We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many-body states in which an arbitrary number of localized fermionic particles coexist with a sea of mobile Cooper pairs with zero momentum. By considering the dice lattice as an example, we provide evidence that these exact eigenstates are, in fact, a manifestation of local integrals of motions of the projected Hamiltonian. In particular, the spin and particle densities retain memory of the initial state for a very long time if localized unpaired particles are present at the beginning of the time evolution. This shows that many-body localization of quasiparticles and superfluidity can coexist even in generic two-dimensional lattice models with flat bands, for which it is not known how to construct local conserved quantities. Our results open interesting perspectives on the old condensed-matter problem of the interplay between superconductivity and localization.

Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended cluster interaction $Q$, we incorporate the effect of gating through an on-site Hubbard-interaction $U$. Within quantum Monte Carlo, we find valence-bond solid, Nel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub the cluster rule, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our paper capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet.

Graphene quantum dots are promising candidates for qubits due to weak spin-orbit and hyperfine interactions. The hyperfine interaction, controllable via isotopic purification, could be the key to further improving the coherence. Here, we use isotopically enriched graphite crystals of both ${}^{12}\mathrm{C}$ and ${}^{13}\mathrm{C}$ grown by a high-pressure-high-temperature method to exfoliate graphene layers. We fabricated Hall bar devices and performed quantum transport measurements, revealing mobilities exceeding ${10}^5{\text{cm}}^2/\text{V}\text{s}$ and a long mean free path of microns, which are as high as natural graphene. Shubnikov–de Haas oscillations, quantum Hall effect up to the filling factor of one, and Brown-Zak oscillations due to the alignment of hBN and graphene are observed thanks to the high mobility. These results constitute a material platform for physics and engineering of isotopically enriched graphene qubits.

In some quantum many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125, 230602 (2020)] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (it is not a symmetry of the Hamiltonian). The quantum many-body scars are invariant under this group, while all other states are not. Here we apply this idea to lattice systems containing $M$ Majorana fermions per site. The Hilbert space for $N$ sites may be decomposed under the action of the $\text{SO}\left(N\right)\times \text{SO}\left(M\right)$ group, and the scars are the $\text{SO}\left(N\right)$ singlets. For any even $M$ there are two families of scars. One of them, which we call the $\eta$ states, is symmetric under the group $\mathrm{O}\left(N\right)$. The other, the $\zeta$ states, has the $\text{SO}\left(N\right)$ invariance. For $M=4$, where our construction reduces to spin-$1/2$ fermions on a lattice with local interactions, the former family are the $N+1\eta$-pairing states, while the latter are the $N+1$ states of maximum spin. We generalize this construction to $M>4$. For $M=6$ we exhibit explicit formulas for the scar states and use them to calculate the bipartite entanglement entropy analytically. For large $N$, it grows logarithmically with the subsystem size. We present a general argument that any group-invariant scars should have the entanglement entropy that is parametrically smaller than that of typical states. The energies of the scars we find are not equidistant in general but can be made so by choosing Hamiltonian parameters. For $M>6$ we find that with local Hamiltonians the scars typically have certain degeneracies. The scar spectrum can be made ergodic by adding a nonlocal interaction term. We derive the dimension of each scar family and show the scars could have a large contribution to the density of states for small $N$.

Motivated by the recent synthesis of a number of Mott insulating square-kagome materials, we explore the rich phenomenology of frustrated magnetism induced by this lattice geometry, also referred to as the squagome or shuriken lattice. On the classical level, square-kagome antiferromagnets are found to exhibit extensive degeneracies, order-by-disorder, and noncoplanar ordering tendencies, which we discuss for an elementary, classical Heisenberg model with nearest-neighbor and cross-plaquette interactions. Having in mind that upon introducing quantum fluctuations noncoplanar order can melt into chiral quantum spin liquids, we provide detailed information on the multitude of noncoplanar orders, including some which break rotational symmetry (possibly leading to nematic quantum orders), as well as a number of (incommensurate) spin spiral phases. Using extensive numerical simulations, we also discuss the thermodynamic signatures of these phases, which often show multistep thermal ordering. Our comprehensive discussion of the classical square-kagome Heisenberg model, often drawing comparisons to the conventional kagome antiferromagnet, sets the stage for future explorations of quantum analogs of the various phases, either conceptually, such as in quantum spin-1/2 generalizations of our model, or experimentally, such as in the Cu-based candidate materials.

We present a metaheuristic conditional neural-network-based method aimed at identifying physically interesting metastable states in a potential energy surface of high rugosity. To demonstrate how this method works, we identify and analyze spin textures with topological charge $Q$ ranging from 1 to $-13$ (where antiskyrmions have $Q<0$) in the Pd/Fe/Ir(111) system, which we model using a classical atomistic spin Hamiltonian based on parameters computed from density functional theory. To facilitate the harvest of relevant spin textures, we make use of the newly developed segment anything model. Spin textures with $Q$ ranging from $-3$ to $-6$ are further analyzed using finite-temperature spin-dynamics simulations. We observe that for temperatures up to around 20 K, lifetimes longer than 200 ps are predicted, and that when these textures decay, new topological spin textures are formed. We also find that the relative stability of the spin textures depend linearly on the topological charge, but only when comparing the most stable antiskyrmions for each topological charge. In general, the number of holes (i.e., non-self-intersecting curves that define closed domain walls in the structure) in the spin texture is an important predictor of stability—the more holes, the less stable the texture. Methods for systematic identification and characterization of complex metastable skyrmionic textures—such as the one demonstrated here—are highly relevant for advancements in the field of topological spintronics.

Accurately predicting the elastic properties of crystalline solids is vital for computational materials science. However, traditional atomistic-scale ab initio approaches are computationally intensive, especially for studying complex materials with a large number of atoms in a unit cell. We introduce a data-driven approach to efficiently predict the elastic properties of crystal structures using SE(3)-equivariant graph neural networks (GNNs). This approach yields important scalar elastic moduli with an accuracy comparable to that of recent data-driven studies. Importantly, our symmetry-aware GNN model also enables the prediction of the strain energy density (SED) and the associated elastic constants, the fundamental tensorial quantities that are significantly influenced by a material's crystallographic group. The model consistently distinguishes independent elements of SED tensors, in accordance with the symmetry of the crystal structures. Finally, our deep learning model possesses meaningful latent features, offering an interpretable prediction of the elastic properties.

Dipolar spin ensembles with random spin positions are attracting much attention because they help us to understand decoherence as it occurs in solid-state quantum bits in contact with spin baths. Also, these ensembles are systems which may show many-body localization, at least in the sense of very slow spin dynamics. We present measurements of the autocorrelations of spins on diamond surfaces at infinite temperature in a doubly rotating frame which eliminates local disorder. Strikingly, the timescales in the longitudinal and the transversal channel differ by more than one order of magnitude, which is a factor much greater than one would have expected from simulations of spins on lattices. A previously developed dynamic mean-field theory for spins (spinDMFT) fails to explain this phenomenon. Thus, we improve it by extending it to clusters (CspinDMFT). This theory does capture the striking mismatch up to two orders of magnitude for random ensembles. Without positional disorder, however, the mismatch is only moderate with a factor below 4. The pivotal role of positional disorder suggests that the strong mismatch is linked to precursors of many-body localization.

The moiré pattern induced by lattice mismatch in transition metal dichalcogenide heterobilayers causes the formation of flat bands, where interactions dominate the kinetic energy. At fractional fillings of the flat valence band, the long-range electron interactions then induce Wigner-Mott crystals. In this paper we investigate the nontrivial electronic phases appearing away from fractional fillings. Either competing phases arise that are characterized as doped Wigner-Mott charge transfer insulators, or alternatively a novel state with frozen charge order is conducting the “electron slush.” We propose that an extremely spatially inhomogeneous local density of states can serve as a key signature of the electron slush.

The charge-density-wave (CDW) amplitude mode of the high-pressure sulfur-IV phase is observed between 83 and 146 $\mathrm{G}\mathrm{Pa}$ using Raman spectroscopy. The energy of this excitation softens with pressure yet remains finite at ${\nu }_{\mathrm{CDW}}>100\mathrm{c}{\mathrm{m}}^{-1}$ up to the critical pressure, which is indicative of a weakly first-order transition. Our ab initio calculations show that the finite energy of the excitation originates from the coupling and mutual stabilization of the CDW modulation and a monoclinic lattice distortion. At the critical pressure, both the CDW modulation and lattice distortion disappear simultaneously. Due to the prevalence of CDW phases, this coupling between the CDW modulation and lattice distortion is expected to be relevant for a wide variety of elements and compounds.

Exciton condensation is a phenomenon that indicates the spontaneous formation of electron-hole pairs, which can lead to a phase transition from a semimetal to an excitonic insulator by opening a gap at the Fermi surface. Although the idea of an excitonic insulator has been proposed for several decades, current theoretical approaches can only provide qualitative descriptions, and a quantitative predictive tool is still lacking. To shed light on this issue, we developed an ab initio method based on finite-temperature density functional theory and many-body perturbation theory to calculate the critical behavior of exciton condensation. Utilizing our methodology on monolayer $\mathrm{TiSe}{}_2$, we identify a phase transition involving lattice distortion and nontrivial electron-hole correlation at a temperature exceeding the critical temperature of phonon softening. By breaking down the components within the gap equation, we demonstrate that exciton condensation, mediated by electron-phonon interaction, is the underlying cause of the charge-density-wave state observed in this compound. Overall, the methodology introduced in this work is general and sets the stage for searching for potential excitonic insulators in natural material systems.

Artificial Kitaev chains, formed by quantum dots coupled via superconductors, have emerged as a promising platform for realizing Majorana bound states. Even a minimal Kitaev chain (a quantum dot–superconductor–quantum dot setup) can host Majorana states at discrete sweet spots. However, unambiguously identifying Majorana sweet spots in such a system is still challenging. In this work, we propose an additional dot coupled to one side of the chain as a tool to identify good sweet spots in minimal Kitaev chains. When the two Majorana states in the chain overlap, the extra dot couples to both and thus splits an even-odd ground-state degeneracy when its level is on resonance. In contrast, a ground-state degeneracy will persist for well-separated Majorana states. This difference can be used to identify points in parameter space with spatially separated Majorana states, using tunneling spectroscopy measurements. We perform a systematic analysis of different relevant situations. We show that the additional dot can help distinguish between Majorana sweet spots and other trivial zero-energy crossings. We also characterize the different conductance patterns, which can serve as a guide for future experiments aiming to study Majorana states in minimal Kitaev chains.

Multiband effects in hybrid structures provide a rich playground for unconventional superconductivity. We combine two complementary approaches based on density-functional theory (DFT) and effective low-energy model theory in order to investigate the proximity effect in a Rashba surface state in contact with an $s$-wave superconductor. We discuss these synergistic approaches and combine the effective model and DFT analysis at the example of a Au/Al heterostructure. This allows us to predict finite-energy superconducting pairing due to the interplay of the Rashba surface state of Au, and hybridization with the electronic structure of superconducting Al. We investigate the nature of the induced superconducting pairing, and we quantify its mixed singlet-triplet character. Our findings demonstrate general recipes to explore real material systems that exhibit interorbital pairing away from the Fermi energy.

We consider suspended bilayer graphene under applied perpendicular electric bias field that is known to generate a single particle gap $2\mathrm{\Delta }$ and a related electric polarization $\mathcal{P}$. We argue that the bias also drives a quantum phase transition from band insulator to superfluid exciton condensate. The transition occurs when the exciton binding energy exceeds the band gap $2\mathrm{\Delta }$. We predict the critical bias (converted to band gap), ${\mathrm{\Delta }}_c\approx 60$ meV, below which the excitons condense. The critical temperature, $T_c\left(\mathrm{\Delta }\right)$, is maximum at $\mathrm{\Delta }\approx 25$ meV, $T_c^{max}\approx 115$ K, decreasing significantly at smaller $\mathrm{\Delta }$ due to thermal screening. Entering the condensate phase, the superfluid transition is accompanied by a cusp in the electric polarization $\mathcal{P}\left(\mathrm{\Delta }\right)$ at $\mathrm{\Delta }\to {\mathrm{\Delta }}_c$, which provides a striking testable signature. Additionally, we find that the condensate prefers to form a pair density wave.

The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matter with topology and correlations. With the rise of the moiré-based design of model systems, realizing a tunable and symmetric honeycomb lattice system with a narrow bandwidth can open access to new phases and insights. We propose the ABBA-stacked twisted double bilayer ${\mathrm{WSe}}_2$ as a realistic and tunable platform for reaching this goal. Adjusting the twist angle allows the bandwidth and the ratio between hopping parameters of different ranges to be tuned. Moreover, the system's small bandwidth and spin rotation symmetry enable effective control of the electronic structure through an in-plane magnetic field. We construct an extended Hubbard model for the system to demonstrate this tunability and explore possible ordered phases using the Hartree-Fock approximation. We find that at a hole filling of $\nu =2$ (two holes per moiré unit cell), an in-plane magnetic field of a few tesla can “dope” the system from a semimetal to a metal. Interactions then drive an instability towards a canted antiferromagnetic insulator ground state. Additionally, we observe a competing insulating phase with sublattice charge polarization. Finally, we discuss the experimental signatures of these insulating phases.

We theoretically investigate superconductivity under a spin-split band structure owing to a collinear-type antiferromagnetic order in quasi-two-dimensional organic compounds $\kappa$-(BEDT-${\mathrm{TTF})}_{2}X$. We find that the magnetic order can induce a Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state, where the Cooper pair possesses a finite center-of-mass momentum. We show this from two types of analyses: (1) an effective model where simple intraband attractive interactions are assumed and (2) many-body calculations of the repulsive Hubbard model based on the fluctuation-exchange approximation and the linearized Eliashberg equation. Our results show the possibility of realizing the FFLO state without applying an external magnetic field.