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 topological superlattice. In this system, topological Dirac states occur at the interfaces between a topological crystalline insulator Pb1-xSnxSe and a trivial insulator, realized in the form of topological quantum wells (TQW) epitaxially stacked on top of each other. Using magnetooptical transmission spectroscopy on high quality MBE grown Pb1-xSnxSe superlattices, we show that the penetration depth of the TQW interface states and therefore their Dirac mass is continuously tunable with temperature. This presents a new pathway to engineer the Dirac mass of topological systems and paves the way towards the realization of emergent quantum states of matter using Pb1-xSnxSe topological superlattices.
New Dirac points appear when periodic potentials are applied to graphene, and there are many interesting effects near these new Dirac points. Here we investigate the $\textit{Zitterbewegung}$ effect of fermions described by a Gaussian wave packet in graphene superlattice near new Dirac points. The $\textit{Zitterbewegung}$ near different Dirac points has similar characteristics, while Fermions near new Dirac points have different group velocities in both $x$- and $y$-direction, which causes the different properties of the $\textit{Zitterbewegung}$ near new Dirac points. We also investigate the…
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.
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…
We demonstrate theoretically the coexistence of Dirac semimetal and topological insulator phases in InSb/$α$-Sn conventional semiconductor superlattices, based on advanced first-principles calculations combined with low-energy $k\cdot p$ theory. By proper interfaces designing, a large interface polarization emerges when the growth direction is chosen along {[}111{]}. Such an intrinsic polarized electrostatic field reduces band gap largely and invert the band structure finally, leading to emerge of the topological Dirac semimetal phase with a pair of Dirac nodes appearing along the (111) crysta…
A graphene superlattice is formed by a one-dimensional periodic potential and is characterized by the emergence of new Dirac points in the electronic structure. The group velocity of graphene's massless Dirac fermions at the new points is drastically reduced, resulting in a measurable effect in the conductance spectroscopy. We show here that tunnel spectroscopy using a superconducting hybrid junction is more sensitive to the formation of Dirac points in the spectrum of graphene superlattices due to the additional contribution of Andreev processes. We examine the transport properties of a graph…
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. …
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…
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 …
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 destructi…
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…
Brown-Zak and Weiss oscillations in a gate-tunable graphene superlattice: A unified picture of miniband conductivity
University of Regensburg（雷根斯堡大学）；I. Institute of Theoretical Physics, University of Hamburg（汉堡大学第一理论物理研究所）；Research Center for Functional Materials, National Institute for Materials Science（国家材料科学研究所功能材料研究中心）；International Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料科学研究所国际材料纳米结构中心）
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 analyze the energy spectrum of graphene in the presence of spin-orbit coupling and a unidirectionally periodic Zeeman field, focusing on the stability and location of Dirac points it may support. It is found that the Dirac points at the $K$ and $K'$ points are generically moved to other locations in the Brillouin zone, but that they remain present when the Zeeman field $\vecΔ(x)$ integrates to zero within a unit cell. A large variety of locations for the Dirac points is shown to be possible: when $\vecΔ\parallel \hat{z}$ they are shifted from their original locations along the direction per…
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…
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…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
Tunable high-Chern-number Chern insulators in rhombohedral tetralayer graphene/hBN moiré superlattices
State Key Laboratory of Micro-nano Engineering Science, Tsung-Dao Lee lnstitute & School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University（上海交通大学微纳电子工程科学国家重点实验室、李政道研究所及物理与天文学院人工结构与量子控制教育部重点实验室）；Department of Physics, City University of Hong Kong（香港城市大学物理系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料研究所材料纳米结构研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）
The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces moiré superlattice that fundamentally modifies graphene's band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moiré superlattice in graphene on hBN yields new, unexpected consequenc…
Strong band engineering in two-dimensional (2D) materials can be achieved by introducing moiré superlattices, leading to the emergence of various novel quantum phases with promising potential for future applications. Presented works to create moiré patterns have been focused on a twist embedded inside channel materials or between channel and substrate. However, the effects of a twist inside the substrate materials on the unaligned channel materials are much less explored. In this work, we report the realization of superlattice multi-Dirac cones with the coexistence of the main Dirac cone in a …
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…
Periodic stacking of topologically trivial and non-trivial layers with opposite symmetry of the valence and conduction bands induces topological interface states that, in the strong coupling limit, hybridize both across the topological and normal insulator layers. Using band structure engineering, such superlattices can be effectively realized using the IV-VI lead tin chalcogenides. This leads to emergent minibands with a tunable topology as demonstrated both by theory and experiments. The topological minibands are proven by magneto-optical spectroscopy, revealing Landau level transitions both…
We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. Using the transfer matrix method, we explicitly determine the dispersion relation in terms of different physical parameters. We numerically analyze such relation and show that there exist three zones: bound, unbound and forbidden states. In the central zone of the band structures, we determine and enumerate the vertical Dirac points, opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity a…
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 …
Graphene/h-BN has emerged as a model van der Waals heterostructure, and the band structure engineering by the superlattice potential has led to various novel quantum phenomena including the self-similar Hofstadter butterfly states. Although newly generated second generation Dirac cones (SDCs) are believed to be crucial for understanding such intriguing phenomena, so far fundamental knowledge of SDCs in such heterostructure, e.g. locations and dispersion of SDCs, the effect of inversion symmetry breaking on the gap opening, still remains highly debated due to the lack of direct experimental res…
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-…
