Rotating effects on the Hall conductivity in a quantum dot

TL;DR

This work analyzes how rotation influences the quantum Hall response in a two-dimensional mesoscopic system by incorporating rotation, a uniform magnetic field, and an Aharonov-Bohm flux into a solvable model of a ring-like confinement. The authors derive the energy spectrum $E_{n,m}$, edge currents via the Byers-Yang relation, and the Hall conductivity $\sigma$, including finite-temperature effects through the Fermi-Dirac distribution. Numerically, they show that moderate rotation preserves quantized Hall plateaus but shifts and modulates them, while larger, THz-scale rotation induces strong AB-like oscillations and a transition region near $\omega_0/2$ where persistent currents vanish. Temperature smearing enhances with rotation, and higher magnetic fields can stabilize plateaus against rotational disruption. The results offer insight into rotating quantum systems and suggest experimental avenues for observing rotation-tuned quantum Hall behavior.

Abstract

We investigate the behavior of the quantized Hall conductivity in a two-dimensional quantum system under rotating effects, a uniform magnetic field, and an Aharonov-Bohm (AB) flux tube. By varying the angular velocity and the AB flux, we analyze their impact on the formation, shifting, and structure of quantized Hall plateaus. Our results reveal that rotation modifies the energy spectrum, leading to slight shifts in the plateau positions and variations in their widths. Additionally, we identify Aharonov-Bohm-type oscillations in $σ_{\text{Hall}}$, which become more pronounced for lower values of the cyclotron frequency $ω_c$, indicating enhanced quantum interference effects in the low-field regime. These oscillations are further modulated by $Ω$, affecting their periodicity and amplitude. The interplay between the confinement frequency $ω_0$, the cyclotron frequency $ω_c$, and the rotational effects plays a crucial role in determining the overall behavior of $σ_{\text{Hall}}$. Our findings provide insights into the interplay between rotation, magnetic field, and quantum interference effects, which are relevant for experimental investigations of quantum Hall systems in rotating systems.

Figures (5)

• Figure 1: Quantization of the Hall conductance as a function of $B~(\mathrm{T})$. Aharonov-Bohm oscillations are superimposed on the Hall plateaus. In Fig. (a), plateaus are shown for different values of $\Omega$ on the order of GHz, while in Fig. (b), they are displayed for different values of $\Omega$ on the order of THz.
• Figure 2: Hall conductivity as a function of $B(\mathrm{~T})$ for different values of $\Omega$, on the order of GHz . In (a), the $B$-axis ranges from 1.08 to 1.16, while in (b), it ranges from 5.5 to 6.
• Figure 3: Behavior of Hall conductance quantization as a function of $\Omega$ (GHz) for $B = 1.3$ T and $B = 1.4$ T. The plots are divided at $\Omega = \frac{w_0}{2}$, emphasizing the distinct behaviors on either side of this threshold.
• Figure 4: Quantization of the Hall conductance. (a) Hall conductance as a function of $B~(\mathrm{T})$ for $\Omega = 242.31$ GHz and $\Omega = 235.68$ GHz. (b) Hall conductance as a function of $\Omega~(\mathrm{GHz})$ for magnetic fields $B = 1.3$ T and $B = 1.4$ T.
• Figure 5: Quantization of the Hall conductance as a function of $B\,(\text{T})$. In (a), the results are shown for the temperatures $T=0.0\,\text{K}$, $T=25.0\,\text{K}$, and $T=50.0\,\text{K}$; in (b), the same temperatures are analyzed for rotational speeds $\Omega=50\,\text{GHz}$ and $\Omega=100\,\text{GHz}$.