Session Z03: 2D Materials: Superconductivity, Ferroelectricity, Density Waves, and Other Correlated States III

Tunable square-lattice Hubbard models from twisted homobilayers

We study the band structures of twisted homobilayers of square lattice materials. At low twist angles, we demonstrate the emergence of flat moire bands. The approximate layer symmetry of the homobilayer further allows to create moire bands with exotic properties, such as dominant next-nearest neighbor hopping that can be tuned with external fields. We thus establish twisted rectangular-lattice bilayers as a platform for the realization of tunable extended $t-t'-U$ Hubbard and J-J' models, which may host exotic superconducting and spin liquid states. Finally, potential candidate materials will be discussed.   

Oral: Wigner Molecular Crystals in 2D moire heterostructures

Semiconductor moiré superlattices provide a versatile platform to engineer new quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid – at a filling of one electron per moiré unit cell. New types of quantum solids should arise at even higher filling factors where the multi-electron configuration of moiré artificial atoms provides new degrees of freedom. Here we report the experimental observation of Wigner molecular crystals emerging from multi-electron artificial atoms in twisted bilayer WS2 moiré superlattices. Moiré artificial atoms, unlike natural atoms, can host qualitatively different electron states due to the interplay between quantized energy levels and Coulomb interactions. Using scanning tunneling microscopy (STM), we demonstrate that Wigner molecules appear in multi-electron artificial atoms when Coulomb interactions dominate. Three-electron Wigner molecules, for example, are seen to exhibit a characteristic trimer pattern. The array of Wigner molecules observed in a moiré superlattice comprises a new crystalline phase of electrons: the Wigner molecular crystal. Our study presents new opportunities for exploring quantum phenomena in moiré quantum solids composed of multi-electron artificial atoms.   

Two-dimensional anisotropic Luttinger Liquids in a moiré superlattice

Fermi Liquid theory is the standard description for two and three-dimensional (2D and 3D) metals and the basis for understanding many quantum phenomena including the quantum Hall effect and superconductivity. 1D Luttinger Liquid (LL) state is one of the examples beyond the standard Fermi Liquid theory and involves strong electron correlations and fractionalized excitations. Substantial theoretical efforts have been made to expand the LL theory to higher dimensions, especially in the context of coupled-wire models consisting of an array of 1D LLs. However, the experimental test for the existence of a stable LL state in 2D or 3D is challenging due to the lack of a suitable material platform with high quality and tunability. In this talk, I will present our experimental search of a stable LL state in 2D based on moiré quantum engineering in small-angle twisted bilayer WTe₂ (tWTe₂) system. We find a new 2D anisotropic electronic phase akin to a LL, stabilized due to interactions in tWTe₂ moiré superlattice.  I will discuss three key transport characteristics of this phase, including (1) an exceptionally large in-plane transport anisotropy, (2) a power-law scaled conductance in the hard transport direction and (3) a nonlinear differential resistance, featuring a zero-bias dip, in the easy transport direction.   

Microscopic insights into the pseudo gap phase of CsV3Sb5

The layered compounds AV₃Sb₅ (A = K, Rb, and Cs) with a vanadium kagome lattice exhibit various interesting electronic phases, such as superconductivity [1] and a 2x2 charge density wave (CDW) [2]. Most notably, CsV₃Sb₅ was found to exhibit a time-reversal symmetry (TRS) broken state without the presence of local magnetic moments [3]. A chiral flux phase that arises within the 2x2 CDW state has been proposed as a possible TRS breaking mechanism. Direct experimental evidence for the chiral flux phase would be desirable to better understand the rich phenomenology of quantum states in these kagome compounds.

We present results from cryogenic scanning tunneling microscopy experiments on cleaved bulk crystals of CsV₃Sb₅. The goal of our study is to shed light on the pseudo gap phase that appears in the low energy local density of states of the 2x2 CDW state.  To this end, we combine high-resolution spectroscopy and quasiparticle interference with scattering experiments in which we study the response of the pseudo gap phase to atomic scale perturbations. We compare our observations with results from microscopic model calculations with the focus on the spectral features of the chiral flux phase.

[1]B.R. Ortiz et al., Rev. Mater. 3 094407 (2019)

[2]H. Zhao et al., Nature 599, 216-221 (2021)

[3]C. Guo et. al., Nature 611, 461-466 (2022)   

Spin Orbit Coupling Effects in the Electronic Band Gap of Hafnium Tri-Selenide

Addressing the global demand for low-cost memory and logic makes semiconducting 2D materials, with diminished edge effects, potentially key to beyond CMOS devices. In this category, transition metal tri-chalcogenides have emerged as prime candidates for exploring materials with versatile applications. Monolayer hafnium tri-selenide (HfSe₃) is particularly promising because of its layered structure, semiconducting properties and diminished edge scattering. Our density functional theory based study, employing the Heyd–Scuseria–Ernzerhof (HSE06) exchange-correlation functional, of the electronic structure of HfSe₃, in both bulk and monolayer forms, reveals two compelling findings. First, the inclusion of spin-orbit coupling unveils a notable band splitting of around 300 meV at the top of valence band, which locates at the center of the Brillouin zone. Second, the indirect band gap of the material reduces with the inclusion of spin-orbit coupling, in both bulk (from 0.95 to 0.78 eV) and monolayer (from 1.24 to 1.06 eV) forms. We examine the layer thickness dependency of HfSe₃ band gap which is larger for the monolayer than its  bulk counterpart and compare our results to recent angle resolved photoemission data.   

Monolayer WTe2 as an excitonic spin density wave

Recently we have demonstrated that that the two-dimensional bulk of monolayer WTe₂ contains electrons and holes bound by Coulomb attraction—excitons—that spontaneously form in thermal equilibrium [1]. The natural paradigm to interpret the ground state is the long-sought ‘excitonic insulator’ (EI), which breaks the pristine symmetry of the crystal though the Bose-Einstein condensation of excitons. Since lowest-energy excitons have finite momentum, one expects the EI to break the periodicity of the crystal, but no charge order has been observed at low temperature [1]. Here we predict that the EI is a spin density wave, on the basis of a full microscopic theory that builds on the ab-initio treatment of excitons [2]. Key to our claim is the strong spin-orbit interaction of WTe₂, which largely enhances the splitting between spin singlet and triplet excitons, and thus stabilizes the spin order. We further discuss the consistency of the computed band structure, photoemission spectra, and chemical potential of the EI with available experimental data. Finally, we propose paths to unveil the macroscopic quantum coherence possibly hidden in the ground state.   

Interplay of proximity-induced spin interactions and correlated phenomena in multilayer graphene systems

We conducted a theoretical investigation on the impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagrams of rhombohedral trilayer graphene (RTG) and Bernal bilayer graphene (BBG). Using emph{ab initio}-fitted effective models of RTG and BBG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr$_2$Ge$_2$Te$_6$ (exchange proximity effect), we explored potential correlated phases at different displacement fields and doping by incorporating Coulomb interactions within the random-phase approximation. Our findings reveal a diverse spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin proximity effects. For instance, we observed the emergence of a spin-valley-coherent phase due to valley-Zeeman coupling. Additionally, proximity-induced exchange coupling removed the spin phase degeneracies by biasing the spin direction, enabling a magneto-correlation effect.   

A Quasi-1D Charge Density Wave in an Intercalated Magnetic Semiconductor

Layered van der Waals materials with an anisotropic in-plane structure offer a promising platform to study quasi-1D electron behavior as a function of charge doping. In this regard, the van der Waals semiconductor CrSBr is a material of particular interest. Its conduction band is nearly flat along Γ–X but dispersive along Γ–Y, leading to transport properties associated with weakly correlated 1D chains. However, the large concentration of bromine vacancies in exfoliated flakes typically limits the effects of electrical gating to the control of defect states, hindering the ability to study the properties of CrSBr when the Fermi energy is within the conduction band. Here, we overcome this limitation through chemical intercalation of CrSBr, which achieves a higher level of doping than is possible through electrical gating alone. Magnetization measurements of the intercalated material reveal a greatly enhanced magnetic ordering temperature and retention of the triaxial magnetic anisotropy of CrSBr. Further, scanning tunneling microscopy measurements reveal a quasi-1D charge density wave persisting to high temperature, highlighting that control of charge doping in CrSBr represents a route to access 1D electronic phases in van der Waals materials.   

Investigation of Electronic States across NbTe2 CDW Domain Boundaries

NbTe₂ is a layered transition metal dichalcogenide which exhibits charge density waves (CDWs) and superconductivity in the bulk. Previous scanning tunneling microscopy and spectroscopy experiments suggested that Fermi-surface nesting and reciprocal lattice reconstruction are important in the formation of CDWs in NbTe₂. These experiments focused on spectroscopy of pristine regions. We will present low temperature scanning tunneling spectroscopy experiments examining the 3x1 CDW in NbTe₂ at 10K. We found a crystalline step and multiple neighboring 60^º and 120^º CDW domain boundaries. We examined the electronic structure across these domain boundaries and in neighboring domains using scanning tunneling spectroscopy. We observed zig-zag features in the dI/dV maps over the domain boundaries for tip bias of 300mV, as compared to 150mV bias maps. These and future experiments will help elucidate CDW domain formation and interlayer coupling in NbTe₂.   

Monolayer-TMD excitons near phases of graphene multilayers

Graphene multilayers and transition metal dichalcogenides (TMDs) both have proven to be incredibly versatile in realizing and controlling exotic states of matter by engineering stacking arrangement, external fields, and proximity effects. In graphene, this includes correlated phases such as spin--valley magnetism, superconductivity, and most recently, the fractional quantum anomalous Hall effect in pentalayers. In monolayer TMDs, excitons with large binding energies dominate the optical response and are sensitive to the many-body states in nearby layers. In this theory work, we derive an explicit expression for the change in the effective electron-hole interaction in the TMD layers by accounting for screening induced by the charge polarizability of graphene multilayers. We use this interaction to explore the shifts in exciton binding energy and the TMD bandgap. We find that the TMD bandgap is significantly affected by screening, sensitive to properties around the Fermi energy of the multilayer graphene, the presence of cyclotron gaps ,and the interlayer distance between the TMD and multilayer graphene. Our theory paves the way to understanding how excitons in monolayer TMDs may act as probe to electronic phases in proximate materials.   

Structural properties of kagome-layered crystals

Recently synthesized kagome metals AV₃Sb₅ (A=K,Rb,Cs) exhibit a Charge Density Wave (CDW) phase along with superconductivity. In this talk, we discuss the electronic and lattice properties leading to the emergence of the CDW phase in the AV3Sb5 compounds, in addition to the possibility of a similar CDW phase in other kagome-layered crystals. We extend the symmetry-based phenomenological Landau theory, originally applied to P6/mmm kagome crystals, to rhombohedrally stacked R-3m kagome systems. Finally, Density Functional Theory (DFT) is used to simulate CsV₃Sb₅ and investigate the relationship between its lattice instabilities and the van Hove singularities. We also explore M₃A₂X₂ shandites, which include rhombohedrally stacked kagome layers, using DFT and consider the effects of doping and pressure. Despite a van Hove singularity appearing at the F point in the shandites, DFT finds no signatures of a structural instability in these compounds.   

Materials screening from noninteracting models

Properly accounting for interactions is one of the chief bottlenecks in understanding material properties, owing to the exponential expansion of the Hilbert space. Mean-field techniques allow for re-contraction of the state space while potentially preserving much of the intricacies of the interacting phase diagram. We establish and verify a correspondence between different interaction channels in the mean-field basis, allowing us to make predictions of one property based on measurements or calculations of another unrelated property. We focus specifically on predicting Tc from the exchange interaction, which is not the pairing glue. Our results provide a basis for high-throughput screening of materials by desired properties, say Tc, directly from the noninteracting model and without the need for self-consistent mean-field calculations.