Bilayer Excitons in the Laughlin Fractional Quantum Hall State

TL;DR

The paper investigates interlayer Coulomb coupling between two Laughlin states in a graphene-based quantum Hall bilayer to realize bilayer excitons that carry neutral anyonic statistics. It combines bulk transport measurements in edgeless double Corbino and Hall-bar geometries with a bilayer ${}^2_0$CF/K-matrix theoretical framework to predict exciton formation, charge, and statistics. Key findings include the observation of exciton pairing that lowers the effective energy scale for bound quasiparticle–quasihole pairs, manifested as a perfect drag signal in Corbino geometry and strong interlayer correlations at specific fillings such as ν1 = ν2 = 3/8, which may host non-Abelian topological order. This work opens a pathway to engineering charge-neutral anyons and exploring exotic excitonic superfluidity and topological phases in quantum Hall bilayers, with potential implications for topological quantum computation.

Abstract

The Laughlin state embodies a universal class of fractional quantum Hall effects arising in two-dimensional electron systems subjected to strong perpendicular magnetic fields. Conventionally described by a single-component wavefunction, the Laughlin state features fractionally charged quasiparticles arising from correlations within one electron species. Here, we explore a novel physical situation by introducing inter-species Coulomb coupling between two intra-species Laughlin states in a quantum Hall graphene bilayer structure. Although quasiparticle excitations typically exhibit charge gaps of tens of Kelvin, we observe that this energy scale is significantly lowered through interlayer excitonic pairing between quasiparticles and quasiholes. Identified via transport measurements, these excitons belong to an unprecedented category of charge-neutral anyons, opening a new avenue for investigating exotic quantum statistics and phases of matter.

Figures (12)

• Figure 1: Laughlin states in a quantum Hall graphene bilayer. (a) Schematic of a single-layer Laughlin state stabilized by intralayer Coulomb interactions. At Landau-level filling $\nu=1/3$, its quasiparticle excitations carry a fractional charge of $e/3$. (b) Schematic of two coupled Laughlin states in a quantum Hall bilayer, each stabilized by intralayer interactions. In this configuration, quasiparticles and quasiholes residing in opposite layers interact through weak interlayer Coulomb coupling. (c–d) Counterflow drag measurements as a function of Landau-level filling along the equal-density line $\nu_1 = \nu_2$. Data are acquired from a quantum Hall bilayer device patterned into a Hall-bar geometry. (c) Longitudinal and (d) transverse responses are shown for the drive and drag layers at $B = 30$ T and $T = 0.3$ K. Insets illustrate the corresponding measurement configurations.
• Figure 2: Pairing between quasiparticles and quasiholes of the Laughlin state. (a) Schematic illustrating how the population of bilayer excitons can be tuned by introducing layer-asymmetric doping. This is achieved by varying the Landau-level fillings of layers 1 and 2 by $\pm \delta$, thereby generating equal numbers of quasiparticles and quasiholes in opposite layers. (b) Hall resistance of the drive layer, $R_{xy,\mathrm{drive}}$, (c) longitudinal resistances of the drive and drag layers, $R_{xx,\mathrm{drive}}$ and $R_{xx,\mathrm{drag}}$, and (d) Hall resistance of the drag layer, $R_{xy,\mathrm{drag}}$, as functions of $\Delta\nu$ measured at total filling $\nu_{\mathrm{total}} = 2/3$. (e) Parallel-flow conductance $G_{\mathrm{PF}}$, (f) counterflow conductance $G_{\mathrm{counter}}$, and (g) drag current ratio $I_{\mathrm{drag}}/I_{\mathrm{drive}}$ as functions of $\Delta\nu$, measured at the same $\nu_{\mathrm{total}} = 2/3$. (h) Map of $G_{\mathrm{PF}}$ and (i) map of $I_{\mathrm{drag}}/I_{\mathrm{drive}}$ across the $\nu_{\mathrm{total}}$–$\Delta\nu$ plane near the Laughlin state at $\nu_1 = \nu_2 = 1/3$ and $B = 28$ T. Near $\Delta\nu = 0$, both $I_{\mathrm{drag}}$ and $I_{\mathrm{drive}}$ vanish, resulting in an ill-defined drag ratio, indicated by the gray-shaded regions. Panels (b-d) are measured in the Hall-bar-shaped device; panels (e-i) are measured in the Corbino-shaped device.
• Figure 3: Exciton binding energy. (a) Arrhenius plot of the parallel-flow current at $\nu_{\mathrm{total}} = 2/3$ and $\Delta\nu = 0.06$. (b–c) Bulk transport measured at $\nu_1 = 1/3$ as a function of $\nu_2$ for (b) $B = 28$ T and (c) $B = 12$ T. The top, middle, and bottom panels show, respectively, the parallel-flow conductance $G_{\mathrm{PF}}$, counterflow conductance $G_{\mathrm{counter}}$, and drag current ratio $I_{\mathrm{drag}}/I_{\mathrm{drive}}$. (d–e) Temperature dependence of (d) drive and drag currents $I_{\mathrm{drive}}$ and $I_{\mathrm{drag}}$, and (e) the drag ratio $I_{\mathrm{drag}}/I_{\mathrm{drive}}$, measured at $\nu_1 = \nu_2 = 1/3$ and $B = 28$ T. The gray-shaded region marks the low-temperature regime where both currents vanish. The red-shaded region indicates the onset of simultaneous $I_{\mathrm{drive}}$ and $I_{\mathrm{drag}}$, corresponding to a perfect drag ratio. At higher temperatures, $I_{\mathrm{drive}}$ and $I_{\mathrm{drag}}$ bifurcate, and the drag ratio departs from unity. Data in this figure are measured in the Corbino-shaped device.
• Figure 4: Exciton pairing at half-filled $\Lambda$-levels. (a) Parallel-flow conductance $G_{\mathrm{PF}}$ as a function of $\nu_{\mathrm{total}}$ and $B$ along the equal-density line, revealing a sequence of magnetic-field–induced transitions in the FQH states, marked by horizontal black lines. In the high-field limit, the FQH states occur at integer and half-integer fillings of the $\Lambda$-levels, indicative of exotic exciton formation. (b) Parallel flow conductance $G_{\mathrm{PF}}$, (c) counterflow conductance $G_{\mathrm{counter}}$, and (d) drag current ratio $I_{\mathrm{drag}}/I_{\mathrm{drive}}$ as functions of $\nu_{\mathrm{total}}$, measured at $B = 31$ T. (e) Hall resistance on the drive layer $R_{xy,\mathrm{drive}}$ and longitudinal drag response $R_{xx,\mathrm{drag}}$ as a function of $\nu_1 = \nu_2$ along the equal-density line, measured in a Hall-bar device at $B = 25$ T. (f) Longitudinal and Hall drag response, $R_{xx,\mathrm{drag}}$ and $R_{xy,\mathrm{drag}}$, as functions of layer imbalance $\Delta\nu$, measured at $\nu_1 = \nu_2 = -3/8$ and $B = 25$ T. Panels (a-d) are measured in the Corbino-shaped device; panels (e-f) are measured in the Hall-bar-shaped device.
• Figure M1: Excitonic pairing in the Corbino geometry. (a) Schematic phase diagram of a quantum Hall bilayer, parameterized by $\nu_{\mathrm{total}}$ and $\Delta\nu$. Black solid lines mark the expected trajectories of layer-decoupled FQH states belonging to the Jain sequence. The red solid line denotes the equal-density line, where the filling factors in the two graphene layers are equal, $\nu_1 = \nu_2$. Red circles indicate the expected locations of Jain states along this line. (b--c) Parallel-flow conductance $G_{\mathrm{PF}}$ (top) and drag ratio $I_{\mathrm{drag}}/I_{\mathrm{drive}}$ (bottom) measured along the equal-density line as a function of $\nu_{\mathrm{total}}$ at (b) $B = 20$ T and (c) $B = 28$ T. The emergence of FQH states is signaled by vanishing $G_{\mathrm{PF}}$, whereas exciton pairing is manifested by perfect drag response with $I_{\mathrm{drag}}/I_{\mathrm{drive}} = 1$. Black vertical dotted lines mark the expected positions of Jain-sequence FQH states, while the red vertical dotted line denotes a half-filled $\Lambda$-level. The green dotted line marks the location of the two-component FQH state identified in previous works Li2019pairingLiu2019interlayerZhang2025fractionalexciton.