We introduce the notion of superstructure Mottness to describe the Mott and Wigner-Mott transition in doped strongly correlated electron systems at commensurate filling fractions away from one electron per site. We show that superstructure Mottness emerges in an inhomogeneous electron system when the superstructure contains an odd number of electrons per supercell. We argue that superstructure Mottness exists even in the absence of translation symmetry breaking by a superlattice, provided that the extended or intersite Coulomb interaction is strong. In the latter case, superstructure Mottness offers a unifying framework for the Mott and Wigner physics and a nonperturbative, strong coupling description of the Wigner-Mott transition. We support our proposal by studying a minimal single-band ionic Hubbard $t$-$U$-$V$-$Δ$ model with nearest neighbor Coulomb repulsion $V$ and a two-sublattice ionic potential $Δ$. The model is mapped onto a Hubbard model with two effective ``orbitals'' representing the two sites within the supercell, the intra and interorbital Coulomb repulsion $U$ and $U^\prime \sim V$, and a crystal field splitting $Δ$. Charge order on the original lattice corresponds to orbital order. Developing a cluster Gutzwiller approximation, we study the effects and the interplay between $V$ and $Δ$ on the Mott and Wigner-Mott transitions at quarter-filling. We provide the mechanism by which the superlattice potential enhances the correlation effects and the tendency towards local moment formation, construct and elucidate the phase diagram in the unifying framework of superstructure Mottness.
We propose a phenomenological understanding of the recently discovered weak Mott insulator in the moiré superlattice of twisted bilayer graphene, especially the emergent superconductivity at low temperature within the weak Mott insulator phase, namely while lowering temperature, the longitudinal resistivity first grows below temperature $T_m$, but then rapidly drops to zero at even lower temperature $T_c$. An emergent superconductor in an insulator phase is very unusual. Here we propose that this phenomenon is due to the pure two-dimensional nature of the bilayer graphene moiré superlattice. W…
We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by t…
We investigate the low-temperature electrical and thermal transport properties in atomically precise metallic heterostructures involving strongly-correlated electron systems. The model of the Mott-insulator/ band-insulator superlattice was discussed in the framework of the slave-boson mean-field approximation and transport quantities were derived by use of the Boltzmann transport equation in the relaxation-time approximation. The results for the optical conductivity are in good agreement with recently published experimental data on (LaTiO$_3)_N$/(SrTiO$_3)_M$ superlattices and allow us to esti…
We use quantum Monte Carlo and exact diagonalization calculations to study the Mott-insulator to superconductor quantum phase transition in a two-dimensional fermionic Hubbard model with attractive interactions in the presence of a superlattice potential. The model introduced offers unique possibilities to study such transitions in optical lattice experiments. We show that, in regimes with moderate to strong interactions, the transition belongs to the 3D-XY universality class. We also explore the character of the lowest energy charge excitations in the insulating and superconducting phases and…
We investigate the electronic reconstruction in (LaNiO$_{3}$)$_n$/(LaAlO$_{3}$)$_3$ (n=3, 5 and 10) superlattices due to the quantum confinement (QC) by d.c. transport and resonant soft x-ray absorption spectroscopy. In proximity to the QC limit, a Mott-type transition from an itinerant electron behavior to a localized state is observed. The system exhibits tendency towards charge-order during the transition. ab initio cluster calculations are in good agreement with the absorption spectra, indicating that the apical ligand hole density is highly suppressed resulting in a strong modification of…
Experiments performed over the last twenty years have revealed striking similarities between several two-dimensional (2D) fermion systems, including diluted two-dimensional electron liquids in semiconductors, 3He monolayers, and layered organic charge-transfer salts. These experimental results, together with recent theoretical advances, provide compelling evidence that strong electronic correlations - Wigner-Mott physics - dominate the universal features of the corresponding metal-insulator transitions (MIT). Here we review the recent theoretical work exploring quantum criticality of Mott and …
We report on the epitaxial strain-driven electronic and antiferromagnetic modulations of a pseudospin-half square lattice realized in superlattices of (SrIrO3)1/(SrTiO3)1. With increasing compressive strain, we find the low-temperature insulating behavior to be strongly suppressed with a corresponding systematic reduction of both the Neel temperature and the staggered moment. However, despite such a suppression, the system remains weakly insulating above the Neel transition. The emergence of metallicity is observed under large compressive strain but only at temperatures far above the Néel tran…
We study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $ν= 1/m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer $m$. In contrast for even integer $m$, the spin sector remains gapless and the resulting insu…
Understanding Mott insulators and charge density waves (CDW) is critical for both fundamental physics and future device applications. However, the relationship between these two phenomena remains unclear, particularly in systems close to two-dimensional (2D) limit. In this study, we utilize scanning tunneling microscopy/spectroscopy to investigate monolayer 1T-NbSe2 to elucidate the energy of the Mott upper Hubbard band (UHB), and reveal that the spin-polarized UHB is spatially distributed away from the dz2 orbital at the center of the CDW unit. Moreover, the UHB shows a root3 x root3 R30° per…
In the field of condensed matter, the quest to obtain an experimental realization of a Kondo lattice has generated a tremendous effort of the community, from both standpoints of experiments and theory. The pursuit of obtaining independent magnetic moments, via charge localization through Coulomb interactions, is paramount for applications in nanotechnology. In particular, systems with simultaneous charge and spin degrees of freedom can manifest both Kondo spin quenching and Mott-Hubbard charge localization. A unified experimental framework illuminating the pathway between the two phenomena is …
We address the effective tight-binding Hamiltonian that describes the insulating Mott state of twisted graphene bilayers at a magic angle. In that configuration, twisted bilayers form a honeycomb superlattice of localized states, characterized by the appearance of flat bands with four-fold degeneracy. After calculating the maximally localized superlattice Wannier wavefunctions, we derive the effective spin model that describes the Mott state. We suggest that the system is an exotic ferromagnetic Mott insulator, with well defined experimental signatures.
We study charge ordering driven by Coulomb interactions on triangular lattices relevant to the Wigner-Mott transition in two dimensions. Dynamical mean-field theory reveals the pinball liquid phase, a charge ordered metallic phase containing quasi-localized (pins) coexisting with itinerant (balls) electrons. Based on an effective periodic Anderson model for this phase, we find an antiferromagnetic Kondo coupling between pins and balls and strong quasiparticle renormalization. Non-Fermi liquid behavior can occur in such charge ordered systems due to spin-flip scattering of itinerant electrons o…
Strong correlation 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 inter-site Coulomb repulsion induces a tendency towards 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 Fe…
We theoretically investigate topological properties of the one-dimensional superlattice anyon-Hubbard model, which can be mapped to a superlattice bose-Hubbard model with an occupation-dependent phase factor by fractional Jordan-Wigner transformation. The topological anyon-Mott insulator is identified by topological invariant and edge modes using exact diagonalization and density-matrix renormalization-group algorithm. When only the statistical angle is varied and all other parameters are fixed, a statistically induced topological phase transition can be realized, which provides new insights i…
Here we present polarized neutron reflectometry measurements exploring thin film heterostructures comprised of a strongly correlated Mott state, GdTiO$_3$, embedded with SrTiO$_3$ quantum wells. Our results reveal that the net ferromagnetism inherent to the Mott GdTiO$_3$ matrix propagates into the nominally nonmagnetic SrTiO$_3$ quantum wells and tracks the magnetic order parameter of the host Mott insulating matrix. Beyond a well thickness of 5 SrO layers, the magnetic moment within the wells is dramatically suppressed, suggesting that quenched well magnetism comprises the likely origin of q…
Spin-orbit-coupled Mott iridates show great similarity with parent compounds of superconducting cuprates, attracting extensive research interests especially for their electron-doped states. However, previous experiments are largely limited within a small doping range due to the absence of effective dopants, and therefore the electron-doped phase diagram remains elusive. Here we utilize an ionic-liquid-gating induced protonation method to achieve electron-doping into a 5d Mott-insulator built with SrIrO3/SrTiO3 superlattice, and achieve a systematic mapping of its electron-doped phase diagram w…
We present a theory describing the mechanism for the two-dimensional (2D) metal-insulator transition (MIT) in absence of disorder. A two-band Hubbard model is introduced, describing vacancy-interstitial pair excitations within the Wigner crystal. Kinetic energy gained by delocalizing such excitations is found to lead to an instability of the insulator to self-doping above a critical carrier concentration $n=n_c$, mapping the problem to a density-driven Mott MIT. This mechanism provides a natural microscopic picture of several puzzling experimental features, including the large effective mass e…
Electron-electron scattering usually dominates the transport in strongly correlated materials. It typically leads to pronounced resistivity maxima in the incoherent regime around the coherence temperature $T^{*}$, reflecting the tendency of carriers to undergo Mott localization following the demise of the Fermi liquid. This behavior is best pronounced in the vicinity of interaction-driven (Mott-like) metal-insulator transitions, where the $T^{*}$ decreases, while the resistivity maximum $ρ_{max}$ increases. Here we show that, in this regime, the entire family of resistivity curves displays a c…
Motivated by the realization of spin-valley Hubbard on triangular moiré superlattice in ABC trilayer graphene aligned with hexagon boron nitride (hBN) and possibly also in twisted transition metal dichalcogenide homobilayers, we study possible Mott insulating phases and pseudogap metals based on symmetry constraint and parton mean field theories. First we show that Luttinger constraint allows two distinct symmetric and featureless Fermi liquids when there is an inter-valley Hund's term breaking $SU(4)$ spin rotation. Especially, there exists a symmetric and featureless "pseudogap metal" with s…
Strong correlation effects, such as a dramatic increase in the effective mass of the carriers of electricity, recently observed in the low density electron gas have provided spectacular support for the existence of a sharp metal-insulator transitions in dilute two dimensional electron gases. Here we show that strong correlations, normally expected only for narrow integer filled bands, can be effectively enhanced even far away from integer filling, due to incipient charge ordering driven by non-local Coulomb interactions. This general mechanism is illustrated by solving an extended Hubbard mode…
A set of broken symmetry two-dimensional ground states are predicted in (111)-oriented (LaNiO$_3$)$_N$/(LaAlO$_3$)$_M$ ($N$/$M$) superlattices, based on density functional theory (DFT) calculations including a Hubbard $U$ term. An unanticipated Jahn-Teller distortion with $d_{z^2}$ orbital polarization and a FM Mott insulating (and multiferroic) phase emerges in the double perovskite (1/1), that shows strong susceptibility to strain-controlled orbital engineering. The LaNiO$_3$ bilayer with graphene topology has a switchable multiferroic (ferromagnetic (FM) and ferroelectric) insulating ground…
We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transiti…
Mott insulator plays a central role in strongly correlated physics, where the repulsive Coulomb interaction dominates over the electron kinetic energy and leads to insulating states with one electron occupying each unit cell. Doped Mott insulator is often described by the Hubbard model3, which can give rise to other correlated phenomena such as unusual magnetism and even high-temperature superconductivity. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott phy…
We consider an interaction-driven scenario for the two-dimensional metal-insulator transition in zero magnetic field (2D-MIT), based on melting the Wigner crystal through vacancy-interstitial pair formation. We show that the transition from the Wigner-Mott insulator to a heavy Fermi liquid emerges as an instability to self-doping, resembling conceptually the solid to normal liquid transition in He3. The resulting physical picture naturally explains many puzzling features of the 2D-MIT.
We study interaction-induced Mott insulators, and their topological properties in a 1D non-Hermitian strongly-correlated spinful fermionic superlattice system with either nonreciprocal hopping or complex-valued interaction. For the nonreciprocal hopping case, the low-energy neutral excitation spectrum is sensitive to boundary conditions, which is a manifestation of the non-Hermitian skin effect. However, unlike the single-particle case, particle density of strongly correlated system does not suffer from the non-Hermitian skin effect due to the Pauli exclusion principle and repulsive interactio…
The Wigner crystal state, first predicted by Eugene Wigner in 1934, has fascinated condensed matter physicists for nearly 90 years2-14. Studies of two-dimensional (2D) electron gases first revealed signatures of the Wigner crystal in electrical transport measurements at high magnetic fields2-4. More recently optical spectroscopy has provided evidence of generalized Wigner crystal states in transition metal dichalcogenide (TMDC) moiré superlattices. Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Scanning tunneling microscopy (S…
Manipulating the orbital state in a strongly correlated electron system is of fundamental and technological importance for exploring and developing novel electronic phases. Here, we report an unambiguous demonstration of orbital occupancy control between t2g and eg multiplets in quasi-twodimensional transition metal oxide superlattices (SLs) composed of a Mott insulator LaCoO3 and a band insulator LaAlO3. As the LaCoO3 sublayer thickness approaches its fundamental limit (i.e. one unit-cell-thick), the electronic state of the SLs changed from a Mott insulator, in which both t2g and eg orbitals …
We devise a model to explain why twisted bi-layer graphene (TBLG) exhibits insulating behavior when $ν=2,3$ charges occupy a unit moiré cell, a feature attributed to Mottness, but not for $ν=1$, clearly inconsistent with Mott insulation. We compute $r_s=E_U/E_K$, where $E_U$ and $E_K$ are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density $10^4$ higher than in the experiments and (ii) a transition to a series of Wigner crystalline states exists as a function of $ν$. We find, for $ν=1$, $r_s$ fails to cross the threshold ($r_s = 37$) for the…
The evolution of a Landau Fermi liquid into a nonmagnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids, exciton condensates and unconventional superconductivity. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice, providing a unique opportunity to drive a metal-insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electricall…
Ab initio calculations are used to predict that a superlattice composed of layers of LaTiO3 and LaNiO3 alternating along the [001] direction is a S=1 Mott insulator with large magnetic moments on the Ni sites, negligible moments on the Ti sites and a charge transfer gap set by the energy difference between Ni d and Ti d states, distinct from conventional Mott insulators. Correlation effects are enhanced on the Ni sites via filling the oxygen p states and reducing the Ni-O-Ni bond angle. Small hole (electron) doping of the superlattice leads to a two-dimensional single-band situation with holes…
Two dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states as well as many body physics of excitons. Here, we present experiments that unite these hitherto separate efforts and show how excitons that are dynamically screened by itinerant electrons to form exciton-polarons, can be used as a spectroscopic tool to study interaction-induced incompressible states of electrons. The MoSe$_2$/hBN/MoSe$_2$ heterostructure that we study exhibits a long-period Moiré superlattice as evidenced by coherent-hole tunneling mediated avoided crossi…
The elementary optical excitations in two dimensional semiconductors hosting itinerant electrons are attractive and repulsive polarons -- excitons that are dynamically screened by electrons. Exciton-polarons have hitherto been studied in translationally invariant degenerate Fermi systems. Here, we show that electronic charge order breaks the excitonic translational invariance and leads to a direct optical signature in the exciton-polaron spectrum. Specifically, we demonstrate that new optical resonances appear due to spatially modulated interaction between excitons and electrons in an incompre…
In a certain regime of low carrier densities and strong correlations, electrons can crystallize into a periodic arrangement of charge known as Wigner crystal. Such phases are particularly interesting in one dimension (1D) as they display a variety of charge and spin ground states which may be harnessed in quantum devices as high-fidelity transmitters of spin information. Recent theoretical studies suggest that the strong Coulomb interactions in Mott insulators and other flat band systems, may provide an attractive higher temperature platform for Wigner crystallization, but due to materials and…
We examine the electronic properties of newly discovered "ferroelectric" metal LiOsO$_3$ combining density-functional and dynamical mean-field theories. We show that the material is close to a Mott transition and that electronic correlations can be tuned to engineer a Mott multiferroic state in 1/1 superlattice of LiOsO$_3$ and LiNbO$_3$. We use electronic structure calculations to predict that the (LiOsO$_3$)$_1$/(LiNbO$_3$)$_1$ superlattice is a type-I multiferroic material with a ferrolectric polarization of 41.2~$μ$C cm$^{-2}$, Curie temperature of 927\,K, and Néel temperature of 671\,K. O…
The moiré superlattice formed by ABC stacked trilayer graphene aligned with a hexagonal boron nitride substrate (TG/h-BN) provides an interesting system where both the bandwidth and the topology can be tuned by an applied perpendicular electric field $D$ . Thus the TG/h-BN system can simulate both Hubbard model physics and nearly flat Chern band physics within one sample. We derive lattice models for both signs of $D$ (which controls the band topology) separately through explicit Wannier orbital construction and mapping of Coulomb interaction. When the bands are topologically trivial, we discu…
We develop a theory for a continuous bandwidth-tuned transition at fixed \textit{fractional} electron filling from a metal with a generic Fermi surface to a `Wigner-Mott' insulator that spontaneously breaks crystalline space-group symmetries. Across the quantum critical point, (i) the entire electronic Fermi surface disappears abruptly upon approaching from the metallic side, and (ii) the insulating charge gap and various order parameters associated with the spontaneously broken space-group symmetries vanish continuously upon approaching from the insulating side. Additionally, the insulating s…
The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $π$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is …
An exotic phase, the bond order wave, characterized by the spontaneous dimerization of the hopping, has been predicted to exist sandwiched between the band and Mott insulators in systems described by the ionic Hubbard model. Despite growing theoretical evidences, this phase still evades experimental detection. Given the recent realization of the ionic Hubbard model in ultracold atomic gases, we propose here to detect the bond order wave using superlattice modulation spectroscopy. We demonstrate, with the help of time-dependent density-matrix renormalization group and bosonization, that this sp…
We report an experimental investigation of the two-dimensional ${J}_{\rm eff}$ = 1/2 antiferromagnetic Mott insulator by varying the interlayer exchange coupling in [(SrIrO$_3$)$_1$, (SrTiO$_3$)$_m$] ($m$ = 1, 2 and 3) superlattices. Although all samples exhibited an insulating ground state with long-range magnetic order, temperature-dependent resistivity measurements showed a stronger insulating behavior in the $m$ = 2 and $m$ = 3 samples than the $m$ = 1 sample which displayed a clear kink at the magnetic transition. This difference indicates that the blocking effect of the excessive SrTiO$_…
We report the nanoscale conductivity imaging of correlated electronic states in angle-aligned WSe2/WS2 heterostructures using microwave impedance microscopy. The noncontact microwave probe allows us to observe the Mott insulating state with one hole per moiré unit cell that persists for temperatures up to 150 K, consistent with other characterization techniques. In addition, we identify for the first time a Mott insulating state at one electron per moiré unit cell. Appreciable inhomogeneity of the correlated states is directly visualized in the hetero-bilayer region, indicative of local disord…
Understanding the mechanism of high temperature (high Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high Tc superconductivity arises from a doped Mott insulator as described by the Hubbard model. An exact solution of the Hubbard model, however, is extremely challenging due to the strong electron-electron correlation. Therefore, it is highly desirable to experimentally study a model Hubbard system in which the unconventional superconductivity can be continuously tuned by varying the Hubbard parameters. Here we report signatures of tunable su…
The interface electronic structure of correlated LaTiO$_3$/SrTiO$_3$ superlattices is investigated by means of the charge self-consistent combination of the local density approximation (LDA) to density functional theory (DFT) with dynamical mean-field theory (DMFT). Utilizing a pseudopotential technique together with a continuous-time quantum Monte-Carlo approach, the resulting complex multiorbital electronic states are addressed in a coherent fashion beyond static mean-field. General structural relaxations are taken into account on the LDA level and cooperate with the driving forces from stro…
Metallic behavior of band-insulator/ Mott-insulator interfaces was observed in artificial perovskite superlattices such as in nanoscale SrTiO3/LaTiO3 multilayers. Applying a semiclassical perspective to the parallel electronic transport we identify two major ingredients relevant for such systems: i) the quantum confinement of the conduction electrons (superlattice modulation) leads to a complex, quasi-two dimensional subband structure with both hole- and electron-like Fermi surfaces. ii) strong electron-electron interaction requires a substantial renormalization of the quasi-particle dispersio…
Ballistic Exciton Flow Driven by Intertwined Exciton-Electron Orders in a Moiré Superlattice
Purdue University（普渡大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；University of Washington（华盛顿大学）；National Institute for Materials Science（国立材料研究所）；RWTH Aachen University（亚琛工业大学）
