The metal insulator transition in cluster dynamical mean field theory: intersite correlation, cluster size, interaction strength, and the location of the transition line
To gain insight into the physics of the metal insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used one, two and four site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The cluster size dependence of the metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects start to occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences (in particular a sharper band edge) persist in the strong coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, and for differences in behavior between the single band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal insulator transition. Implications for the theoretical treatment of doped manganites are discussed.
Using the nonlocal coherent-potential approximation we study the effect of intersite spatial correlations on the transition from band insulator to metal as well as from metal to Mott insulator in the "alloy analogy" approach to the paramagnetic solution of the half-filled ionic Hubbard model. We find that intersite spatial correlations enhance the metallic phase.
A simple effective model for a description of magnetically ordered insulators is analysed. The tight binding Hamiltonian consists of the effective on-site interaction (U) and intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbours. The phase diagrams of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We show that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous p…
We study the one- and two- dimensional extended Hubbard model by means of the Composite Operator Method within the 2-pole approximation. The fermionic propagator is computed fully self-consistently as a function of temperature, filling and Coulomb interactions. The behaviors of the chemical potential (global indicator) and of the double occupancy and nearest-neighbor density- density correlator (local indicators) are analyzed in detail as primary sources of information regarding the instability of the paramagnetic (metal and insulator) phase towards charge ordering driven by the intersite Coul…
A simple effective model of charge ordered insulators is studied. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). In the analysis of the phase diagrams we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. The phase separated states have not been taken into account in previous analyses. Our investigations of two cases of the on-site interaction: attraction …
We study with exact diagonalization the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, $V$, to the band width drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing $V$ is compared to the observed optical conductivity of several layered molecular crystals with the theta and beta'' crystal structures.
We present a theoretical investigation of the electronic structure of rutile (metallic) and M$_1$ and M$_2$ monoclinic (insulating) phases of VO$_2$ employing a fully self-consistent combination of density functional theory and embedded dynamical mean field theory calculations. We describe the electronic structure of the metallic and both insulating phases of VO$_2$, and propose a distinct mechanism for the gap opening. We show that Mott physics plays an essential role in all phases of VO$_2$: undimerized vanadium atoms undergo classical Mott transition through local moment formation (in the M…
We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two dimensional square lattice using determinant Quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic (AF) order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.
Routes to enhance superconducting instability are explored for doped Mott insulators. With the help of insights for criticalities of metal-insulator transitions, geometrical design of lattice structure is proposed to control the instability. A guideline is to explicitly make flat band dispersions near the Fermi level without suppressing two-particle channels. In a one-dimensional model, numerical studies show that our prescription with finite-ranged hoppings realizes large enhancement of spin-gap and pairing dominant regions. We also propose several multi-band systems, where the pairing is dri…
In the present paper we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the mod…
The Hubbard model with additional intersite interaction `$V$' (the extended Hubbard model) is investigated by the correlator projection method (CPM). CPM is a newly developed numerical method which combines the equation-of-motion approach and the dynamical mean-field theory. Using this method, properties of the extended Hubbard Model at quarter filling are discussed with special emphasis on the metal-insulator transition induced by electron-electron correlations. The result shows a metal-insulator transition to a charge ordered insulator with antiferromagnetic order at low temperatures, but a …
We describe a recent implementation of the combined GW and dynamical mean field (DMFT) method "GW+DMFT" for the two-dimensional Hubbard model with on-site and nearest-neighbor repulsion. We clarify the relation of the GW+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free energy functional of the model. Furthermore, we describe a numerically exact technique for the self-consistent solution of the GW+DMFT equations, namely the hybridization expansion continuous-time algorithm for solving the dynamical impurity model that arises withi…
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we repro…
Femtosecond relaxation of photo-excited quasiparticles in the one dimensional Mott insulator ET-F2TCNQ are measured as a function of external pressure, which is used to tune the electronic structure. By fitting the static optical properties and measuring femtosecond decay times at each pressure value, we correlate the relaxation rates with the electronic bandwidth t and on the intersite correlation energy V. The scaling of relaxation times with microscopic parameters is different than for metals and semiconductors. The competition between localization and delocalization of the Mott-Hubbard exc…
Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of the extended Hubbard model of hard-core bosons on the pyrochlore lattice with partial fillings. When the intersite repulsion is dominant, the system is in a cluster Mott insulator phase with an integer number of bosons localized inside the tetrahedral units of the pyrochlore lattice. We show that the full phase diagram contains three cluster Mott insulator phases with 1/4, 1/2, and 3/4 boson fillings, respectively. We further demonstrate that all three cluster Mott insulators are Coulomb liquid phases an…
We employ dynamical density-matrix renormalization group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of `small' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard…
We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter $F_0^a$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism --- negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-in…
The ground state for the half-filled $t-t'$ Hubbard model is treated within the Hartree-Fock approximation and the slave boson approach including correlations. The criterium for the metal-insulator transition in the Slater scenario is formulated using an analytical free-energy expansion in the next-nearest-neighbor transfer integral $t'$ and in direct antiferromagnetic gap $Δ$. The correlation effects are generally demonstrated to favor the first-order transition. For a square lattice with a strong van Hove singularity, accidental close degeneracy of antiferromagnetic and paramagnetic phases i…
Quantum Monte Carlo and semiclassical methods are used to solve two and four site cluster dynamical mean field approximations to the square lattice Hubbard model at half filling and strong coupling. The energy, spin correlation function, phase boundary and electron spectral function are computed and compared to available exact results. The comparision permits a quantitative assessment of the ability of the different methods to capture the effects of intersite spin correlations. Two real space methods and one momentum space representation are investigated. One of the two real space methods is f…
A recently proposed configuration-interaction based impurity solver is used in combination with the single-site and four-site cluster dynamical mean field approximations to investigate the three-band copper oxide model believed to describe the electronic structure of high transition temperature copper-oxide superconductors. Use of the configuration interaction solver enables verification of the convergence of results with respect to the number of bath orbitals. The spatial correlations included in the cluster approximation substantially shift the metal-insulator phase boundary relative to the …
In this work we focus on the study of phase separation in the zero-bandwidth extended Hubbard with nearest-neighbors intersite Ising-like magnetic interactions $J$ and on-site Coulomb interactions $U$. The system has been analyzed by means of Monte Carlo simulations (in the grand canonical ensemble) on two dimensional square lattice (with $N=L\times L =400$ sites) and the results for $U/(4J)=2$ as a function of chemical potential and electron concentration have been obtained. Depending on the values of interaction parameters the system exhibits homogeneous (anti-)ferromagnetic (AF) or non-orde…
We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case…
The pyrochlore iridate In$_2$Ir$_2$O$_7$ is a strong $J_{\mathrm{eff}} = 1/2$ Mott insulator with frustrated magnetism. Despite the large trigonal crystal field, a small admixture of $J_{\mathrm{eff}} = 3/2$ component in the $J_{\mathrm{eff}} = 1/2$ bands and a small splitting of $J_{\mathrm{eff}} = 3/2$ bands are observed as compared with other pyrochlore iridates A$_2$Ir$_2$O$_7$ (A: trivalent cation). We argue that the reduced inter-site hopping between the $J_{\mathrm{eff}} = 1/2$ and the $J_{\mathrm{eff}} = 3/2$ manifold plays a predominant role in the distinct behavior of In$_2$Ir$_2$O$_…
Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in t…
We present an explanation for the puzzling spectral and transport properties of layered cobaltates close to the band-insulator limit, which relies on the key effect of charge ordering. Blocking a significant fraction of the lattice sites deeply modifies the electronic structure in a way that is shown to be quantitatively consistent with photoemission experiments. It also makes the system highly sensitive to interactions (especially to intersite ones), hence accounting for the strong correlations effects observed in this regime, such as the high effective mass and quasiparticle scattering rate.…
Spectral ellipsometry has been used to determine the dielectric function of an untwinned crystal of LaMnO_3 in the spectral range 0.5-5.6 eV at temperatures 50 K < T < 300 K. A pronounced redistribution of spectral weight is found at the Neel temperature T_N = 140 K. The anisotropy of the spectral weight transfer matches the magnetic ordering pattern. A superexchange model quantitatively describes spectral weight transfer induced by spin correlations. This analysis implies that the lowest-energy transitions around 2 eV are intersite d-d transitions, and that LaMnO_3 is a Mott-Hubbard insulator…
The electronic properties of many transition metal oxide systems require new ideas concerning the behaviour of electrons in solids for their explanation. A recent example, subsequent to that of cuprate superconductors, is of rare earth manganites doped with alkaline earths, namely $Re_{1-x}A_x MnO_3$, which exhibit colossal magnetoresistance, metal insulator transition and many other poorly understood phenomena. Here we show that the strong Jahn Teller coupling between the twofold degenerate ($d_{x^2 -y^2}$ and $d_{3z^2 -r^2}$) $e_g$ orbitals of $Mn$ and lattice modes of vibration (of the oxyg…
We unveil the microscopic origin of largely debated magnetism in the Mo$_{3}$O$_{8}$ cluster systems. Upon considering an extended Hubbard model at 1/6 filling on the anisotropic kagomé lattice formed by the Mo atoms, we argue that its ground state is determined by the competition between kinetic energy and intersite Coulomb interactions, which is controlled by the trimerisation of the kagomé lattice into the Mo$_{3}$O$_{13}$ clusters. Based on first-principles calculations, we show that the strong interaction limit is realised in LiZn$_{2}$Mo$_{3}$O$_{8}$ revealing a plaquette charge order wi…
Normal states of the attractive Hubbard model, especially in two dimension, are studied in the light of a transition from a Fermi liquid to an insulating or gapped state. A series of variational Monte Carlo calculations with better statistics is carried out to estimate accurately expectation values by several many-body wave functions. Although a relatively clear crossover is observed even in the plain Gutzwiller wave function, the states in both regimes are metallic. Meanwhile, a substantial metal-insulator transition takes place at |U|\sim W (band width) in an improved wave function in which …
We have performed systematic angle-resolved photoemission spectroscopy of the topological crystalline insulator (TCI) Pb1-xSnxTe to elucidate the evolution of its electronic states across the topological phase transition. As previously reported, the band structure of SnTe (x = 1.0) measured on the (001) surface possesses a pair of Dirac-cone surface states located symmetrically across the Xbar point in the (110) mirror plane. Upon approaching the topological phase transition into the trivial phase at x_c ~ 0.25, we discovered that Dirac cones gradually move toward the Xbar point with its spect…
We study spatial correlation effects in multiorbital systems, especially in a paramagnetic metallic state subject to Hund's coupling. We apply a cluster extension of the dynamical mean-field theory (DMFT) to the three-orbital Hubbard model away from half filling, where previous single-site DMFT studies revealed that local correlation effects caused by Hund's coupling bring about unusual strongly-correlated metallic behaviors. We find that Hund's coupling significantly affects the nonlocal correlations, too; it strongly modulates the electron distribution in the momentum space so as to make a m…
We present a model example of a quantum critical behavior of renormalized single-particle Wannier function composed of Slater s-orbitals and represented in an adjustable Gaussian STO-7G basis, which is calculated for cubic lattices in the Gutzwiller correlated state near the metal-insulator transition (MIT). The discussion is carried out within the extended Hubbard model and the method of approach proposed earlier [cf. Eur. Phys. J. B {\bf 66}, 385 (2008)]. The component atomic-wave-function size, the Wannier function maximum, as well as the system energy, all scale with the increasing lattice…
The electronic structure of the quasi-lowdimensional vanadium sulfide \bavs3 is investigated for the different phases above the magnetic ordering temperature. By means of density functional theory and its combination with dynamical-mean field theory, we follow the evolution of the relevant low-energy electronic states on cooling. Hence we go in the metallic regime from the room temperature hexagonal phase to the orthorhombic phase after the first structural transition, and close with the monoclinic insulating phase below the metal-insulator transition. Due to the low symmetry and expected inte…
The four-site DCA method of including intersite correlations in the dynamical mean field theory is used to investigate the metal-insulator transition in the Hubbard model. At half filling a gap-opening transition is found to occur as the interaction strength is increased beyond a critical value. The gapped behavior found in the 4-site DCA approximation is shown to be associated with the onset of strong antiferromagnetic and singlet correlations and the transition is found to be potential energy driven. It is thus more accurately described as a Slater phenomenon (induced by strong short ranged …
Despite many efforts to rationalize the strongly correlated electronic ground states in doped Mott insulators, the nature of the doping induced insulator to metal transition is still a subject under intensive investigation. Here we probe the nanoscale electronic structure of the Mott insulator Sr$_2$IrO$_{4-δ}$ with low-temperature scanning tunneling microscopy and find enhanced local density of states (LDOS) inside the Mott gap at the location of individual apical oxygen site defects. We visualize paths of enhanced conductance arising from the overlapping of defect states which induces finite…
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $z$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $1/\sqrt{z}$, and becomes exact on the infinite-$z$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with …
Mott transition plays a key role in strongly correlated physics but its nature is not yet fully understood. Motivated by recent development of Schwinger boson approach for the Kondo lattice, we propose in this work a novel slave fermion algorithm to study the Mott transition. Upon local approximation, our method yields a phase diagram with a zero-temperature continuous (Mott) metal-insulator transition at finite Coulomb interaction $U$ for the half-filled one-band Hubbard model on a square lattice, and the resistivity exhibits a critical scaling around the quantum Widom line. We argue that the…
The recent advances in angle resolved photoemission techniques allowed the unambiguous experimental confirmation of spin charge decoupling in quasi one dimensional (1D) Mott insulators. This opportunity stimulates a quantitative analysis of the spectral function $A(k,ω)$ of prototypical one dimensional correlated models. Here we combine Bethe Ansatz results, Lanczos diagonalizations and field theoretical approaches to obtain $A(k,ω)$ for the 1D Hubbard model as a function of the interaction strength. By introducing a {\it single spinon approximation}, an analytic expression is obtained, which …
The nature of the correlated phases found in some graphene heterostructures is under debate. We use dynamical mean-field theory (DMFT) to analyze the effect of local correlations close to half-filling on one of such systems, the ABC trilayer graphene aligned with hexagonal boron nitride (ABC/hBN), which presents a moiré superlattice. This system has shown insulating phases at integer fillings of the moiré lattice, precisely the fillings at which a sufficiently strong Coulomb interaction (U$_{\rm Mott}$) may produce a metal-insulator Mott transition. Our calculations show that the electronic st…
It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo scre…
An enduring question in correlated systems concerns whether superconductivity is favoured at a quantum critical point (QCP) characterised by a divergent quasiparticle effective mass. Despite such a scenario being widely postulated in high Tc cuprates and invoked to explain non-Fermi liquid transport signatures, experimental evidence is lacking for a critical divergence under the superconducting dome. We use ultra-strong magnetic fields to measure quantum oscillations in underdoped YBa2Cu3O6+x, revealing a dramatic doping-dependent upturn in quasiparticle effective mass at a critical metal-insu…
We analyze the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model, which describes complex fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. In a recent work [Phys. Rev. Research 2, 033084 (2020)] it has been shown that, upon varying filling or chemical potential, there exists a first-order quantum phase transition between a non-Fermi liquid (nFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low…
A slave boson representation for the degenerate Hubbard model is introduced. The location of the metal to insulator transition that occurs at commensurate densities is shown to depend weakly on the band degeneracy M. The relative weights of the Hubbard sub-bands depend strongly on M, as well as the magnetic properties. It is also shown that a sizable Hund's rule coupling is required in order to have a ferromagnetic instability appearing. The metal to insulator transition driven by an increase in temperature is a strong function of it.
We investigate the effect of oxygen-oxygen hopping on the three-band copper-oxide model relevant to high-$T_c$ cuprates, finding that the physics is changed only slightly as the oxygen-oxygen hopping is varied. The location of the metal-insulator phase boundary in the plane of interaction strength and charge transfer energy shifts by $\sim 0.5$eV or less along the charge transfer axis, the quasiparticle weight has approximately the same magnitude and doping dependence and the qualitative characteristics of the electron-doped and hole-doped sides of the phase diagram do not change. The results …
We provide an explicit lattice model of bosons with two separately conserved boson species [$U(1)\times U(1)$ global symmetry] realizing a direct transition between an integer quantum Hall effect of bosons and a trivial phase, where any intermediate phase is avoided by an additional symmetry interchanging the two species. If the latter symmetry is absent, we find intermediate superfluid phases where one or the other boson species condenses. We know the precise location of the transition since at this point our model has an exact non-local anti-unitary particle-hole-like symmetry that resembles…
Dark Metastable Conduction Channels near a Metal-Insulator Transition
Bar-Ilan University（巴伊兰大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）
Employing a Keldysh-Eilenberger technique, we theoretically study the generation of a sponta- neous supercurrent and the appearance of the $ϕ$0 phase shift parallel to uniformly in-plane mag- netized superconducting interfaces made of the surface states of a three-dimensional topological insulator. We consider two weakly coupled uniformly magnetized superconducting surfaces where a macroscopic phase difference between the s-wave superconductors can be controlled externally. We find that, depending on the magnetization strength and orientation on each side, a spontaneous supercurrent due to the…
We calculate exact zero-temperature real space properties of a substitutional magnetic impurity coupled to the edge of a zigzag silicene-like nanoribbon. Using a Lanczos transformation [Phys. Rev. B 91, 085101 (2015)] and the density matrix renormalization group method, we obtain a realistic description of stanene and germanene that includes the bulk and the edges as boundary one-dimensional helical metallic states. Our results for substitutional impurities indicate that the development of a Kondo state and the structure of the spin correlations between the impurity and the electron spins in t…
The high-temperature superconductivity in copper oxides emerges under strong influence of spin correlations in doped Mott insulators. Recent discoveries of charge-order (CO) correlations in Y-based hole-doped cuprates as well as in electron-doped cuprates suggest that charge correlations should also play an important role on the electronic states of cuprates, although those correlations have been so far detected mainly by x-ray scattering measurements. Here we show signatures of CO correlations in transport properties of electron-doped cuprates as anomalous enhancement of the metal-to-insulato…
Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional second-order topological insulators and superconductors. In this work, we show that the existence of sublattice degrees of freedom can enrich the tunability of bound states on the boundary and hence lift the constraint on their locations. We take the Kane-Mele model with honeycomb-lattice structure to illustrate the underlying physics. With the introduction of an in-plane exchange field to the model, we find that the boundary Dirac mass induced by the exchange field has a sensitive dependence on the bounda…
In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-$\downarrow$ are itinerant (with hopping amplitude $t$), whereas those with spin-$\uparrow$ are localized. The particles interact via on-site $U$ and intersite $V$ density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equival…
We present a comprehensive dynamical mean field study of the triangular lattice moiré Hubbard model, which is believed to represent the physics of moiré bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, str…
