Negative dynamic conductance of a quantum wire with unscreened Coulomb interaction

TL;DR

The paper tackles negative dynamic conductance (NDC) and time-of-flight instability in an ungated quantum wire with unscreened Coulomb interaction under DC bias. It develops a self-consistent 1D model that reduces the problem to an effective potential $U(x)$ and uses a Green's-function formalism to capture image-charge effects, with the AC response treated perturbatively to obtain the admittance $Y(\\omega)$. The main finding is that strong e–e interactions rearrange the potential into a near-cathode barrier and a long flat region, promoting population inversion and narrowing unstable $k$-space, which markedly increases the maximum NDC and shifts its frequency compared to linear-potential models. This suggests low-threshold NDC (on the order of a few millivolts) in ungated QWr devices and points to potential microwave-generation and nonlinear transport phenomena in space-charge-limited 1D nanostructures.

Abstract

Dynamic conductance and time-of-flight current instability in a quantum wire connected to electron reservoirs under DC bias voltage are studied in the absence of a gate screening the Coulomb interaction of electrons. Due to a strong electron-electron interaction, dramatic rearrangements of the charge density distribution and the potential landscape in the wire occur at a sufficiently high DC bias voltage. The applied voltage is screened mainly near the cathode contact, and an almost flat potential profile is established in the most of the wire. Thus, the size of the region of a population inversion of electronic states greatly increases, and the band of wave vectors that form unstable modes of electronic waves significantly reduces. As a result, the conditions for the occurrence of the time-of-flight instability are greatly facilitated and the negative dynamic conductivity increases.

Figures (5)

• Figure 1: Schematic energy diagram of a QWr connected to electron reservoirs to which a bias voltage $V_{dc}$ is applied. The thin black line represents the energy diagram of the unbiased QWr. The dotted line shows the potential landscape without the charge accumulated in the QWr. $\mu_{L, R}$ is the chemical potential in the left and right reservoirs, $\varepsilon_F$ is the Fermi energy in the unbiased wire. Wavy lines indicate energy relaxation processes in the reservoir.
• Figure 2: Effective 1D potential in a QWr coupled to reservoirs for various bias voltages. The parameters used in the calculations are: $L$=5 $\mu$m, $d$=20 nm, $a$=1.25 $\mu$m, $R$=0.75 $\mu$m, $Lk_F$= 100, $g\approx 30$. The applied voltage normalized to the Fermi energy in the reservoirs, $V = V_{dc}/\mu_L$, ($\mu_L$ = 5.5 m$e$V) is shown below each line.
• Figure 3: Real part of the admittance as a function of frequency calculated for parameters of Fig. \ref{['profile']} for two voltages $V_{dc}=1.0\,\mu_L$ and $V_{dc}=1.4\,\mu_L$. Inset shows the frequency dependency of the real parts of $Y_+$ and $Y_-$ for $V_{dc}=1.4\,\mu_L$.
• Figure 4: Maximum NDC as a function of the DC bias voltage for the realistic potential landscape of the QWr (red line) and the linear potential approximation. The calculations were carried out for parameters of Fig. \ref{['profile']}
• Figure 5: Maximum NDC as a function of the QWr length in the regime of the rebuilt potential landscape. The calculations were carried out for parameters of Fig. \ref{['profile']} and the bias voltage $V_{dc}/\mu_L =1.4$.