Flat bands in lattice models have provided useful platforms for studying strong correlation and topological physics. Recently, honeycomb superlattices have been shown to host flat bands that persist in the presence of local perturbations respecting lattice symmetries. We analytically derive the flat band energies in the presence of longer range hopping and find that the energies of flat bands are tunable by these perturbations. In real space, the wave function is constructed from standing waves on each honeycomb edge, allowing the construction of plaquette and loop eigenstates due to destructive interference in real space that give rise to the flat bands robust against long range hoppings.
We consider a system of spinless fermions on the honeycomb lattice with substrate-induced modulated electrostatic potentials tripling the unit cell. The resulting non-Abelian SU(2) gauge fields act cooperatively to realize a quadratic band crossing point (QBCP). Using a combination of mean-field theory and renormalization group techniques, we show that in the QBCP regime, arbitrarily weak repulsive electronic interactions drive the system into the quantum anomalous Hall state. This proves that substrate-induced local voltages are an effective knob to induce the spontaneous formation of a topol…
The efficiency of optical emitters can be dramatically enhanced by reducing the effective mode volume (the Purcell effect). Here we predict an analogous enhancement for electron-phonon (el-ph) scattering, achieved by compressing the electronic Wannier orbitals. Reshaping of Wannier orbitals is a prominent effect in graphene moiré superlattices (SLs) where the orbitals are tunable by the twist angle. A reduction of the orbital effective volume leads to an enhancement in the effective el-ph coupling strength, yielding the values considerably bigger than those known for pristine monolayer graphen…
Topological spin textures, like skyrmions, have significant potential for spintronics applications. The main purpose of this work is to study further the topological spin textures on the discrete lattice with magnetic fields. In this work, we study a classical rotated Heisenberg model with Dzyaloshinskii-Moriya interaction, bond-dependent anisotropy and easy-axis anisotropy on the honeycomb lattice via Monte Carlo simulations. We mainly focus on phase diagrams with magnetic fields, especially on the non-trivial phases only existing with fields. The results demonstrate the emergence of field-in…
Artificial lattices have served as a platform to study the physics of unconventional superconductivity. We study semiconductor artificial graphene -- a honeycomb superlattice imposed on a semiconductor heterostructure -- which hosts the Dirac physics of graphene but with a tunable periodic potential strength and lattice spacing, allowing control of the strength of the electron-electron interactions. We demonstrate a new mechanism for superconductivity due to repulsive interactions which requires a strong lattice potential and a minimum doping away from the Dirac points. The mechanism relies on…
We provide a comprehensive microscopic understanding of the nucleation of topological quantum liquids, a general mechanism where interactions between non-Abelian anyons cause a transition to another topological phase, which we study in the context of Kitaev's honeycomb lattice model. For non-Abelian vortex excitations arranged on superlattices, we observe the nucleation of several distinct Abelian topological phases whose character is found to depend on microscopic parameters such as the superlattice spacing or the spin exchange couplings. By reformulating the interacting vortex superlattice i…
Superlattice in graphene generates extra Dirac points in the band structure and their number depends on the superlattice potential strength. Here, we have created a lateral superlattice in a graphene device with a tunable barrier height using a combination of two gates. In this Letter, we demonstrate the use of lateral superlattice to modify the band structure of graphene leading to the emergence of new Dirac cones. This controlled modification of the band structure persists up to 100 K.
We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding …
In this paper, we report on the controllable negative differential resistance (NDR) in a proposed planar graphene superlattice structure. High value of peak to valley ratio (PVR) is predicted. This is significant because of appearance of NDR with high PVR at low biases. Our finding is important since beside the other potential applications of the graphene, proposes implementation of the graphene based superlattice in electronic devices such as resonant tunneling diode and filters.
The terahertz emission from difference-frequency in biased superlattices is calculated with the excitonic effect included. Owing to the doubly resonant condition and the excitonic enhancement, the typical susceptibility can be as large as $10^{-5}$ m/V. The doubly resonant condition can always be realized by adjusting the bias voltage and the laser frequencies, thus the in-situ tunable emission is efficient in a range of several terahertz. Continuous wave operation with 1% quantum efficiency and $μ$W output power is feasible as the signal absorption in undoped superlattices is negligible.
We show that, if graphene is subjected to the potential from an external superlattice, a band gap develops at the Dirac point provided the superlattice potential has broken inversion symmetry. As a numerical example, we calculate the band structure of graphene in the presence of an external potential due to periodically patterned gates arranged in a triangular graphene superlattice (TGS) with broken inversion symmetry, and find that a band gap is created at both the original and "second generation" Dirac point. The gap can be controlled, in principle, by changing the external potential and the…
Topological Flat Minibands and Fractional Chern Insulators in Rashba Systems with Tunable Superlattice Potentials
University of Science and Technology of China（中国科学技术大学）；International Center for Quantum Design of Functional Materials (ICQD), Hefei National Research Center for Physical Sciences at Microscale, University of Science and Technology of China（中国科学技术大学合肥微尺度物质科学国家研究中心量子功能材料国际中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
The two inequivalent valleys in graphene preclude the protection against inter-valley scattering offered by an odd-number of Dirac cones characteristic of Z2 topological insulator phases. Here we propose a way to engineer a chiral single-valley metallic phase with quadratic crossover in a honeycomb lattice through tailored \sqrt{3}N *\sqrt{3}N or 3N *3N superlattices. The possibility of tuning valley-polarization via pseudo-Zeeman field and the emergence of Dresselhaus-type valley-orbit coupling are proposed in adatom decorated graphene superlattices. Such valley manipulation mechanisms and me…
It is well known that stacking domains form in moiré superlattices due to the competition between the interlayer van der Waals forces and intralayer elastic forces, which can be recognized as polar domains due to the local spontaneous polarization in bilayers without centrosymmetry. We propose a theoretical model which captures the effect of an applied electric field on the domain structure. The coupling between the spontaneous polarization and field leads to uneven relaxation of the domains, and a net polarization in the superlattice at nonzero fields, which is sensitive to the moiré period. …
Using full-potential density functional calculations within local density approximation (LDA), we found mechanically tunable band-gap in ZnO monolayer (ML-ZnO) in graphene-like honeycomb structure, by simulated application of in-plane homogeneous biaxial strain. Unstrained ML-ZnO was found to have a direct band gap of energy 1.68 eV within LDA; the actual band gap would be more, since LDA is known to underestimate the gap. Within our simulated strain limit of about plus or minus 10%, the band gap remains direct and shows a strong non-linear variation with strain. The results may find applicati…
We combined periodic ripples and electrostatic potentials to form curved graphene superlattices and studied the effects of space-dependent Fermi velocity induced from curvature on their electronic properties. With equal periods and symmetric potentials, the Dirac points do not move, but their locations shift under asymmetric potentials. This shift can be tuned by curvature and potentials. Tunable extra gaps in band structures can appear with unequal periods. The existence of new Dirac points is proposed, such that these new Dirac points can appear under smaller potentials with curvature, and t…
In this Letter, a tunable valley polarization is investigated for honeycomb systems with broken inversion symmetry such as transition-metal dichalcogenide MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. As compared to circular pumping, elliptical pumping is more universal and effective method to create coherent valley polarization. When two valleys of MX2 monolayers are doped or polarized, a novel anomalous valley orbital magnetic moment Hall effect driven by opposite Berry curvatures at different valleys is predicted and can generate orbital magnetic moment current without t…
Superlattice engineering provides the means to reshape the fabric felt by quasiparticles moving in a material. Here we argue that bandstructure engineering with superlattices can be pushed to the extreme limit by stacking gapped van der Waals (vdW) materials on patterned dielectric substrates. Specifically, we find that high quality vdW patterned dielectric superlattices (PDS) realize a series of robust flat bands that can be directly switched on and off by gate voltage in situ. In contrast to existing superlattice platforms, these flat bands are realized without the need for fine tuning. Inst…
We investigate the electronic structure of the flat bands induced by moiré superlattices and electric fields in nearly aligned ABC trilayer graphene-boron nitride interfaces where Coulomb effects can lead to correlated gapped phases. Our calculations indicate that valley-spin resolved isolated superlattice flat bands that carry a finite Chern number $C = 3$ proportional to layer number can appear near charge neutrality for appropriate perpendicular electric fields and twist angles. When the degeneracy of the bands is lifted by Coulomb interactions these topological bands can lead to anomalous …
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 report an efficient technique to induce gate-tunable two-dimensional superlattices in graphene by the combined action of a back gate and a few-layer graphene patterned bottom gate complementary to existing methods. The patterned gates in our approach can be easily fabricated and implemented in van der Waals stacking procedures allowing flexible use of superlattices with arbitrary geometry. In transport measurements on a superlattice with lattice constant $a=40$ nm well pronounced satellite Dirac points and signatures of the Hofstadter butterfly including a non-monotonic quantum Hall respons…
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
We investigate theoretically the anisotropic electronic and optical behaviors of a monolayer black phosphorus (phosphorene) modulated by periodic potential superlattices in arbitrary directions. We demonstrate that different strength and orientation of the phosphorene potential superlattice can give rise to distinct energy spectra, i.e., tuning the intrinsic electronic anisotropy. Accordingly, the anisotropic effective mass, and optical absorption modulated by superlattice strength and orientation are addressed systematically. This feature enables tuning capability more than one order of magni…
We present ab initio calculations which show that the direct-band-gap, effective masses and Fermi velocities of charge carriers in ZnO monolayer (ML-ZnO) in graphene-like honeycomb structure are all tunable by application of in-plane homogeneous biaxial strain. Within our simulated strain limit of $\pm 10$%, the band gap remains direct and shows a strong non-linear variation with strain. Moreover, the average Fermi velocity of electrons in unstrained ML-ZnO is of the same order of magnitude as that in graphene. The results promise potential applications of ML-ZnO in mechatronics/straintronics …
The unique zero energy Landau Level of graphene has a particle-hole symmetry in the bulk, which is lifted at the boundary leading to a splitting into two chiral edge modes. It has long been theoretically predicted that the splitting of the zero-energy Landau level inside the {\it bulk} can lead to many interesting physics, such as quantum spin Hall effect, Dirac like singular points of the chiral edge modes, and others. However, so far the obtained splitting with high-magnetic field even on a hBN substrate are not amenable to experimental detection, and functionality. Guided by theoretical cal…
We develop a theory of interaction effects in graphene superlattices, where tunable superlattice periodicity can be used as a knob to control the gap at the Dirac point. Applied to graphene on hexa-boron-nitride (G/h-BN), our theory predicts substantial many-body enhancement of this gap. Tunable by the moire superlattice periodicity, a few orders of magnitude enhancement is reachable under optimal conditions. The Dirac point gap enhancement can be much larger than that of the minigaps opened by Bragg scattering at principal superlattice harmonics. This naturally explains the conundrum of large…
This thesis studies how the rudimentary attributes of graphene's charge carriers, and local moments on its surface, can be directly manipulated and controlled with electrostatic potentials. We first consider bilayer graphene subject to a spatially varying electrostatic potential that forms two neighbouring regions with opposite interlayer bias. Along the boundary, 1D chiral "kink" states emerge. We find that these 1D modes behave as a strongly interacting Luttinger liquid whose properties can be tuned via an external gate. Next, we consider superlattices in bilayer graphene. Superlattices are …
The recently observed unconventional ferroelectricity in AB bilayer graphene sandwiched by hexagonal Boron Nitride (hBN) presents a new platform to manipulate correlated phases in multilayered van der Waals heterostructures. We present a low-energy continuum model for AB bilayer graphene encapsulated by the top and bottom layers of either hBN or graphene, with two independent twist angles. For the graphene/hBN heterostructures, we show that twist angle asymmetry leads to a layer polarization of the valence and conduction bands. We also show that an out-of-plane displacement field not only tune…
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…
Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moiré superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent electrically tunable …
Relativistic Dirac fermions are ubiquitous in condensed matter physics. Their mass is proportional to the material energy gap and the ability to control and tune the mass has become an essential tool to engineer quantum phenomena that mimic high energy particles and provide novel device functionalities. In topological insulator thin films, new states of matter can be generated by hybridizing the massless Dirac states that occur at material surfaces. In this work, we experimentally and theoretically introduce a platform where this hybridization can be continuously tuned: the Pb1-xSnxSe topologi…
Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moiré superlattice. Such superlattices are known to host bulk valley currents at tiny angles ($α\approx 0.3 ^\circ$) and flat bands at magic angles ($α\approx 1^\circ$). We show that tuning the twist angle to $α^*\approx 0.8^\circ$ generates flat bands away from charge neutrality with a triangular superlattice periodicity. When doped with $\pm 6$ electrons per moiré cell, these bands are half-filled and electronic interactions produce a symmetry-…
In heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch or rotation between the layers results in long-wavelength moiré superlattices. These moiré patterns can drive significant band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity, magnetism, fractional Chern insulating states, and moiré excitons. Here, we investigate monolayer graphene encapsulated between two crystals of boron nitride (BN), where the rotational alignment between all three components can be varied. …
Based on first-principles calculations, we find novel valley-polarized quantum anomalous Hall (VP-QAH) phases with a large gap-0.19 eV at an appropriate buckled angle and tunable topological phase transitions driven by the spontaneous magnetization within a half-hydrogenated Bi honeycomb monolayer. Depending on the magnetization orientation, four different phases can emerge, i.e., two VP-QAH phases, ferromagnetic insulating and metallic states. When the magnetization is reversed from the +$\mathbf{z}$ to -$\mathbf{z}$ directions, accompanying with a sign change in the Chern number (from -1 to …
Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van-der-Waals and dielectric forces exerted by the tip which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data of suspended monolayer graphene in constant-current mode revealing a surprising honeycomb structure with amplitude of 50$-$200 pm and lattice constant of 10-40 nm. The apparent lattice constant is reduced by increasing the tunneling current $I$, but does not depend systematically on tunneling voltage $V$ or scan speed $v_{\rm scan}$. The honeycomb lattice of …
Low-buckled silicene is a prototypical quantum spin Hall insulator with the topological quantum phase transition controlled by an out-of-plane electric field. We show that this field-induced electronic transition can be further tuned by an in-plane hydrostatic biaxial strain $\varepsilon$, owing to the curvature-dependent spin-orbit coupling (SOC): There is a $Z_2$ = 1 topological insulator phase for biaxial strain $|\varepsilon|$ smaller than 0.07, and the band gap can be tuned from 0.7 meV for $\varepsilon = +0.07$ up to a fourfold 3.0 meV for $\varepsilon = -0.07$. First-principles calculat…
We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with armchair boundaries. In contrast with fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After introducing an external on-site potential at the outermost sites we find that the energy spectra of the edge states are tunable. Additionally, when a non-trivial gap is induced, we find that some of the edge states are topologically protected and also tunable. Our results may explain the origin of the novel edge states recently observed in photonic lattices. We a…
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall eff…
We propose a novel class of temperature-tunable semiconductor metamaterials that exhibit negative refraction in the terahertz spectral range. These metamaterials are based on doped semiconductor superlattices with ultrathin barriers of about 1 nm thickness. Due to the tunnel transparency of the barriers, layers of the superlattice cannot be considered as isolated and, therefore, the classical homogenization approach is inapplicable. We develop a theory of quantum homogenization which is based on the Kubo formula for conductivity. The proposed approach takes into account the wave functions of t…
We study a Dirac Harper model for moiré bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For sufficiently long moiré period the we find low energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position dependent mass inversions. We analyze their charge distributions, mode count and valley-coherence using exact symmetries of the lattice model and approximate symmetries of a…
Twisted moiré superlattices (TMSs) are fascinating materials with exotic physical properties. Despite tremendous studies on electronic, photonic and phononic TMSs, it has never been witnessed that TMSs can exhibit higher-order band topology. Here, we report on the experimental observation of higher-order topological states in acoustic TMSs. By introducing moiré twisting in bilayer honeycomb lattices of coupled acoustic resonators, we find a regime with designed interlayer couplings where a sizable band gap with higher-order topology emerges. This higher-order topological phase host unique topo…
