We compare the energies of the Laughlin liquid and a charge density wave in a weak magnetic field for the upper Landau level filling factors $\nu_N = 1/3$ and $1/5$. The charge density wave period has been optimized and was found to be $\simeq 3R_c$, where $R_c$ is the cyclotron radius. We conclude that the optimal charge density wave is more energetically preferable than the Laughlin liquid for the Landau level numbers $N \ge 2$ at $\nu_N = 1/3$ and for $N \ge 3$ at $\nu_N = 1/5$. This implies that the $1/3$ fractional quantum Hall effect cannot be observed for $N \ge 2$, in agreement with the experiment.

The geometry of an inductor made of a long thin wire and having the highest possible Q-factor is found by numerical optimization. As frequency increases, the Q-factor first grows linearly and then according to a square-root law, while the cross-section of the optimal coil evolves from near-circular to sickle-shaped.

Terahertz nanospectroscopy reveals many-body interactions in graphene

The problem of electrostatic screening of a charged line by undoped or weakly doped graphene is treated beyond the linear-response theory. The induced electron density is found to be approximately doping independent, n(x)∼x-2log2x, at intermediate distances x from the charged line. At larger x, twin p-n junctions may form if the external perturbation is repulsive for graphene charge carriers. The effect of such inhomogeneities on conductance and quantum capacitance of graphene is calculated. The results are relevant for transport properties of graphene grain boundaries and for local electrostatic control of graphene with ultrathin gates.

We theoretically investigate charged collective modes in a two-dimensional conductor with hot electrons where the instantaneous mode frequencies gradually increase or decrease with time. We show that the loss compensation or even amplification of the modes may occur. We apply our theory to two types of collective modes in graphene, the plasmons and the energy waves, which can be probed in optical pump-probe experiments.

All known superfluid and superconducting states of condensed matter are enabled by composite bosons (atoms, molecules and Cooper pairs) made of an even number of fermions. Temperatures where such macroscopic quantum phenomena occur are limited by the lesser of the binding energy and the degeneracy temperature of the bosons. High-critical temperature cuprate superconductors set the present record of ~100 K. Here we propose a design for artificially structured materials to rival this record. The main elements of the structure are two monolayers of a transition metal dichalcogenide separated by an atomically thin spacer. Electrons and holes generated in the system would accumulate in the opposite monolayers and form bosonic bound states--the indirect excitons. The resultant degenerate Bose gas of indirect excitons would exhibit macroscopic occupation of a quantum state and vanishing viscosity at high temperatures.

We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical potential, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor $\sigma^{(3)}$ whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for $\sigma^{(3)}$ for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments.