Plasmons probe the quantum response: Electronic systems are typically considered as classical Fermi liquids, and the quantum mechanical interactions and processes are usually only accessed at very low temperatures and high magnetic fields. Lundeberg et al. used tunable plasmons to probe the quantum response of the electron gas of graphene (see the Perspective by Basov and Fogler). They studied shape deformations of the Fermi surface during a plasmon oscillation, as well as many-body electronic effects. Science , this issue p. 187 ; see also p. 132

The electronic properties of the two-dimensional material silicene are strongly influenced by the application of a perpendicular electric field $E_z$ and of an exchange field $M$ due to adatoms positioned on the surface or a ferromagnetic substrate. Within the random phase approximation, we investigate how electron-electron interactions are affected by these fields and present analytical and numerical results for the dispersion of plasmons, their lifetime, and their oscillator strength. We find that the combination of the fields $E_z$ and $M$ brings a spin and valley texture to the particle-hole excitation spectrum and allows the formation of spin- and valley-polarized plasmons. When the Fermi level lies in the gap of one spin in one valley, the intraband region of the corresponding spectrum disappears. For zero $E_z$ and finite $M$ the spin symmetry is broken and spin polarization is possible. The lifetime and oscillator strength of the plasmons are shown to depend strongly on the number of spin and valley type electrons that form the electron-hole pairs.

We study ballistic transport of Dirac fermions in silicene through arrays of barriers, of width $d$, in the presence of an exchange field $M$ and a tunable potential of height $U$ or depth $-U$. The spin- and valley-resolved conductances as functions of $U$ or $M$, exhibit resonances away from the Dirac point (DP) and close to it a pronounced dip that becomes a gap when a critical electric field $E_z$ is applied. This gap widens by increasing the number of barriers and can be used to realize electric field-controlled switching of the current. The spin $p_s$ and valley $p_v$ polarizations of the current near the DP increase with $E_z$ or $M$ and can reach 100% for certain of their values. These field ranges widen significantly by increasing the number of barriers. Also, $p_s$ and $p_v$ oscillate nearly periodically with the separation between barriers or wells and can be inverted by reversing $M$.

The conductance, the transmission, and the reflection probabilities through rectangular potential barriers and $p$-$n$ junctions are obtained for bilayer graphene taking into account the four bands of the energy spectrum. We have evaluated the importance of the skew hopping parameters ${\gamma }_3$ and ${\gamma }_4$ to these properties and show that for energies $E>{\gamma }_1/100$ their effect is negligible. For high energies two modes of propagation exist and we investigate scattering between these modes. For perpendicular incidence both propagation modes are decoupled, and scattering between them is forbidden. This extends the concept of pseudospin as defined within the two-band approximation to a four-band model and corresponds to the (anti)symmetry of the wave functions under in-plane mirroring. New transmission resonances are found that appear as sharp peaks in the conductance which are absent in the two-band approximation. The application of an interlayer bias to the system (1) breaks the pseudospin structure, (2) opens a band gap that results in a distinct feature of suppressed transmission in the conductance, and (3) breaks the angular symmetry with respect to normal incidence in the transmission and reflection.

We investigate silicene superlattices in the presence of a tunable barrier potential $U$, an exchange field $M$, and a perpendicular electric field $E_z$. The resulting miniband structure depends on the spin and valley indices and on the fields $M$ and $E_z$. These fields determine the minigaps and also affect the additional Dirac points brought about by the periodic potential $U$. In addition, we consider diffusive transport and assess its dependence on the spin and valley indices as well as on temperature. The corresponding spin and valley polarizations strongly depend on the potential $U$ and can be made almost 100% at very low temperatures at particular values of the Fermi energy.