Exploiting Negative Capacitance for Unconventional Coulomb Engineering

TL;DR

This work introduces a stabilized negative-capacitance approach to Coulomb engineering in a two-dimensional electron system (2DES) by placing it between a conventional dielectric and a negative-capacitance medium (MF2IM). In the long-wavelength limit, the engineered interaction becomes $V_{\text{eff}}(q)\approx e^{2}/[C_{nc}+C_{d}+C_{q}]$, enabling an effective attraction when $C_{nc}<0$ while remaining stable under $C_{nc}+C_{d}+C_{q}<0$. A domain-based model for PbTiO$_3$ and realistic dielectrics is used to estimate the pairing strength $\lambda - \mu^{*}$, with results around $0.2$–$0.3$ in feasible regimes, suggesting possible superconducting-like pairing in 2DESs. The work maps out design rules across carrier density, ferroelectric thickness, and dielectric choice, while outlining limitations such as the static long-wavelength approximation and the need for finite-$q$ and finite-$T$ extensions. Overall, it presents a pathway to stabilize interaction-driven electronic phases, including superconductivity, at elevated temperatures through NC-enabled Coulomb engineering.

Abstract

It is known that the many-body ground state of a two-dimensional electron system can be tuned through Coulomb engineering by controlling the permittivity of the surrounding media. However, permittivities are traditionally restricted to positive values. In this paper we argue that the negative capacitance effect demonstrated in appropriately engineered structures can open new vistas in Coulomb engineering. Negative permittivities transform the natural repulsive interaction of electrons into an attractive one raising the intriguing possibility of a superconducting ground state. Using models of two-dimensional electron systems with linear and parabolic dispersion relations coupled to environments with negative capacitance, we estimate the strength and sign of the engineered Coulomb interaction and outline parameter regimes that could stabilize correlated electronic phases.

Figures (3)

• Figure 1: Central idea. (a) System schematic - a two-dimensional electron system (2DES) surrounded by dielectric (conventional) and negative capacitance (NC) media, with respective thicknesses $L_{d}$ and $L_{nc}$. When the NC material is a ferroelectric, this configuration will be referred to as a Metal-Ferroelectric-2DES-Insulator-Metal (MF2IM) structure. (b) Tunability of the engineered 2DES Coulomb interaction $V_{\text{eff}}$ in the long-wavelength approximation as per Eq. (\ref{['Eq3']}), shown as a function of geometric capacitances $C_{nc}$ and $C_{d}$, and quantum capacitance $C_{q}$. The dashed black line indicates the limit of conventional Coulomb engineering ($C_{nc}>0$, region I). Notably, $V_{\text{eff}}$ can become $\textit{negative}$ (region III) if $C_{nc}$ is sufficiently negative.
• Figure 2: Critical length scales. (a) Definition of two regimes based on three length scales. The wavelength of low-energy electron scattering in the 2DES relative to $2d$ (twice the domain width) in ferroelectric periodic domain texture (PDT) governs whether dispersion $\varepsilon^{f}_{z}(q)$ is important in extrinsic NC systems ($2d$ should be replaced by an appropriate lattice-related length scale in the case of intrinsic NC) and relative to $|\eta_{f}|L_{f}$ determines whether the linear approximation of gate screening effect is valid. (b), (c) Illustration of effective Coulomb interaction energy $V_{\text{eff}}$ as a function of wavenumber $q$ as per Eqs. (\ref{['Eq1']}) and (\ref{['Eq2']}), shown for linear and parabolic 2DES with typical $v_{F}$ and $m^{*}$ values. In both cases, 2DES carrier density $n$ was varied to access the long-wavelength (low $n = 10^{15}/\text{m}^{2}$) and short-wavelength (high $n = 10^{17}/\text{m}^{2}$) regimes. Note that changing $L_{f}$ (fixed at $4~\text{nm}$ for this figure) is an alternate way to access these regimes.
• Figure 3: Critical energy scales and pairing strength. (a) Fermi energy $E_{F}$ of the 2DES, expressed in units of PDT single-mode energy $\hbar\omega_{0}$ for ferroelectric $\text{PbTiO}_{3}$, plotted as a function of Fermi wavenumber $k_{F}$ normalized to the ferroelectric thickness $L_{f} = 4~\text{nm}$. The long-wavelength regime described in Fig. \ref{['Fig2']} is accessed in the limit of low density, shown as encircled region. (b) Pairing strength parameter $\lambda - \mu^{*}$ calculated for a linear 2DES in the long-wavelength approximation as a function of balancing parameter $\zeta$ defined in Eq. (\ref{['Eq13']}), shown for two different values of Fermi velocity $v_{F}$. Here, carrier density was fixed at $n = 1\times 10^{15} / \text{m}^{2}$. Inset highlights where typical material systems (NC/DE) fall, according to the models used in this work.