Laughlin pumping assisted by surface acoustic waves

TL;DR

The paper reports a quantitative experimental realization of Laughlin pumping in both integer and fractional quantum Hall states using a Corbino device configuration. A surface acoustic-wave–assisted charge-reset protocol enables zero-bias pumping measurements, yielding a pumping coefficient $n_{\,Phi}$ that closely tracks the Hall conductance $\\sigma_{xy}$ and revealing direct fractional charge pumping for $\\nu=4/3$ and $5/3$. The SEA technique simultaneously unlocks access to ultralow longitudinal conductivity $\\sigma_{xx}$, allowing extraction of effective activation gaps that differ markedly from conventional transport. Together, these results bring Laughlin’s gedanken experiment to life and open new avenues for probing non-equilibrium dynamics and the internal structure of quantum Hall states.

Abstract

The quantum Hall effect is a fascinating electrical transport phenomenon signified by precise quantization of Hall conductivity $σ_\mathrm{xy}$ and vanishing longitudinal conductivity $σ_\mathrm{xx}$. Laughlin proposed an elegant explanation in which adiabatic insertion of a flux tube pumps charge through the system. This analysis unveils the fundamental role of gauge invariance and provides a compelling argument about the fractional charge of fractional quantum Hall states. While it has been used extensively as a theoretical tool, a quantitative experimental investigation is lacking despite multiple attempts. Here we report successful realizations of Laughlin pumping in several integer and fractional quantum Hall states. One essential technical innovation is using surface acoustic waves to periodically clear the charges accumulated during the pumping process. Magnetic fluxes are inserted at a constant rate so there is no need to perform complicated data fitting. Furthermore, our setting can reliably extract $σ_\mathrm{xx}$ that is several orders of magnitude lower than the limit of conventional techniques. Effective energy gaps can be deduced from the temperature dependence of $σ_\mathrm{xx}$, which are drastically different from those provided by conventional transport data. This work not only brings a famous gedanken experiment to reality but also serves as a portal for many future investigations.

Figures (14)

• Figure 1: Illustration of the measurement protocol and raw experimental data. (a) Schematic of Laughlin pumping on a cylinder. The magnetic field $\vec{B}$ is along the radial direction and the Landau orbitals are exponentially localized along the axial direction (red dashed curves). One additional flux tube is inserted along the axis of the cylinder. Its strength is adiabatically tuned from zero to $h/e$, which induces an electrical field $\vec{E}$ along the perimeter of the cylinder. Each Landau orbital shifts gradually to its neighbor in this process. If the orbitals carry electrons, an electric current flows from one end of the cylinder to the other. The flowing direction is perpendicular to $\vec{E}$, so the system has a nonzero Hall conductance. (b) The Corbino disk version of Laughlin pumping. One flux tube is inserted at the center such that an azimuthal electric field is generated and the Landau orbitals shift along the radial direction. This pumps electrons between the two sections of the Corbino disk. (c) Schematic of our device. When electrons are pumped across the system, they are drained into one capacitor that connects one contact from each section. Its voltage is measured from which the amount of pumped charge is computed. SAWs are launched by three IDTs to clear accumulated charges. (d) Laughlin pumping of the $\nu=2$ integer QHS. The horizontal axis is aligned with the $\nu=2$ plateau in panel (f). We can only observe useful signals in a small region around the plateau center. If the sweeping direction of $B$ is reversed (black arrows), the pumping direction changes accordingly. The data in the orange and blue dashed boxes is presented in Figs. 1c and 3a, respectively. (e) One typical measuring cycle. The voltage (red solid curve) increases with the magnetic field $B$. An exponential fitting (blue dashed curve) of the data is performed to extract the pumping rate at zero bias (green dashed line) as well as the longitudinal conductivity. SAWs are switched on periodically to reset the voltage. (f & g) The longitudinal conductivity obtained by conventional transport measurements. We indicate the positions of several QHSs.
• Figure 2: Accurate determination of the pumping coefficient. (a) For up and down sweeps in Fig. \ref{['Figure1']}e, we obtain the pumping coefficients $n_{\Phi-}$ and $n_{\Phi+}$ (orange and blue curves), respectively. Their difference is $2\tilde{n}_{\Phi}$ and their average (green curve) reflects non-ideal effects in our measurements. (b) Quantized $\tilde{n}_{\Phi}$ on the $\nu=1$ plateau in Device I. The seven data sets correspond to different $|dB/dt|$ ranging from 0.05 to 0.1 T/min. (c) Comparison of $\tilde{n}_{\Phi}$ in Device I, II, and III. To discharge the capacitor properly, we use different SAW power (-35 or -40 dBm) and switching frequency (from 17.37 to 77 mHz) in panels (b) and (c). (d) $\tilde{n}_{\Phi}$ on several integer plateaus in Device I (solid symbol) and III (open symbol). The horizontal axis in panels (a-d) is $\nu^{*}$ defined in the main text. (e) $\tilde{n}_{\Phi}$ on the $\nu=4/3$ and $5/3$ plateaus in Device III with horizontal axis being $\nu^{*}_{\rm CF}$ (see SI Sec. VI). (f) Comparison of $\tilde{n}_{\Phi}$ and $\sigma_\mathrm{xy}$. The data points are plateau heights averaged over all traces, which match the expected $\tilde{n}_{\Phi}=\sigma_\mathrm{xy}$ (gray dashed line). The error bar is smaller than the size of the symbol.
• Figure 3: Extraction of minuscule $\sigma_\mathrm{xx}$ on quantum Hall plateaus. (a) Zoom-in view of the blue dashed box in Fig. \ref{['Figure1']}e. (b) Each curved segment in panel (a) is modeled by a circuit that consists of a leaking resistance $R$ in parallel with the capacitor $C$. We can extract the time constant $\tau=RC$ by fitting each segment and then convert $R$ to the longitudinal conductivity $\sigma_\mathrm{xx}$. (c) $\sigma_\mathrm{xx}$ vs. $1/T$ at exactly $\nu=1$ and $2$. The solid circles (squares) are obtained by our new method (conventional transport measurements). The open symbols are extrapolated values at $\nu^*=0$ (see SI Sec. VII). Arrhenius fitting is performed to extract the activation gaps that are displayed in the vicinity of each data set (in units of meV). (d-e) The evolution of $\sigma_\mathrm{xx}$ on several quantum Hall plateaus when the filling factor varies. For integer (fractional) QHSs, the horizontal axis is $\ell_{B}/\alpha^{*}$ ($\ell_{\rm CF}/\alpha^{*}$) (see SI Sec. VI). The solid (open) symbols in panel (d) are from Device I (IV). The fitting parameter $f$ defined in the main text are indicated for different data sets.
• Figure S1: (a) Device I installed on the sample holder and the cold-finger. (b,c) Sample photo and schematic diagrams. The 2DES mesa has square Corbino geometry with eight contacts (labeled 1–8) and three IDTs (labeled A–C). (d) An on-off modulated (at about 100 mHz) excitation RF signal is applied to the emitting IDT used to excite the SAW.
• Figure S2: Conventional quasi-DC transport measurement in the absence of the SAW. (a) Longitudinal magneto-conductance $\sigma_\mathrm{xx}$ taken from a Corbino sample made from wafer A. The sample has a standard circular Corbino geometry with the inner and outer radii $r_1=400$ µ m, $r_2=600$ µ m, respectively. We apply a voltage of 10 µ V between inner and outer contacts µ V and measure the current flowing through the sample. (b) Longitudinal magneto-resistance $R_\mathrm{xx}$ taken from a Van der Pauw geometry sample (device IV) made from wafer C.