Observation of Superfluidity and Meissner Effect of Composite Bosons in GaAs Quantum Hall System

Abstract

The quantum Hall effect (QHE) is theoretically understood as a superfluid condensate of composite bosons (CBs) -- bound states of electrons and magnetic flux quanta. While dissipationless transport is consistent with this picture, other signatures of superfluidity, such as the Meissner effect, remain elusive. Here, we present direct experimental evidence for CB superfluidity by probing the system's response to a controlled, time-varying magnetic field in Corbino disk geometries. We simultaneously observe the quantized Laughlin charge pumping and a new, quantized charge accumulation phenomenon, governed by the relation $ΔQ_{\rm a}/e = ν\,(ΔΦ/Φ_0)$. This relation signifies that the system actively maintains the fixed electron-to-flux ratio that defines the CBs, neutralizing excess flux by drawing in a precise number of electrons. Crucially, devices with multiple concentric top gates reveal that this charge accumulation is uniformly distributed across the bulk of the QHE fluid, demonstrating that it is a collective, bulk property rather than an edge effect -- a key signature of a superfluid condensate. Furthermore, the presence of a top gate determines the screening mechanism: in a "grand canonical" setting with a gate, low Coulomb energy favors a charge-mediated screening (generalized Meissner effect); without a gate, the system enters a "canonical" regime, exhibiting fixed electron density like type-II superconductors. These observations confirm the CB superfluid nature of the QHE ground state and establish a versatile platform for studying macroscopic quantum coherence and its screening transitions in two dimensions.

Figures (4)

• Figure 1: Experimental setup and sample structure. (a) The schematic of the charge pumping ($I_1$ and $I_2$) and charge accumulation ($Q_\text{a}$) under uniform $B_\text{AC}$. $B_\text{AC}$ penetrating the sample area results in $Q_\text{a}$ and a difference between $I_1$ and $I_2$ (all AC signals). (b) The AC field generation setup. Samples were placed inside the AC coil structure and cooled by the mixing chamber (MC). (c) Sample structures and measurement circuits of a Corbino-disk-shaped sample. $I_1$ and $I_2$ were measured from the voltage across capacitances $C_\text{p1}$ and $C_\text{p2}$, while $Q_\text{a}$ was measured by a current preamplifier. Each of the three circuits was measured separately while the others were connected to ground. For samples with multiple top gates, all $Q_\text{a}$ were measured simultaneously. Coulomb potential rise of accumulated electrons is greatly reduced by the capacitance coupling of the top gate, determined by the thickness of the dielectric layer and $E_\text{a}$ generated by $Q_\text{a}$. (d) Photos of single-gate and multi-gate samples (Devices I and IV).
• Figure 2: Quantized charge pumping and charge accumulation in single-top-gate devices.$Q_\text{pump-inner}$, $Q_\text{pump-outer}$, and $Q_\text{a}$ signals were measured from a Corbino-disk-shaped sample with contact radii of 400 to 600 µm (Device I). Each charge signal is divided by the effective flux variation $\Phi_\text{AC}$ respectively ($\pi r_1^2 B_\text{AC}$ for inner charge pumping, $\pi r_2^2 B_\text{AC}$ for outer charge pumping, and $\pi (r_2^2-r_1^2) B_\text{AC}$ for charge accumulation) to show the quantization. (a) The raw signals of $Q_\text{pump-inner}$ are compared with the $\sigma_{xx}$ curve of the same sample. Quantized in-phase plateaus of $Q_\text{pump-inner}/\Phi_\text{AC}$ appear, consistent with vanishing $\sigma_{xx}$. (b) Antisymmetrized (same as below) $Q_\text{pump-inner}$ and $Q_\text{pump-outer}$ are plotted against the relative filling factor $\nu^* = B_{(\nu = 1)}/B_\text{DC}-\nu$ ($B_{(\nu = 1)} = 4.23$ T). In-phase $Q_\text{pump}/\Phi_\text{AC}$ signals show clear quantized plateaus, while quadrature signals vanish to zero within the plateaus, revealing the consistent phase between $Q_\text{pump}$ and $B_\text{AC}$. The right vertical axis $Q_\text{pump}/B_\text{AC}$ has different scales at upper and lower quadrants, showing the difference between $Q_\text{pump-inner}$ and $Q_\text{pump-outer}$. (c) $Q_\text{a}$ signals plotted against $\nu^*$. The same vertical axes are used as in (b). In-phase components of $Q_\text{a}/\Phi_\text{AC}$ also show quantized plateaus, with quadrature components vanishing. (d) Sketch of charge measurement on single-gate samples. Measurement circuits are described in Fig. \ref{['fig:fig1']}(c).
• Figure 3: Condensate of CBs and uniformly distributed charge accumulation confirmed by multi-top-gate samples. (a) Schematic of CB superfluid at $\nu=1$ and the dynamic charge accumulation process responding to flux variations. The contact of the sample places the system in a grand canonical ensemble for electrons, while the gate of the sample greatly reduces the Coulomb potential increase caused by accumulated charge. As a result, the transfer of electrons effectively absorbs extra flux quanta and preserves the condensed CB state to maintain the lowest energy of the grand canonical ensemble. (b) Sketch of charge measurement on multi-gate samples. $Q_\text{a}$ measured on different top gates is labeled. $Q_\text{a TG3-1}$ and $Q_\text{a TG3-2}$ compare the edge and bulk regions of the QHE system (Device III). $Q_\text{a TG5-3}$ and $Q_\text{a TG5-4}$ compare different bulk regions (Device IV). (c-d) $\eta_\text{a}/B_\text{AC}$ signals measured on multi-gate samples, where $\eta_\text{a}$ is the charge accumulation density calculated by $\eta_\text{a} = Q_\text{a}/A$ ($A$ the top gate area for each). Signals of $\nu=1$ and $\nu=2$ plateaus are plotted for every labeled gate, exhibiting consistent and quantized values.
• Figure 4: Charge pumping signals controlled by the existence of the gate, reflecting the existence of charge accumulation. Charge pumping signals of an ultrahigh mobility Corbino-disk-shaped sample with contact radii of 400 to 600 µm (Device V) were measured first with and then without a grounded top gate. The difference between charge pumping signals of both rings manifests the charge accumulation. The blue and red dashed lines represent the theoretical value of pumped charge at outer and inner ring separately. The orange dashed line represents the theoretical value of pumped charge without charge accumulation for both inner and outer rings (see Supplementary Materials for details). (a-b) The charge pumping signals of the sample with (a) and without (b) a top gate at $f = 7.7977$ Hz. In-phase charge pumping data of part $\nu = 1$ plateaus are shown. Sketches of sample and measurement wires are represented in each figure. (c) $f$ dependence of the in-phase inner-ring pumped charge at $\nu = 1$ is compared for both gate cases. Both signals are stable to $f$ variation. (d) In-phase charge pumping signals measured at each exact integer filling factors ($\nu_0$) are compared. The signals are divided by $\nu_0$ to have the same theoretical values for different $\nu_0$.