Although spin is a fundamental quantum number, measuring spin transport in traditional solid state systems is extremely challenging. This poses a major obstacle to detecting interesting quantum states including certain spin liquids. In this paper we propose a platform that not only allows for the electrical measurement of spin transport, but in which a variety of exotic quantum phases may be stabilized. Our proposal involves two moiré superlattices, built from transition metal dichalcogenides (TMD) or graphene, separated from one another by a thin insulating layer. The two Coulomb coupled moiré layers, when suitably aligned, give rise to a layer pseudospin degree of freedom. The transport of pseudospin can be accessed from purely electrical measurements of counter-flow or Coulomb drag conductivity. Furthermore, these platforms naturally realize Hubbard models on the triangular lattice with $N = 4\, {\rm or}\, 8$ flavors. The flavor degeneracy motivates a large-N approximation from which we obtain the phase diagram of Mott insulators at different electron fillings and correlation strengths. In addition to conventional phases such as psuedospin superfluids and crystallized insulators, exotic phases including chiral spin liquids and a $U(1)$ spinon Fermi surface spin liquid are also found, all of which will show smoking gun electrical signatures in this setup.
Motivated by recent observation of nematicity in Moiré systems, we study three different orbital orders that potentially can happen in Moiré systems: (1) the nematic order; (2) the valley polarization; and (3) the "compass order". Each order parameter spontaneously breaks part of the spatial symmetries of the system. We explore physics caused by the quantum fluctuations close to the order-disorder transition of these order parameters. Especially, we recognize that the symmetry of the Moiré systems leads to a crucial difference of the effective theory describing the nematic order from the stand…
We propose moiré bilayer as a platform where exotic quantum phases can be stabilized and electrically detected. Moiré bilayer consists of two separate moiré superlattice layers coupled through the inter-layer Coulomb repulsion. In the small distance limit, an SU(4) spin can be formed by combining layer pseudospin and the real spin. As a concrete example, we study an SU(4) spin model on triangular lattice in the fundamental representation. By tuning a three-site ring exchange term $K\sim \frac{t^3}{U^2}$, we find SU(4) symmetric crystallized phase and an SU(4)$_1$ chiral spin liquid (CSL) at th…
Emergent magnetism and spin liquids in an extended Hubbard description of moiré bilayers
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Cologne（科隆大学）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara（法国美国理论科学中心，CNRS，KITP，圣塔芭芭拉）；Canadian Institute for Advanced Research（加拿大高级研究院）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）
Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moiré superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all th…
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…
We theoretically explore 2d moiré heterostructures in lattice-commensurate magnetic fields as platforms for quantum simulation of a paradigmatic model of non-Fermi liquid physics: a Fermi-surface coupled to a fluctuating gauge field. In these moiré-Hofstadter (MH) systems, long-wavelength acoustic phonons exhibit singular interactions with electrons analogous to those of electrons with 2d gauge fields. This leads to a breakdown of Fermi-liquid theory at low temperatures. We show that a combination of large moiré-unit cell size, tunable Fermi-surface topology, and enhanced coupling to interlaye…
Recently Chern insulators with Chern number $C=1$ and $C=2$ in zero (or very small) magnetic field have been observed in two moire graphene systems: twisted bilayer graphene and ABC trilayer graphene, both aligned with a hexagonal Boron-Nitride (h-BN) substrate. These Chern insulator states arise due to many body effects in the Chern bands of these systems when they are partially filled to a total integer filling $ν_T = 1,3$ (including spin and valley degrees of freedom). A simple possible explanation is from Hartree-Fock mean field theory which predicts valley and spin polarization in the zer…
Twisting moiré heterostructures to the flatband regime allows for the formation of strongly correlated quantum states, since the dramatic reduction of the bandwidth can cause the residual electronic interactions to set the principal energy scale. An effective description for such correlated moiré heterostructures, derived in the strong-coupling limit at integer filling, generically leads to spin-valley Heisenberg models. Here we explore the emergence and stability of spin liquid behavior in an SU(2)$^{\mathrm{spin}}\otimes$SU(2)$^{\mathrm{valley}}$ Heisenberg model upon inclusion of Hund's-ind…
Bandwidth-Limited Critical Currents in Electrically Tunable Moiré Bands
ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学技术研究院）；Massachusetts Institute of Technology（麻省理工学院）；National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；Dept. of Physics & Astronomy, University of Manchester（物理与天文学系，曼彻斯特大学）；COMMIT, Department of Physics and NANOlight Center of Excellence, University of Antwerp（安特卫普大学物理系及NANOlight卓越中心）
Quantum spin-liquid van der Waals magnets such as TaS$_2$, TaSe$_2$, and RuCl$_3$ provide a natural platform to explore new exotic phenomena associated with spinon physics, whose properties can be controlled by exchange proximity with ferromagnetic insulators such as CrBr$_3$. Here we put forward a twisted van der Waals heterostructure based on a quantum spin-liquid bilayer encapsulated between ferromagnetic insulators. We demonstrate the emergence of spinon flat bands and topological spinon states in such heterostructure, where the emergence of a topological gap is driven by the twist. We fur…
Moiré flatbands, occurring, e.g., in twisted bilayer graphene at magic angles, have attracted ample interest due to their high degree of experimental tunability and the intriguing possibility of generating novel strongly interacting phases. Here we consider the core problem of Coulomb interactions within fractionally filled spin and valley polarized Moiré flatbands and demonstrate that the dual description in terms of holes, which acquire a nontrivial hole dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. I…
The interplay between strong correlations and non-trivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of t…
We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moiré superlattices. For AA stacking, a gapped Z2 quantum spin liquid phase emerges at a finite Jc. We show that this phase survives in the well-controlled large-J limit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finite-q inter-layer hybridization is stabilized. This connects inequivalent Dirac points, effectively `untwisting' the system. Our study thus provides insight into the spin-liquid phases of bilayer spin-orbital Kitaev m…
We propose a realization of Kondo-lattice physics in moiré superlattices at the interface between a WX$_2$ homobilayer and MoX$_2$ monolayer (where X=S,Se). Under appropriate gating conditions, the interface-WX$_2$-layer forms a triangular lattice of local moments that couple to itinerant electrons in the other WX$_2$-layer via a gate-tunable Kondo exchange interaction. Using a parton mean-field approach we identify a range of twist-angles which support a gate-tuned quantum phase transition between a heavy-fermion liquid with large anomalous Hall conductance and a fractionalized chiral spin-li…
Spin-Valley Anderson Impurity for Moiré Systems: Fermi Liquid, Pairing, and Pseudogap
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Department of Physics and Astronomy, Seoul National University（首尔大学物理天文学系）；Center for Theoretical Physics, Seoul National University（首尔大学理论物理中心）；Institute for Data Innovation in Science, Seoul National University（首尔大学科学数据创新中心）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics including phenomena such as spin-charge separation. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions (2D), especially in models of closely packed arrays of 1D quantum wires, each being described as a LL. Such coupled-wire models have been successfully used to construct 2D anisotropic non-Fermi liquids, quantum Hall states, topological phases, and quantum spin liquids. However, an experimental demonstrati…
Anisotropic Moiré Fractional Chern Insulators and Their Phase Transitions
Nanyang Technological University（南洋理工大学）；Hong Kong University of Science and Technology（香港科技大学）；Center for Theoretical Condensed Matter Physics, The Hong Kong University of Science and Technology（香港科技大学理论凝聚态物理中心）
We report the observation of a quantum anomalous Hall effect in twisted bilayer graphene showing Hall resistance quantized to within .1\% of the von Klitzing constant $h/e^2$ at zero magnetic field.The effect is driven by intrinsic strong correlations, which polarize the electron system into a single spin and valley resolved moiré miniband with Chern number $C=1$. In contrast to extrinsic, magnetically doped systems, the measured transport energy gap $Δ/k_B\approx 27$~K is larger than the Curie temperature for magnetic ordering $T_C\approx 9$~K, and Hall quantization persists to temperatures o…
We study the transport properties of long quantum wires by generalizing the Luttinger liquid approach to allow for the finite lifetime of the bosonic excitations. Our theory accounts for long-range disorder and strong electron interactions, both of which are common features of experiments with quantum wires. We obtain the electrical and thermal resistances and thermoelectric properties of such quantum wires. We cast our results in terms of the thermal conductivity and bulk viscosity of the electron liquid and give the temperature scale above which the transport can be described by classical hy…
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…
Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin liquid phase in the Kitaev material $α$-$\mathrm{RuCl}_{3}$. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid's hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to `perfectly' convert electrons from the former into emergent fermions in the latter---thereby enabling variations of tr…
We show that spin-spin correlations in a non-Abelian Kitaev spin liquid are associated with a characteristic inhomogeneous charge density distribution in the vicinity of $\mathbb{Z}_2$ vortices. This density profile and the corresponding local electric fields are observable, e.g., by means of surface probe techniques. Conversely, by applying bias voltages to several probe tips, one can stabilize Ising anyons ($\mathbb{Z}_2$ vortices harboring a Majorana zero mode) at designated positions, where we predict a clear Majorana signature in energy absorption spectroscopy.
Carnegie Mellon University（卡内基梅隆大学）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Harvard University（哈佛大学）；Delft University of Technology（代尔夫特理工大学）
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 introduce a new model for quasi one-dimensional materials, motivated by intriguing but not yet well-understood experiments that have shown two-dimensional polymer films to be promising materials for thermoelectric devices. We consider a two-dimensional material consisting of many one-dimensional systems, each treated as a Luttinger liquid, with weak (incoherent) coupling between them. This approximation of strong interactions within each one-dimensional chain and weak coupling between them is the "quasi-atomic limit." We find integral expressions for the (interchain) transport coefficients,…
In recent years, there have been numerous examples of twisted bilayer systems that host remarkable physical properties that are not found in their untwisted counterparts. Motivated by this, we study the properties of twisted bilayers of the Kitaev honeycomb model in the Abelian spin liquid phase. We show that for strong, short-ranged, interlayer interactions, a super-lattice of non-Abelian defects forms in the twisted bilayer system. These non-Abelian defects are wormhole-like genons that allow anyons from one layer to tunnel to the other layer. We find that when a magnetic field is applied to…
The observation of strongly-correlated states in moiré systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g. to describe Mott insulators where the local moments are coupled spin-valley degrees of freedom. Here, we discuss a numerical renormalization group scheme to explore the formation of spin-valley ordered and unconventional spin-valley liquid states at zero temperature based on a pseudo-fermion representation. Our generalization of the conventional pseudo-fermion functional renormalization group approach for $\mathfrak{su}$(2) spins is capabl…
Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favors ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields---a longstanding technological goal in spintronics and multiferroics---can be achieved only indirectly. Here, we experimentally demonstrate direct electric field control of magnetic states in an orbital Chern insulator, a magnetic system in which non-trivial band topology favors long range order of orbital angular momentum but the spins are thought to remain disordered. We us…
We compute the electrical conductivity for liquid hydrogen at high pressure using quantum Monte Carlo. The method uses Coupled Electron-Ion Monte Carlo to generate configurations of liquid hydrogen. For each configuration correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give AC electrical conductivity directly. The extrapolated DC conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transiti…
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…
Emergent Gauge Flux and Spin Ordering in Magnetized Triangular Spin Liquids: Applications to Hofstadter-Hubbard Model
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学北京量子器件重点实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
Fermi-liquid versus non-Fermi-liquid/'strange-metal' fits to the electrical resistivity in the quantum critical magnetic regime of an unconventional superconductor
Institute for Materials Research, Tohoku University（东北大学材料研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS（格勒诺布尔阿尔卑斯大学，法国原子能和替代能源委员会，格勒诺布尔国立理工学院，IRIG，PHELIQS）
In this paper we explore possible phases arising from doping neutral excitons into a Mott insulator in the context of moiré bilayers. We consider two moiré layers coupled together only through inter-layer repulsion and there is a U(2)$\times$ U(2) symmetry. The densities of the two layers can be tuned to be $n_t=x,n_b=1-x$ with $n_t+n_b=1$. $x=0$ limit is a layer polarized Mott insulator and small $x$ regime can be reached by doping inter-layer excitons at density $x$. Charge gap can remain finite at small $x$, as is demonstrated experimentally in the WSe$_2$-hBN-WSe$_2$/WS$_2$ system. To capt…
Coherent Modulation of Two-Dimensional Moiré States with On-Chip THz Waves
Columbia University（哥伦比亚大学）；Washington University（华盛顿大学）；University of Washington（华盛顿大学）；National Institute for Materials Science（国立材料研究所）；Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）
