This study proposes an ultrahigh-sensitivity split-ring resonator-based microwave sensor for retrieving the complex permittivity of liquid samples. An interdigital capacitor structure was used to expand the sensing area and the sensitivity. A defected ground structure and A parallel dual split-ring resonator were introduced to improve the quality factor. A polydimethylsiloxane microfluidic channel substrate was placed above the interdigital capacitor structure. The channel route coincided with the interdigital gap to fully utilize the strong electric field. Ethanol–water solutions with varying ethanol fractions were injected into the channel as the testing liquid. It was demonstrated that the variation in resonant frequency can be used to retrieve the dielectric properties of liquid samples. The proposed sensor used a small liquid volume of ~0.68 μL and provided values in good agreement with the reference data.

This paper proposes a novel differential through-silicon via (D-TSV) structure, which is filled with vertically aligned carbon nanotube (VACNT) array. Two metal pads are deposited on the sides of the surface of the proposed D-TSV to form differential signal transmission paths. The equivalent circuit model is established for the proposed D-TSV, with the frequency-dependent impedance extracted using partial-element equivalent-circuit (PEEC) method. By virtue of the equivalent circuit model, the electrical performance of the proposed D-TSV is investigated, with some design guidance presented.

Atomic collapse in graphene nanoribbons behaves in a fundamentally different way as compared to monolayer graphene due to the presence of multiple energy bands and the effect of edges. For armchair nanoribbons we find that bound states gradually transform into atomic collapse states with increasing impurity charge. This is very different in zigzag nanoribbons where multiple quasi-one-dimensional bound states are found that originates from the zero-energy zigzag edge states. They are a consequence of the flat band and the electron distribution of these bound states exhibits two peaks. The lowest-energy edge state transforms from a bound state into an atomic collapse resonance and shows a distinct relocalization from the edge to the impurity position with increasing impurity charge.

The modification of the quantum states in a Dice lattice due to a Coulomb impurity are investigated. The energy-band structure of a pristine Dice lattice consists of a Dirac cone and a flat band at the Dirac point. We use the tight-binding formalism and find that the flat band states transform into a set of discrete bound states whose electron density is localized on a ring around the impurity mainly on two of the three sublattices. Its energy is proportional to the strength of the Coulomb impurity. Beyond a critical strength of the Coulomb potential atomic collapse states appear that have some similarity with those found in graphene with the difference that the flat band states contribute with an additional ringlike electron density that is spatially decoupled from the atomic collapse part. At large value of the strength of the Coulomb impurity the flat band bound states anticross with the atomic collapse states.

Atomic collapse can be observed in graphene because of its large “effective” fine structure constant, which enables this phenomenon to occur for an impurity charge as low as $Z_c\sim 1–2$. Here we investigate the effect of the sublattice symmetry on molecular collapse in two spatially separated charge tunable vacancies, which are located on the same (A-A type) or different (A-B type) sublattices. We find that the broken sublattice symmetry: (1) does not affect the location of the main bonding and antibonding molecular collapse peaks, (2) but shifts the position of the satellite peaks, because they are a consequence of the breaking of the local sublattice symmetry, and (3) there are vacancy characteristic collapse peaks that only occur for A-B type vacancies, which can be employed to distinguish them experimentally from the A-A type. As the charge, energy, and separation distance increase, the additional collapse features merge with the main molecular collapse peaks. We show that the spatial distribution around the vacancy site of the collapse states allows us to differentiate the molecular from the frustrated collapse.

The interplay between a magnetic field and the Coulomb potential from a charged vacancy on the electron states in graphene is investigated within the tight-binding model. The Coulomb potential removes locally Landau level degeneracy, while the vacancy introduces a satellite level next to the normal Landau level. These satellite levels are found throughout the positive-energy region, but in the negative-energy region, they turn into atomic collapse resonances. Crossings between Landau levels with different angular quantum number $m$ are found. Unlike the point impurity system in which an anticrossing occurs between Landau levels of the same $m$, in this work anticrossing is found between the normal Landau level and the vacancy-induced level. The atomic collapse resonance hybridizes with the Landau levels. The charge at which the lowest Landau level $m=-1,N=1$ crosses $E=0$ increases with enhancing magnetic field. A Landau level scaling anomaly occurs when the charge is larger than the critical charge $\beta \approx 0.6$ and this critical charge is independent of the magnetic field.