Quantum Hall-like effect for neutral particles with magnetic dipole moments in a quantum dot

TL;DR

This work addresses quantum-Hall-like transport in neutral particles by leveraging the Aharonov-Casher coupling between magnetic dipoles and a radial electric field in a two-dimensional quantum dot with harmonic confinement. The authors derive a planar Hamiltonian, treat the line-charge singularity with self-adjoint extension methods, and show a Landau-like spectrum $E_{n,m}=\hbar\omega_0(2n+1\pm|m-\xi|)$ with $\xi=2s\mu\lambda/\hbar$. They predict a quantized Hall conductivity, $\sigma_{\text{Hall}}=-\frac{\mu_B^2}{h}(n+1)\,\mathrm{sgn}(m-\xi)$ (in appropriate units), whose sign is controlled by spin, and demonstrate robust plateaus up to about 25 K across GaAs quantum dots and cold-atom platforms. This electric-field–driven, magnetic-field-free topological transport in neutral matter offers a practical route toward spin-controlled quantum Hall physics and broader topological phases without charges or external magnetic fields.

Abstract

We predict a new class of quantum Hall phenomena in completely neutral systems, demonstrating that the interplay between radial electric fields and dipole moments induces exact $e^2/h$ quantization without the need for Landau levels or external magnetic fields. Contrary to conventional wisdom, our theory reveals that: (i) the singularity of line charges does not destroy topological protection, (ii) spin-control of quantization emerges from boundary conditions alone, and (iii) the effect persists up to 25 K, surpassing typical neutral systems. These findings establish electric field engineering as a viable route to topological matter beyond magnetic paradigms.

Figures (7)

• Figure 1: Schematic representation of the proposed system: (a) A quantum dot (green region) with harmonic confinement potential $V(r) = \frac{1}{2}M\omega_0^2r^2$ surrounds a charged wire (red cylinder) generating the radial electric field $\mathbf{E} = (2\lambda/r)\hat{\mathbf{r}}$ (blue arrows). Magnetic dipoles $\boldsymbol{\mu}$ (red arrows) experience the effective gauge potential $\mathbf{A}_{\text{eff}} = \boldsymbol{\mu} \times \mathbf{E}$.
• Figure 2: Energy spectrum $E_{n,m}$ for cases (a) $s = +1$ and (b) $s = -1$, considering different principal quantum numbers $n = 0, 1, \ldots, 4$ and angular momenta $m = -2, -1, \ldots, 3$, with charge density values $\lambda = 1{,}5,\, 2{,}0,\, 2{,}5,\, 3{,}0 \times 10^{2}\,\mathrm{nC}/\mathrm{m}$. Each color represents a distinct value of $m$. The circle-shaped markers indicate the case $s = +1$ (spin up) and the diamond-shaped markers represent $s = -1$ (spin down).
• Figure 3: Energy spectrum $E_{n,m}$ as a function of the angular momentum quantum number $m$, for fixed charge density $\lambda = 0.025$ nC/m and quantum numbers $n = 0,1,\dots,5$. Each color corresponds to a different value of $n$ ($n=0$ in black, $n=1$ in blue, $n=2$ in green, $n=3$ in red, $n=4$ in orange, and $n=5$ in brown). The solid curves represent the case $s=+1$ (spin-up), and the dashed curves represent the case $s=-1$ (spin-down). The mirror-like behavior of the energy levels around $m=0$ is a direct consequence of the AC coupling parameter $\xi$, which changes sign with the spin orientation.
• Figure 4: Quantum Hall-like conductivity in units of $\mu_B^2/h$ (left axis) and $e^2/h$ (right axis) as a function of the scaled linear charge density $\lambda \times 10^2$ (in nC/m), computed for the spin projections $s = +1$ (green) and $s = -1$ (red). The spin inversion reflects a mirrored structure of Hall plateaus with respect to the axis $\sigma_{\text{Hall}} = 0$.
• Figure 5: Quantum Hall-like conductivity maps in units of $e^2/h$ for neutral particles with magnetic dipole moments as functions of the scaled linear charge density $\lambda \times 10^2$ (in nC/m) and effective Fermi energy $F$ (in meV). (a) Corresponds to spin-up ($s=+1$), and (b) to spin-down ($s=-1$). The color scale indicates the magnitude and sign of $\sigma_{\mathrm{Hall}}$. The distinct plateaus demonstrate the quantization of conductivity. Note the clear antisymmetric behavior between spin-up and spin-down states, where the sign of the Hall conductivity is inverted upon spin reversal. The dashed lines highlight specific reference values for $F$ ($F_0=12$ meV) and $\lambda$ ($\lambda_0=1.95$) for illustrative purposes, showing cuts where plateaus are prominent. The expanded range of $\lambda$ compared to previous results reveals additional plateau structures in the lower $\lambda$ regime.