Negative compressibility in graphene-terminated black phosphorus heterostructures

Abstract

Negative compressibility is a many-body effect wherein strong correlations give rise to an enhanced gate capacitance in two-dimensional (2D) electronic systems. We observe capacitance enhancement in a newly emerged 2D layered material, atomically thin black phosphorus (BP). The encapsulation of BP by hexagonal boron nitride sheets with few-layer graphene as a terminal ensures ultraclean heterostructure interfaces, allowing us to observe negative compressibility at low hole carrier concentrations. We explain the negative compressibility based on the Coulomb correlation among in-plane charges and their image charges in a gate electrode in the framework of Debye screening.

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

“…Very recently, the decrease of the chemical potential with increasing density has been directly observed by ARPES spectroscopy in two-dimensional monolayers of WSe 2 [13] and quasi-three dimensional spin-orbit correlated materials [14], by conductivity measurements in graphene-MoS 2 heterostructures, [15] and by capacitance measurements in graphene-terminated black phosphorous heterostructures. [16] In these experiments the electronic densities are considerably larger than in conventional semiconductor heterostructures, ruling out the spontaneous occurrence of inhomogeneous phases.…”

Recent advances in synthesis, properties, and applications of phosphorene

“…10), whereas phosphorene 2D electron gas shows exceptional Hall mobility of up to 6000 cm 2 V −1 s −1 and quantum Hall effect in high-quality van der Walls heterostructures. 82 Recent studies have also found that trions and excitons in phosphorene can be tuned by using a transistor topography set-up. 83 It is noted that trions can be used in spintronic-based devices due to their non-zero spin.…”

“…In high-quality phosphorene-based heterostructures with negative compressibility, a many-body effects strong correlations lead to an enhanced capacitance in 2D electronic systems, suggesting potential for low-power nanoelectronics and optoelectronics. 82 The anisotropy of transport in phosphorene can also be incorporated into devices. FET device performance and speed may be increased by orientating the conducting channel along the AM direction.…”

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

“…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. It was shown that an increase in the gate capacitance of a phosphorene field-effect transistor (FET) originates from such negative compressibility at low electron densities.…”

“…17 Encapsulation of few-layer phosphorene by h-BN sheets has resulted in new ultraclean heterostructures which could be ideal anisotropic 2D systems with high mobility and a possible negative com-pressibility of electron/hole gas (κ −1 = n 2 ∂µ/∂n), where n is the density and µ is the chemical potential of the interacting system. 1,[18][19][20] A negative compressibility results from electron-electron interactions, in which the exchange and correlation energies lower the chemical potential as the electron density decreases. 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.…”