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.
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