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arXiv:2512.16509 · International Conference on Solid State Devices and Materials (SSDM)

Supersolid crystals of dipolar excitons in a lattice

Corentin Morin, Camille Lagoin, Tanul Gupta, Nora Reinić, Adbhut Gupta, Kirk Baldwin, Loren N. Pfeiffer, Guido Pupillo, Dubin François

Published Sep 15, 2026• 0 citations
arXivHTMLPDF

Abstract

In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For example, supersolids combine density order that manifests as symmetry-breaking spatial arrangement, and frictionless superfluid flow. However, supersolids have proven to only exist under very stringent conditions, with evidence limited to a few spontaneously fragmented superfluids observed in the weakly-interacting regime. Here, we demonstrate a framework to realize crystalline supersolids in the strong interaction regime, by confining dipolar bosons in a lattice with long-range hopping. We show that dipolar excitons realize this lattice model. At fractional lattice fillings of one quarter, one third and one half we observe mesoscopic quantum crystals across around 100 sites that spontaneously break the lattice translational symmetry. At the same time, coherent long-range hopping induces off-diagonal long-range order such that the exciton solids are superfluids. Our numerical methods quantitatively confirm that supersolidity builds up in the ground-state of the lattice Hamiltonian.

DOI
10.7567/ssdm.2026.j-1-01

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In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For example, supersolids combine density order that manifests as symmetry-breaking spatial arrangement, and frictionless superfluid flow. However, supersolids have proven to only exist under very stringent conditions, with evidence limited to a few spontaneously fragmented superfluids observed in the weakly-interacting regime. Here, we demonstrate a framework to realize crystalline supersolids in the strong interaction regime, by confining dipolar bosons in a lattice with long-range hopping. We show that dipolar excitons realize this lattice model. At fractional lattice fillings of one quarter, one third and one half we observe mesoscopic quantum crystals across around 100 sites that spontaneously break the lattice translational symmetry. At the same time, coherent long-range hopping induces off-diagonal long-range order such that the exciton solids are superfluids. Our numerical methods quantitatively confirm that supersolidity builds up in the ground-state of the lattice Hamiltonian.
Abstract The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in a lattice potential. For bosons, in the last two decades the Hubbard Hamiltonian has been deeply scrutinised in the regime of short-range on-site interactions. On the other hand, extensions to longer-range off-site couplings between neighbouring lattice sites have remained mostly elusive experimentally. Entering this regime constitutes a well identified research frontier where quantum matter phases can spontaneously break the lattice symmetry. Here we unveil one of such phases, precisely the long-sought-after checkerboard solid. It is accessed by confining semiconductors dipolar excitons in a two-dimensional square lattice. The exciton checkerboard is signalled by a strongly minimised compressibility at half-filling of the lattice sites, in quantitative agreement with theoretical expectations. Our observations thus highlight that dipolar excitons enable controlled implementations of extended Bose-Hubbard Hamiltonians.
Enriching condensed-matter systems with quantum optical phenomena currently drives intense research efforts, particularly to introduce collective quantum correlations. Here we access this paradigm, by confining dipolar excitons in a nanoscopic lattice where long-range hopping, and nearest-neighbour dipolar repulsions, dress the Bose-Hubbard Hamiltonian. Long-range hopping is evidenced by the spontaneous buildup of many-body sub-radiance, signalled by an algebraic slowdown of excitons radiative dissipation. In addition, we observe a threshold increase of temporal coherence for dipolar quantum solids only. It suggests that excitons condense in a single sub-radiant state for Mott-like phases. These combine then spatial order and collectively extended coherence, in a single degree of freedom. Our study unveils that nanoscopic exciton arrays provide a unique platform to design new frontiers of strongly-correlated lattice models with long-range correlations.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.
We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.
Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance due to the appearance of a crystal structure and phase invariance due to phase locking of single-particle wave functions, responsible for superfluid phenomena. While originally predicted to be present in solid helium, ultracold quantum gases provided a first platform to observe supersolids, with particular success coming from dipolar atoms. Phase locking in dipolar supersolids has been probed through e.g. measurements of the phase coherence and gapless Goldstone modes, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases and supersolids with two-dimensional crystalline order, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase. Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with multiple spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars.
Superfluids under specific conditions can exhibit spontaneous breaking of continuous translation symmetries and form exotic spatially ordered states of matter known as supersolids. Despite its early theoretical prediction, it took over half-a-centrury to experimentally demonstrate the supersolid phase in ultracold atomic Bose-Einstein condensates, forming due to long-range interatomic interactions. Here we propose as a promising new platform for supersolidity exciton-polariton superfluids, confined in annular optically induced traps. The supersolid phase emerges due to effective attractive interactions, mediated by the normal excitonic component of the system. Experimental demonstration of spontaneously formed spatially ordered phase is in agreement with detailed mean-field theoretical analysis and numerical simulation. The spontaneous character of the observed supersolid transition is further evidenced by the formation of specific zero-energy Nambu-Goldstone modes in the collective excitation spectrum.