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arXiv:1709.09789 · Physical review. B./Physical review. B

Emergent orbitals in the cluster Mott insulator on a breathing kagome lattice

Gang Chen, Patrick A. Lee

Published Jan 12, 2018• 36 citations
arXivHTMLPDF

Abstract

Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the intersite charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3, as observed in ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$. Furthermore, at low temperatures, each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin-liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ are discussed, including an argument that the charge ordering must be short ranged if the charge per Mo is slightly off stoichiometric.

DOI
10.1103/physrevb.97.035124

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•Jan 1, 2015•0 citations
Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the intersite charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3, as observed in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​. Furthermore, at low temperatures, each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin-liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ are discussed, including an argument that the charge ordering must be short ranged if the charge per Mo is slightly off stoichiometric.
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, we study a single-band extended Hubbard model on an anisotropic kagome lattice with the 16\frac{1}{6}61​ electron filling. Due to the partial filling of the lattice, the intersite repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters rather than at lattice sites. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. The nature of charge excitations in cluster Mott insulators can be quite different from conventional Mott insulator and we show that there exists a cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 13\frac{1}{3}31​ of the total spinon excitations are magnetically active. Based on these results, we propose that the two Curie-Weiss regimes of the spin susceptibility in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic Kagome lattice with the 1/6 electron filling. Due to the partial filling of the lattice, the inter-site repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters, rather than at lattice sites. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. However, the nature of charge excitations in different cluster Mott insulators could be quite different and we show that there exists a novel cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 1/3 of the total spinon excitations are magnetically active. The strong coupling limit of the same model is also analyzed via a Kugel-Khomskii-like model. Based on these results, we propose that the anomalous behavior of the finite-temperature spin-susceptibility in LiZn2Mo3O8 may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.
Searching of materials, where a long-range magnetic order is suppressed by quantum fluctuations and a quantum spin liquid state realizes, is one of the central problems in the modern condensed matter physics. A possible candidate for such a state on the breathing Kagome lattice LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ is scrutinized by hard x-ray photoemission spectroscopy (HAXPES), cluster dynamical mean-field theory (cDMFT), and exact diagonalization of an extended Hubbard model. The Mo 3d3d3d core level HAXPES peaks of LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ are accompanied by shoulders on their lower energy side which are absent in Zn2Mo3O8{\mathrm{Zn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}Zn2​Mo3​O8​. The shoulder peaks observed only in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ indicate Mo3+{\mathrm{Mo}}^{3+}Mo3+ and Mo4+{\mathrm{Mo}}^{4+}Mo4+ charge fluctuations. The cDMFT calculations not only describe experimental valence-band HAXPES spectra demonstrating importance of the correlation effects, but also feature nonlocal spin fluctuations. Exact diagonalization taking into account intertrimer Coulomb repulsion demonstrates long-range charge fluctuations consistent with HAXPES results.
Motivated by twisted transition metal dichalcogenides (TMDs), we study an extended Hubbard model with both on-site and off-site repulsive interactions, in which Mott insulating states with concomitant charge order occur at fractional fillings. To resolve the charge ordering as well as the fate of the local moments formed thereby, we perform large-scale density matrix renormalization group calculations on cylindrical geometries for several filling fractions and ranges of interaction strength. Depending on the precise parameter regime, both antiferromagnetically ordered as well as quantum-disordered states are found, with a particularly prominent example being a quantum spin liquid-type ground state on top of charge-ordering with effective Kagomé geometry. We discuss the different mechanisms at play in stabilizing various electronic and magnetic states. The results suggest that moiré TMDs are a promising venue for emergent quantum magnetism of strongly interacting electrons.
Strong correlations effects, which are often associated to the approach to a Mott insulating state, in some cases may be observed even far from half filling. This typically happens whenever the intersite Coulomb repulsion induces a tendency toward charge ordering, an effect that confines the electrons, and in turn favors local moment formation, i.e., Mott localization. A distinct intermediate regime then emerges as a precursor of such a Wigner-Mott transition, which is characterized by both charge and spin correlations, displaying large mass enhancements and strong renormalizations of other Fermi-liquid parameters. Here we present a careful study of a quarter-filled extended Hubbard model---a simple example where such physics can be studied in detail, and discuss its relevance for the understanding of the phenomenology of low-density two-dimensional electron gases.
Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.