cantilevers is critical for high-sensitivity measurements, yet existing models for width-varying cantilevers often rely on approximations that lead to significant discrepancies with experimental data. Unlike prior studies, this work introduces a refined analytical framework to precisely compute resonance frequencies and mode shapes, including higher-order modes, for overhang- and T-shaped microcantilevers, validated through targeted experimental comparisons. By systematically analyzing the effects of overhang length, we reveal previously unreported multi-maxima mode shapes and demonstrate how geometric tuning can controllably shift resonant frequencies. Furthermore, we establish a quantitative relationship between modal sensitivity and cantilever-surface coupling strength, providing actionable design principles for optimizing AFM cantilever performance. Our results not only reconcile theoretical predictions with experimental observations but also offer practical guidelines for tailoring cantilever geometry to achieve specific frequency responses in applications such as nanomechanical imaging and surface property mapping. This work advances the design of next-generation AFM probes by bridging the gap between analytical models and real-world operational demands.

Polariton lasing is a promising phenomenon with potential applications in next-generation lasers that operate without the need for population inversion. Applying a perpendicular magnetic field to a quantum well (QW) significantly alters the properties of exciton-polaritons. In this theoretical study, we investigate how the lasing threshold of QW exciton-polaritons depends on the magnetic field. By modifying the exciton's effective mass and Rabi splitting, the magnetic field induces notable changes in the relaxation kinetics, which directly affect the lasing threshold. For low-energy pumping, an increase in the magnetic field delays the lasing threshold, while for high-energy pumping, the threshold is reached at much lower pump intensities. Furthermore, increasing both the pump energy and the magnetic field enhances relaxation efficiency, leading to a substantially larger number of condensed polaritons. Our result gives insights into the modulation of exciton-polariton condensation through magnetic fields, with potential implications for the design of low-threshold polariton lasers.

We theoretically investigate the nonlinear effects of a magnetic field on the relaxation process of exciton-polaritons toward Bose-Einstein condensation in GaAs quantum wells. Our study reveals that the modification of the exciton's effective mass, Rabi splitting, and dispersion significantly alters the relaxation rate of polaritons as they approach condensation. By employing a quasi-stationary pump, we clarify the dynamics of the total and condensed polariton populations in response to varying magnetic field strengths. Notably, we demonstrate that under low-energy pumping conditions, the presence of a magnetic field significantly suppresses condensation. This suppression is attributed to the decreased scattering rate between energy levels, which is a consequence of the reduced steepness in the high-energy dispersion. Conversely, increasing both the pump energy and the magnetic field can enhance relaxation efficiency, leading to a substantially larger number of condensed polaritons.

We demonstrate that coupled AlGaN/GaN quantum wells with asymmetric widths (L_1-L_2&lt;30 A achieve up to 4.5 times higher mobility than single wells at optimal separation (d = 100 A). Crucially, mobility surpasses single wells when d>40 A reversing the trend at smaller distances. This enhancement stems from double-layer screening that suppresses remote/background impurities and dislocations, while LO phonon scattering remains unaffected. For identical wells, coupled systems underperform single wells at d<40 A but exceed them beyond this threshold. Peak gains occur at cryogenic temperatures (77 K). Our results provide a robust theoretical framework to optimize mobility in AlGaN/GaN heterostructures, reducing experimental trial-and-error in quantum device engineering.

We theoretically study the thermoelectric transport S in a double-layer bilayer graphene (BLG-GaAs-BLG) system on dielectric substrates (h-BN, Al2O3, HfO2). Electrons interact with GaAs acoustic phonons via both the deformation potential (acDP) and piezoelectric (acPE) scattering. Results show that piezoelectric scattering dominates the total transport, especially at low carrier density and high dielectric constant. Substrate dielectric constant significantly influences thermopower S, and the thermopower of the materials is in the order of HfO2 > Al2O3 > h-BN. When densities on two BLG layers are unequal, the contribution from acDP scattering Sd decreases (increases) at low (high) densities versus equal densities, while acPE scattering Sg remains stable, making S largely Sg-dependent. Increasing interlayer distance d enhances S, while higher temperature boosts Sd (notably at low densities) with minimal effect on Sg. These insights and substrate-dependent trends demonstrate substrate engineering as a key parameter for optimizing BLG thermoelectric devices

Coating and reflecting thin films for energy harvesting purposes are interesting topics in both theoretical and experimental research. The thin film could help to enhance the absorption of the system via its specific optical properties depending on the optical wavelength and the stacked layer thickness. Here, by using Maxwell's equations for the electromagnetic fields penetrating thin films, we examined in detail the absorption of a CTS layer coated by nanometer-thick thin films of several materials, Au, Ag, Cu, Al, and figured out the optimal thickness range for the outer layers of the solar cell to optimize thermal energy harvesting from the light. In particular, the absorption has been shown to be significantly enhanced thanks to the optical cavity effect, and the maximal absorption of the system could reach 60\% for ... These results could help in suitably choosing the detailed thickness for the structure of the solar cell and other energy harvesting objects.

High-harmonic (HH) frequencies in microcantilever impose several applications in precision detection thanks to the higher sensitivity of the higher modes in comparison to the fundamental modes. In this study, we showed that by tuning the cantilever length via changing the clamped position, the dimensional ratio of the overhang to the main cantilever part is altered and the HHs could be effectively obtained. Multiple HH frequencies have been achieved, from 4th to 8th order of the second- and from 11th to 26th order of the third-mechanical mode versus the first mode, and these orders are much higher if higher modes are used. The analytical calculation is in agreement with available results of other groups. HH behavior when the cantilever is interaction with sample is also examined and is strongly depending on the overhang parameters. These results could guide the experimentalist in the tuning and controlling of the HHs in detecting objects.