We theoretically study the Coulomb drag resistivity and plasmon modes behavior for a system composed of two parallel p-type doped GaS monolayers with Mexican-hat valence energy band using the Boltzmann transport theory formalism. We investigate the effect of temperature,$\ T$, carrier density,$\ p$, and layer separation,$\ d$, on the plasmon modes and drag resistivity within the energy-independent scattering time approximation. Our results show that the density dependence of plasmon modes can be approximated by$\ p^{0.5}$. Also, the calculations suggest a$\ d^{0.2}$ and a$\ d^{0.1}$ dependencies for the acoustic and optical plasmon energies, respectively. Interestingly, we obtain that the behavior of drag resistivity in the double-layer metal monochalcogenides swings between the behavior of a double-quantum well system with parabolic dispersion and that of a double-quantum wire structure with a large carrier density of states. In particular, the transresistivity value reduces exponentially with increasing the distance between layers. Furthermore, the drag resistivity changes as$\ T^{2}/p^{4}$ ($\ T^{2.8}/p^{4.5}$) at low (intermediate) temperatures. Finally, we compare the drag resistivity as a function of temperature for GaS with other Mexican-hat materials including GaSe and InSe and find that it adopts higher values when the metal monochalcogenide has smaller Mexican-hat height.
We present the ballistic quantum transport of a p-n-p bilayer silicene junction in the presence of spin-orbit coupling and electric field using a four-band model in combination with the transfer-matrix approach. A Mexican-hat shape of the low-energy spectrum is observed similarly to bilayer graphene under an interlayer bias. We show that while bilayer silicene shares some physics with bilayer graphene, it has many intriguing phenomena that have not been reported for the latter. First, the confined state producing a significantly non-zero transmission in Mexican hat. Second, the cloaking of the…
Mexican-hat dispersion of band electrons in two-dimensional materials attracts a lot of interest, mainly due to the Van Hove singularity of the density of states near the band edge. In this paper, we show that there is one more feature of such a dispersion, which also leads to nontrivial effects. It consists in the fact that the sign of the effective mass in the momentum space near the central extremum is opposite to the sign of the mass outside this region. For this reason, any localized potential that repels quasiparticles in the outer region attracts quasiparticles in the central region and…
Post-transition metal chalcogenides (PTMCs) such as GaSe, GaS, InSe, and InS have been proposed as promising thermoelectric materials due to low lattice conductivity, originating from the atomically layered structure, high Seebeck coefficient, and the anticipation that its figure-of-merit be improved when thinned to few-layers as the band structure turns into Mexican-hat valence band (MHVB). Here we show by ab initio calculations that the MHVB should be present even on thick films of InSe/GaSe type-II heterostructures, and a 50% enhancement on thermoelectric figure-of-merit zT at room-temperat…
Application of a perpendicular electric field induces a band gap in bilayer graphene, and it also creates a "Mexican hat" structure in the dispersion relation. This structure has unusual implications for the hydrogen-like bound state of an electron to a Coulomb impurity. We calculate the ground state energy of this hydrogen-like state as a function of the applied interlayer voltage and the effective fine structure constant. Unlike in the normal hydrogen atom, the resulting wavefunction has many nodes even in the ground state. Further, the electron state undergoes "atomic collapse" into the Dir…
The mid-infrared (MIR), far-infrared (FIR) to terahertz (THz) frequencies are the least developed parts of the electromagnetic spectrum for applications. Traditional semiconductor technologies like laser diodes and photodetectors are successful in the visible light range, but are still confronted with great challenges when extended into the MIR/FIR/THz range. In this paper, we demonstrate that topological insulators (TIs), especially those with Mexican-hat band structure (MHBS), provide a route to overcome these challenges. The optical responses of MHBS TIs can be one to two orders of magnitud…
Energy spectrum of biased bilayer graphene near the bottom has a "Mexican-hat"-like shape. For the Fermi level within the Mexican hat we predict that, apart from conventional magnetooscillations which vanish with temperature, there are additional magnetooscillations which are weakly sensitive to temperature. These oscillations are also insensitive to a long-range disorder. Their period in magnetic field scales with bias, V, as V^2. The origin of these oscillations is the disorder-induced scattering between electron-like and hole-like Fermi-surfaces, specific for Mexican hat.
We study the effect of electron-electron interactions in the electronic properties of a biased graphene bilayer. This system is a semiconductor with conduction and valence bands characterized by an unusual ``mexican-hat'' dispersion. We focus on the metallic regime where the chemical potential lies in the ``mexican-hat'' in the conduction band, leading to a topologically non-trivial Fermi surface in the shape of a ring. We show that due to the unusual topology of the Fermi surface electron-electron interactions are greatly enhanced. We discuss the possibility of an instability towards a ferrom…
We investigate the effect that the intrinsic spin-orbit and the inter- and intra-layer Rashba interactions have on the energy spectrum of either an unbiased or a biased graphene bilayer. We find that under certain conditions, a Dirac cone is formed out of a parabolic band and that it is possible to create a "Mexican hat"-like energy dispersion in an unbiased bilayer. In addition, in the presence of only an intralayer Rashba interaction, the K (K') point splits into four distinct ones, contrarily to the case in single-layer graphene, where the splitting also takes place, but the low-energy disp…
The band inversion has led to rich physical effects in both topological insulators and topological semimetals. It has been found that the inverted band structure with the Mexican-hat dispersion could enhance the interband correlation leading to a strong intrinsic plasmon excitation. Its frequency ranges from several $\mathrm{meV}$ to tens of $\mathrm{meV}$ and can be effectively tuned by the external fields. The electron-hole asymmetric term splits the peak of the plasmon excitation into double peaks. The fate and properties of this plasmon excitation can also act as a probe to characterize th…
We control the thickness of GaSe on the level of individual layers and study the corresponding optical absorption via highly sensitive differential transmission measurements. Suppression of excitonic transitions is observed when the number of layers is smaller than a critical value of 8. Through ab-initio modelling we are able to link this behavior to a fundamental change in the band structure that leads to the formation of a valence band shaped as an inverted Mexican hat in thin GaSe. The thickness-controlled modulation of the optical properties provides attractive resources for the developme…
We report density-functional-theory calculations of the electronic band structures and optical absorption spectra of two-dimensional crystals of Ga$_2$X$_2$ (X=S, Se, and Te). Our calculations show that all three two-dimensional materials are dynamically stable indirect-band-gap semiconductors with a Mexican-hat dispersion of holes near the top of the valence band. We predict the existence of Lifshitz transitions---changes in the Fermi-surface topology of hole-doped Ga$_2$X$_2$---at hole concentrations $n_{S}=7.96\times 10^{13}$ cm$^{-2}$, $n_{Se}=6.13\times 10^{13}$ cm$^{-2}$, and $n_{Te}=3.5…
