Electrically induced charge-density waves in a two-dimensional electron liquid: Effects of negative electronic compressibility

Abstract

We show that the negative electronic compressibility of two-dimensional electronic systems at sufficiently low density enables the generation of charge density waves through the application of a uniform force field, provided no current is allowed to flow. The wavelength of the density oscillations is controlled by the magnitude of the (negative) screening length, and their amplitude is proportional to the applied force. Both are electrically tunable.Introduction -The occurrence of negative compressibility is a peculiar feature of electronic systems, whose stability against long-range Coulomb repulsion is ensured by the presence of a background charge, such as ionized atomic cores in metals, ionized dopants, or gates in semiconductors.[1] At moderately low density, the chemical potential of the electrons decreases with increasing density, implying a negative compressibility (see Fig. 1). This happens when the negative exchange and correlation contributions to the energy, arising from the electron-electron interaction, dominate over the positive kinetic energy -which is inevitable at sufficiently low density. [1][2][3][4][5] In an ordinary system, a negative compressibility would be a sign of instability, leading to collapse or phase separation, but the electron liquid is generally protected against such instabilities by its background charge. It is only at extremely low densities or at very high magnetic fields that non-uniform phases such as the Wigner crystal [6] or stripe and bubble phases [7] are expected to occur.

Anisotropic charge density wave in electron-hole double monolayers: Applied to phosphorene

“…For equal effective masses, i.e., isotropic energy bands, our results agree with Hrolak et al. 1 Our numerical results are applied to phosphorene.…”

“…This effect has been observed to enhance the capacitance of semiconductor 2D electronic systems by a few percent above the expected geometric capacitance 21 and is experimental evidence for the formation of a charge-density-wave (CDW) phase. 1 Negative compressibility has been recently observed in atomically thin BP wherein strong correlations results in an enhanced gate capacitance. 18 Importantly, negative compressibility occurs at densities as high as n ≈ 10 12 cm −2 which is achievable in experiment.…”

“…When the compressibility of the drag layer is negative, the force exerted by this electric field results in CDW phases with a wavelength determined by the absolute value of the compressibility. 1 We generalize the method of Ref. [1] to investigate the controlled formation of a CDW phase caused by a negative electronic compressibility.…”

“…1 We generalize the method of Ref. [1] to investigate the controlled formation of a CDW phase caused by a negative electronic compressibility. The CDW is normally understood to be an intrinsic instability of the electronic structure of the system.…”

Quantum supercapacitors

“…However, situations where a negative exchange and correlation contribution to the energy dominates over the positive kinetic energy do exist. In this case, the compressibility K = n −2 ∂n/∂µ of the electron gas is negative [35, 43,44] leading to C q < 0 and C > C g . Such quantum mechanical enhancement of the total capacitance as compared to the classical value has been observed in several systems including two-dimensional electron double layers formed in GaAs semiconductor quantum wells [45], the interface between two oxides (LaAlO 3 /SrTiO 3 ) [46], 2D monolayers of WSe 2 [47], and graphene-MoS 2 heterostructures [48].…”