The rare-earth telluride compound EuTe4 exhibits a charge density wave (CDW) and an unconventional thermal hysteresis transition. Herein, we report a comprehensive study of the CDW states in EuTe4 by using low-temperature scanning tunneling microscopy. Two types of charge orders are observed at 4 K, including a newly discovered spindle-shaped pattern and a typical stripe-like pattern. As an exotic charge order, the spindle-shaped CDW is off-axis and barely visible at 77 K, indicating that it is a hidden order developed at low temperature. Based on our first-principles calculations, we reveal the origins of the observed electronic instabilities. The spindle-shaped charge order stems from a subsequent transition based on the stripe-like CDW phase. Our work demonstrates that the competition and cooperation between multiple charge orders can generate exotic quantum phases.

While radiation scattering data provides insight inside the microstructure of liquids, the Debye relation relating the scattering intensityI(k) to the atom-atom structure factorsSab(k)shows that, ultimately, it is these individual structure correlation functions which contain the relevant information about the micro-structure. However, these quantities are not observables, except in few cases where one can invert the Debye relation to obtain the structure functions. In the majority of other cases, the need for model dependent computer simulations is unavoidable. The resulting calculations reveal that the scattering pre-peak is the result of cancellations between positive pre-peaks and negative anti-peaks contributions from the atom-atom structure factors. What of systems where this cancellation is such that it entirely suppresses the scattering pre-peak? One would be tempted to falsely conclude that there is no underlying micro-heterogeneity. Hence, the structure functions appear as hidden variables, and it is important to understand the relation between their features and the micro-structure of the system. Through the computer simulation study of various mono-ols, ranging from methanol to 1-nonanol, as well as the branched octanols, we show how the features of the atom-atom pair correlation functiongab(r)affect that of the structure factorsSab(k), and reveal that the micro-structure is ultimately the result of the charge ordering between different atoms in the system.

The emergence of charge order in doped Mott insulators has received considerable attention due to its relevance to a variety of realistic materials and experiments. To investigate the interplay between magnetic and charge order, we have studied the semiclassical Kondo lattice model, which includes both electronic and magnetic degrees of freedom. By combining Langevin dynamical simulations with the kernel polynomial method, our results reveal the presence of charged stripe order, checkerboard order, and non-uniform charge disorder in the near-half-filling regime. Importantly, our simulations show that both the doping level and the strength of thes-dexchange coupling play a crucial role in facilitating charge order formation. These phases give rise to distinct electronic structures as well as excitations in the magnetic dynamics, providing insights into the underlying mechanism of charge ordering phenomena.

The metal-hydride-based \"topochemical reduction\" process has produced several thermodynamically unstable phases across various transition metal oxide series with unusual crystal structures and nontrivial ground states. Here, by such an oxygen (de-)intercalation method we synthesis a samarium nickelate with ordered nickel valences associated with tri-component coordination configurations. This structure, with a formula of Sm9Ni9O22 as revealed by four-dimensional scanning transmission electron microscopy (4D-STEM), emerges from the intricate planes of {303}pc ordered apical oxygen vacancies. X-ray spectroscopy measurements and ab initio calculations show the coexistence of square planar, pyramidal, and octahedral Ni sites with mono-, bi-, and tri-valences. It leads to an intense orbital polarization, charge-ordering, and a ground state with a strong electron localization marked by the disappearance of ligand-hole configuration at low temperature. This nickelate compound provides another example of previously inaccessible materials enabled by topotactic transformations and presents an interesting platform where mixed Ni valence can give rise to exotic phenomena.

Charge ordering (CO) phenomena have been widely debated in strongly-correlated electron systems mainly regarding their role in high-temperature superconductivity. Here, the structural and charge distribution in NdNiO2 thin films prepared with and without capping layers, and characterized by the absence and presence of CO are elucidated. The microstructural and spectroscopic analysis is done by scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) and hard X-ray photoemission spectroscopy (HAXPES). Capped samples show Ni1+ , with an out-of-plane (o-o-p) lattice parameter of around 3.30 Å indicating good stabilization of the infinite-layer structure. Bulk-sensitive HAXPES on Ni-2p shows weak satellite features indicating large charge-transfer energy. The uncapped samples evidence an increase of the o-o-p parameter up to 3.65 Å on the thin film top with a valence toward Ni2+ in this region. Here, 4D-STEM demonstrates (303)-oriented stripes which emerge from partially occupied apical oxygen. Those stripes form quasi-2D coherent domains viewed as rods in the reciprocal space with Δqz ≈ 0.24 reciprocal lattice units (r.l.u.) extension located at Q = ( ± 1 3 , 0 , ± 1 3 $\\pm \\frac{1}{3},0,\\pm \\frac{1}{3}$ ) and ( ± 2 3 , 0 , ± 2 3 $\\pm \\frac{2}{3},0,\\pm \\frac{2}{3}$ ) r.l.u. The stripes associated with oxygen re-intercalation concomitant with hole doping suggest a possible link to the previously reported CO in infinite-layer nickelate thin films.

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking \"d-density wave\" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from ab initio calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some low-frequency C2z-breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to S=1/2 fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite W1 and W2 (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive W1>0, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state (T=0) diagram for W2≤0 as well as finite temperature (T>0) phase diagrams for W2=0 are presented. Two different types of charge order within 3×3 unit cell can occur. At T=0, for W2=0 phase separated states are degenerated with homogeneous phases (but T>0 removes this degeneration), whereas attractive W2<0 stabilizes phase separation at incommensurate fillings. For U/W1<0 and U/W1>1/2 only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive 0