Evidence for a charged vortex lattice in an exciton superfluid
Authors: Ryan L. Lee, Jungwoo Lee, Viliam Vaňo, Bo Zou, Cheng-Li Chiu, Kenji Watanabe, Takashi Taniguchi, Allan MacDonald, Ali Yazdani
Abstract
Lattices of quantized vortices are a defining property of rotating superfluids and of type-II superconductors in magnetic fields. Realizing an analogous vortex lattice in an exciton superfluid-formed from bound electron-hole pairs-has remained challenging because excitons are electrically neutral. Building on previous theoretical studies of the low-energy excitations in an exciton superfluid, recent theory has predicted that in a strong magnetic field, a weakly charged exciton superfluid can stabilize a vortex-antivortex lattice arising from the mutual repulsion of fractionally charged vortex cores. Here we report evidence for this predicted vortex lattice in a bilayer exciton condensate by imaging its charged vortices with the scanning tunnelling microscope. The condensate forms between Landau levels of two graphene layers separated by a thin hexagonal boron nitride barrier in a perpendicular magnetic field. We find that the vortex lattice periodicity scales with the total excess charge and is insensitive to its distribution between the two layers, in quantitative agreement with theoretical predictions. Our observations provide evidence for phase coherence in an exciton superfluid system.
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Closest papers
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Vortex Lattice States of Bilayer Electron-Hole Fluids in Quantizing Magnetic Fields.Bo Zou, A. MacDonald · 2024 · Physical Review Letters · cited 5 times · Not summarized yet
Vortex Lattice States predicts the charged vortex–antivortex lattice in weakly charged electron–hole fluids that this paper tests by imaging.
Abstract
We show that the ground state of a weakly charged two-dimensional electron-hole fluid in a strong magnetic field is a broken translation symmetry state with interpenetrating lattices of localized vortices and antivortices in the electron-hole-pair field. The vortices and antivortices carry fractional charges of equal sign but unequal magnitude and have a honeycomb-lattice structure that contrasts with the triangular lattices of superconducting electron-electron-pair vortex lattices. We predict that increasing charge density or a weakening magnetic field drives a vortex delocalization transition that would be signaled experimentally by an abrupt increase in counterflow transport resistance.
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Quantum-vortex excitons beyond band topologyJin-Hyun Choi, Sang-Hoon Han, Young-Kwon Han et al. · 2026 · Not summarized yet
Quantum-vortex excitons studies bound excitons in flat Chern bands, focusing on exciton wavefunction winding rather than a charged condensate lattice.
Abstract
Optically exciting a typical low-dimensional semiconductor produces a nodeless \(s\)-type exciton as its lowest-energy bound state. Here, we explain how Coulomb phase matching stabilises a quantum-vortex exciton as the lowest bound state in flat Chern bands. Using a prototypical Yin--Yang kagome lattice, we demonstrate that increasing the spin--orbit coupling drives a transition of the lowest exciton from a quantum-vortex state to a zero-winding state, while leaving the band Chern numbers unchanged. We trace this behaviour to a gauge-invariant combination of exciton phase differences and Bloch-overlap phases that can reduce the Coulomb energy. By comparing states with identical wavefunction …
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Excitonic superfluid phase in double bilayer grapheneJ.-I.-A. Li, T. Taniguchi, K. Watanabe et al. · 2016 · Nature Physics · cited 311 times · Not summarized yet
Excitonic superfluid phase reports an exciton condensate in double bilayer graphene, providing experimental background for this study of its charged vortices.
Abstract
Strongly interacting bosons have been predicted to display a transition into a superfluid ground state, similar to Bose–Einstein condensation. This effect is now observed in a double bilayer graphene structure, with excitons as the bosonic particles. A spatially indirect exciton is created when an electron and a hole, confined to separate layers of a double quantum well system, bind to form a composite boson1,2. Such excitons are long-lived, and in the limit of strong interactions are predicted to undergo a Bose–Einstein condensate-like phase transition into a superfluid ground state1,2,3. Here, we report evidence of an exciton condensate in the quantum Hall effect regime of double-layer str…
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Quantum Hall drag of exciton condensate in grapheneXiao-Meng Liu, Kenji Watanabe, T. Taniguchi et al. · 2016 · Nature Physics · cited 295 times · Not summarized yet
Quantum Hall drag reports exciton condensation in graphene layers separated by boron nitride, the platform underlying this study's vortex imaging.
Abstract
An electronic double layer, subjected to a high magnetic field, can form an exciton condensate: a Bose–Einstein condensate of Coulomb-bound electron–hole pairs. Now, exciton condensation is reported for a graphene/boron-nitride/graphene structure. An exciton condensate is a Bose–Einstein condensate of electron and hole pairs bound by the Coulomb interaction1,2. In an electronic double layer (EDL) subject to strong magnetic fields, filled Landau states in one layer bind with empty states of the other layer to form an exciton condensate3,4,5,6,7,8,9. Here we report exciton condensation in a bilayer graphene EDL separated by hexagonal boron nitride. Driving current in one graphene layer generat…
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Exciton Condensation in Bilayer Quantum Hall SystemsJ. Eisenstein · 2013 · Annual Review of Condensed Matter Physics · cited 240 times · Not summarized yet
Exciton Condensation in Bilayer Quantum Hall Systems reviews the predicted and observed exciton condensate in bilayer systems that this paper examines through vortex lattices.
Abstract
The condensation of excitons, bound electron-hole pairs in a solid, into a coherent collective electronic state was predicted more than 50 years ago. Perhaps surprisingly, the phenomenon was first observed in a system consisting of two closely spaced parallel two-dimensional electron gases in a semiconductor double quantum well. At an appropriate high magnetic field and low temperature, the bilayer electron system condenses into a state resembling a superconductor, only with the Cooper pairs replaced by excitons consisting of electrons in one layer bound to holes in the other. In spite of being charge neutral, the transport of excitons within the condensate gives rise to several spectacular …
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Bose–Einstein condensation of excitons in bilayer electron systemsJ. Eisenstein, A. Macdonald · 2004 · Nature · cited 708 times · Not summarized yet
Bose–Einstein condensation of excitons reviews quantum Hall bilayer condensates and their charged vortices, the background for this paper's lattice study.
Abstract
An exciton is the particle-like entity that forms when an electron is bound to a positively charged ‘hole’. An ordered electronic state in which excitons condense into a single quantum state was proposed as a theoretical possibility many years ago. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron–electron bilayers as in electron–hole bilayers. In current quantum Hall excitonic condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extremely large bilayer …
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Exciton superfluidity in two-dimensional bilayers at zero and high magnetic fieldsS.S.S. Sarma, Yang-Zhi Chou · 2026 · Not summarized yet
Exciton superfluidity in two-dimensional bilayers analyzes coherence and superfluidity across zero-field and quantum Hall bilayers rather than imaging charged vortex lattices.
Abstract
We study interlayer exciton superfluidity versus layer separation in two-dimensional electron-hole bilayers at zero magnetic field and quantum Hall bilayers at total filling $\nu_T=1$. Unscreened Hartree-Fock theory predicts coherence at every finite separation, with an energy scale decaying inversely with separation at large distances. We examine how screening, correlations, and spatial instabilities modify this prediction. At zero field, we solve the linearized gap equation with the full momentum and frequency dependence of the interaction screened within the random-phase approximation, without an imposed cutoff. The apparent plasmon enhancement of pairing in the ladder approximation is la…
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Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions.K. Moon, H. Mori, Kun Yang et al. · 1994 · Physical Review B (Condensed Matter) · cited 380 times · Not summarized yet
Spontaneous interlayer coherence describes charged vortices in quantum Hall bilayers, providing a basis for interpreting the imaged lattice.
Abstract
At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs can be neutral or ca…
Prior work it builds on
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Crossover between strongly coupled and weakly coupled exciton superfluidsXiao-Meng Liu, J.-I.-A. Li, Kenji Watanabe et al. · 2020 · Science · cited 93 times · Not summarized yet
Crossover between strongly coupled and weakly coupled exciton superfluids studies interaction regimes in graphene bilayers, not vortex-lattice formation.
Abstract
Description Following a crossover Superfluidity in fermionic systems occurs through the pairing of fermions into bosons, which can undergo condensation. Depending on the strength of the interactions between fermions, the pairs range from large and overlapping to tightly bound. The crossover between these two limits has been explored in ultracold Fermi gases. Liu et al. observed the crossover in an electronic system consisting of two layers of graphene separated by an insulating barrier and placed in a magnetic field. In this two-dimensional system, the pairs were excitons formed from an electron in one layer and a hole in the other. The researchers used magnetic field and layer separation to…
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Direct observation of a magnetic-field-induced Wigner crystalYen-Chen Tsui, Min-Hao He, Yuwen Hu et al. · 2023 · Nature · cited 127 times · Not summarized yet
Direct observation of a magnetic-field-induced Wigner crystal uses scanning tunnelling microscopy to image an electron crystal, a competing interpretation distinguished here by charge scaling.
Abstract
Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2–11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magn…
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Strongly correlated excitonic insulator in atomic double layersLi-Guo Ma, P. Nguyen, Zefang Wang et al. · 2021 · Nature · cited 286 times · Not summarized yet
Strongly correlated excitonic insulator studies correlated exciton fluids and crystalline phases in atomic double layers, rather than vortices in a graphene condensate.
Abstract
Excitonic insulators (EIs) arise from the formation of bound electron–hole pairs (excitons)1,2 in semiconductors and provide a solid-state platform for quantum many-boson physics3–8. Strong exciton–exciton repulsion is expected to stabilize condensed superfluid and crystalline phases by suppressing both density and phase fluctuations8–11. Although spectroscopic signatures of EIs have been reported6,12–14, conclusive evidence for strongly correlated EI states has remained elusive. Here we demonstrate a strongly correlated two-dimensional (2D) EI ground state formed in transition metal dichalcogenide (TMD) semiconductor double layers. A quasi-equilibrium spatially indirect exciton fluid is cre…
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Imaging interlayer exciton superfluidity in a 2D semiconductor heterostructureJacob Cutshall, Fateme Mahdikhany, Anna S. Roche et al. · 2025 · Science Advances · cited 37 times · Not summarized yet
Imaging interlayer exciton superfluidity directly images coherence in a 2D semiconductor heterostructure, applying imaging to exciton superfluidity rather than charged vortices.
Abstract
Excitons, which are Coulomb bound electron-hole pairs, are composite bosons and thus at low temperature can form a superfluid state with a single well-defined amplitude and phase. We directly image this macroscopic exciton superfluid state in an hBN-separated MoSe2-WSe2 heterostructure. At high density, we identify quasi-long-range order over the entire active area of our sample, through spatially resolved coherence measurements. By varying the exciton density and sample temperature, we map out the phase diagram of the superfluid. We observe the superfluid phase persisting to a temperature of 15 K, which is in excellent agreement with theoretical predictions. This works paves the way to real…
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Spontaneous interlayer coherence in double-layer quantum Hall systems: Symmetry-breaking interactions, in-plane fields, and phase solitons.Kun Yang, K. Moon, L. Belkhir et al. · 1996 · Physical Review B (Condensed Matter) · cited 62 times · Not summarized yet
Symmetry-breaking interactions analyzes interlayer coherence and phase solitons in quantum Hall bilayers, theoretical background for charged defects in this system.
Abstract
At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. The system can be mapped to an equivalent system of pseudospin 1/2 particles with pseudospin-dependent interactions and easyplane magnetic order. In this paper we discuss how the presence of a weak interlayer tunneling term alters the properties of double-layer systems when the broken symmetry is present. We use the energy functional and equations of motion derived earlier to evaluate the zero-temperature response functions of the double-layer system and use our results to discuss analogies between this system and Josephson-couple…
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