Laughlin Pumping in Topological Quantum Systems

• Laughlin pumping is a quantized charge transport phenomenon where threading a magnetic flux in a multiply-connected geometry induces discrete charge transfer linked to topological invariants.
• Experimental realizations use Corbino geometries and SAW-assisted protocols to accurately measure Hall conductance and detect fractionally charged quasiparticles.
• Extensions to hybrid topological systems reveal fractionalization effects and chiral Majorana modes, offering robust diagnostics for non-Abelian excitations.

Laughlin pumping is a quantized charge transport phenomenon in two-dimensional (2D) topological systems, originating from the adiabatic insertion of magnetic flux and foundational to the theoretical understanding of both the integer and fractional quantum Hall effects. In the Laughlin scenario, threading a quantized magnetic flux through a multiply-connected geometry, such as a cylinder or Corbino annulus, induces discrete charge transfer, directly linked to the topological invariants—most notably the Hall conductivity. This conceptual framework not only provided the original physical argument for the quantization of Hall conductance but also predicted the existence and transport of fractionally charged quasiparticles in the fractional quantum Hall regime. Recent advances have extended Laughlin pumping into experimental reality and new topological platforms, including quantum anomalous Hall insulators (QAHI) and chiral topological superconductors (CTSC) (Wang et al., 17 Jan 2026, Cao et al., 18 Sep 2025).

1. Theoretical Foundations of Laughlin Pumping

Laughlin’s original theory considers a 2D electron system on a cylinder subjected to quantized magnetic flux changes. For a total threaded flux $\Delta\Phi$, the system responds with a circumferential electric field $E_\theta$ due to Faraday’s law, generating a Hall current $I_r = \sigma_{xy}E_\theta$ in the radial direction. Integrating this current over time yields the total pumped charge:

$Q = \int I_r(t)\,dt = \sigma_{xy} \Delta\Phi$

On a Hall plateau with filling factor $\nu$ and quantized Hall conductivity $\sigma_{xy} = \nu e^2/h$, threading a single magnetic flux quantum ($h/e$) causes the transfer of $Q = \nu e$ charge from one boundary to another. For integer $\nu$, charge transport is an integer multiple of $e$, whereas fractional $\nu$ produces $Q = \nu e < e$, which compellingly demonstrates the fractionalization of charge inherent to the fractional quantum Hall effect. Gauge invariance and the spectral gap guarantee that the wave function remains single-valued (up to a phase), enforcing quantization. The flux-threading argument is topological, depending solely on global invariants rather than microscopics, and provides direct evidence for fractionally charged quasiparticles (Wang et al., 17 Jan 2026).

2. Experimental Realization and Methodologies

The practical realization of Laughlin pumping requires:

1. Multiply-Connected Geometry: An annular (Corbino) sample is employed to ensure that flux threading drives a radial Hall current measurable between inner and outer contacts.
2. Controlled Flux Insertion: Magnetic flux is swept at a constant rate using a DC field, converting flux changes to predictable voltage ramps.
3. Charge Detection and Reset Protocol: A capacitor bridges the inner and outer contacts, accumulating charge as the Hall current pumps electrons. The resultant voltage $V(t)$ is monitored by a high-impedance electrometer.

Continuous charge build-up eventually back-biases the pump. This is resolved via the "sonication of electron accumulation" protocol, utilizing surface acoustic waves (SAWs) to transiently increase the longitudinal conductivity $\sigma_{xx}$ by multiple orders of magnitude, allowing periodic in situ discharge of the capacitor. Each SAW pulse resets the charge accumulation, enabling repeated measurement cycles. The flux-pumping coefficient:

$$n_\Phi \equiv (Q/e)/(\Delta\Phi/(h/e)) = \sigma_{xy}/(e^2/h)$$

is extracted directly from the slope of $V(t)$ segments at zero bias (Wang et al., 17 Jan 2026).

Key Experimental Component	Function	Reference
Corbino geometry	Enables radial Hall current	(Wang et al., 17 Jan 2026)
DC field sweep	Provides constant $\frac{dB}{dt}$	(Wang et al., 17 Jan 2026)
SAW reset (SEA protocol)	Clears accumulated charge	(Wang et al., 17 Jan 2026)

3. Quantitative Observations and Measurement Capabilities

Laughlin pumping via SAW-assisted protocols enables:

• Direct Measurement of Hall Conductance: Plateaus in $n_\Phi$ observed up to $\nu = 7$ agree within 1–2% to theoretical values and extend to robust fractional states, such as $\nu = 4/3, 5/3$.
• Detection of Fractional Quasiparticle Charge: The quantized pumped charge for fractional filling factors directly corresponds to fractionally charged quasiparticles, e.g., threading one flux quantum at $\nu = 1/3$ pumps precisely $e/3$ (Wang et al., 17 Jan 2026), with no reliance on indirect probes like shot-noise or Coulomb blockade.
• Ultrahigh Resolution of Longitudinal Conductivity: Fitting the curvature of $V(t)$ allows extraction of $\sigma_{xx}$ down to $10^{-13}\,\Omega^{-1}$, substantially below the limit of conventional Corbino transport. Temperature dependence of $\sigma_{xx}$ yields effective activation gaps much smaller than those inferred from biased transport, indicating the sensitivity of Laughlin pumping to different excitation spectra.

Compared to Hall-bar or gate-modulated approaches, this technique offers direct charge counting, elimination of AC artifacts, and high-resolution measurement capability for both $\sigma_{xy}$ and $\sigma_{xx}$. Experimental limitations include the necessity for extremely low residual $\sigma_{xx}$ and the integration complexity of SAW transducers with ultrahigh-mobility heterostructures (Wang et al., 17 Jan 2026).

4. Extensions to Topological Junctions and Majorana Physics

Recent theoretical and experimental works have generalized Laughlin pumping to hybrid structures, including QAHI–CTSC–QAHI junctions. In such systems, adiabatic flux threading can be mediated by chiral Dirac modes (CDMs), which pump a unit charge per flux quantum, or by the interplay with chiral Majorana modes (CMMs).

• Chiral Dirac Mediation: The inner CDM in the QAHI segment accumulates the full flux-induced Aharonov–Bohm phase, and one flux quantum results in the quantized transfer of a full electron charge, reflecting the system's Chern number (Cao et al., 18 Sep 2025).
• Chiral Majorana Mediation: When the CTSC hosts only a single propagating Majorana (N=1), it remains charge-neutral and carries no momentum, thus segments of the interferometer traversed by the Majorana do not couple to the inserted flux. The result is fractionalization of the effective flux quantum such that pumping a unit charge may require a non-integer multiple of the standard flux quantum, set by device geometry and vortex parity. This phenomenon serves as a distinctive signature of chiral Majorana physics and enables direct detection of CMMs via transport (Cao et al., 18 Sep 2025).

The fractionalization is described by:

$\Delta\Phi = q \Phi_0, \quad q = 2\pi/\varphi_\pm$

where $\varphi_\pm$ are geometric angles associated with CDM–CMM mode conversions and $\Phi_0 = h/q$ is the superconducting flux quantum.

5. Implications for Topological Classification and Quantum Transport

Laughlin pumping acts as an operational probe of topological order:

• Chern Number Measurement: Direct correspondence exists between the number of pumped electrons per flux quantum and the Chern number in integer and fractional quantum Hall states (Wang et al., 17 Jan 2026, Cao et al., 18 Sep 2025).
• Fractionalization and Non-Abelian Excitations: The manifestation of fractional charge pumping at fractional $\nu$ quantitatively supports the identification of fractional quantum Hall states and non-Abelian phases in engineered platforms. For instance, the ability to resolve $\nu = 5/2$ plateaus would enable direct studies of non-Abelian quasiparticles.
• Detection of Chiral Majorana Modes: Fractional flux pumping due to the presence of CMMs provides a robust, transport-based diagnostic that is less susceptible to parasitic channels than conductance or spectroscopy methods.

Platform	Pumped Charge per Flux Quantum	Diagnostic Value
QHE (integer $\nu$)	$\nu e$	Measures Chern number
FQHE (fractional $\nu$)	$\nu e < e$	Reveals fractional quasiparticles
QAHI–CTSC–QAHI	$q e,~q < 1$ (CMM)	Fingerprint of chiral Majorana modes

6. Future Directions and Open Questions

Laughlin pumping provides a quantitative realization of a foundational gedanken experiment, establishing new methodologies for probing quantum Hall platforms and engineered topological phases. Emerging directions include:

• Exploration of Fragile Quantum Hall States: Direct pumping studies for non-Abelian states such as $\nu = 5/2$ and engineered fractional Chern insulators.
• Extension to Spin Pumping: Investigating the possibility of spin analogs of Laughlin pumping in systems with spin-momentum locked states (Cao et al., 18 Sep 2025).
• Impact of Disorder and Interactions: The distinct activation gaps observed via zero-bias pumping suggest sensitivity to low-energy, possibly interaction-induced, excitations not visible in biased transport.
• Higher-Order Fractional Pumping: Generalization to multicomponent Majorana networks, enabling further insight into topological phases and vortex parity dynamics.
• Technical Enhancements: Addressing the challenges involved in fabricating coherent, low-disorder junctions and realizing well-defined geometry for controlled flux partitioning.

Laughlin pumping constitutes a fundamental transport process with deep implications for topological quantum matter, offering both stringent experimental tests of theoretical constructs and precision tools for probing emergent excitations in two-dimensional electron systems (Wang et al., 17 Jan 2026, Cao et al., 18 Sep 2025).