Symmetry-Protected Moiré Band Engineering and Enhanced Electron-Phonon Coupling in Xe/Bi2Se3 Superlattices: Path to Topological Superconductivity.

How Magical Is Magic-Angle Graphene?

Moiré is More: Access to New Properties of Two-Dimensional Layered Materials

Recent Advances in Topological Quantum Materials by Angle-Resolved Photoemission Spectroscopy

In the present study, we employ the angle-resolved photoemission spectroscopy (ARPES) technique to study the electronic structure of topological states of matter. In particular, the so-called topological crystalline insulators (TCIs) Pb1-xSnxSe and Pb1-xSnxTe, and the Mn-doped Z2 topological insulators (TIs) Bi2Te3 and Bi2Se3. The Z2 class of strong topological insulators is protected by time-reversal symmetry and is characterized by an odd number of metallic Dirac type surface states in the surface Brillouin zone. The topological crystalline insulators on the other hand are protected by the individual crystal symmetries and exhibit an even number of Dirac cones. The topological properties of the lead tin chalcogenides topological crystalline insulators can be tuned by temperature and composition. Here, we demonstrate that Bi-doping of the Pb1-xSnxSe(111) epilayers induces a quantum phase transition from a topological crystalline insulator to a Z2 topological insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy in the bulk. As a consequence a gap appears at ⌈¯, while the three Dirac cones at the M points of the surface Brillouin zone remain intact. We interpret this new phase transition is caused by lattice distortion. Our findings extend the topological phase diagram enormously and make strong topological insulators switchable by distortions or electric field. In contrast, the bulk Bi doping of epitaxial Pb1-xSnxTe(111) films induces a giant Rashba splitting at the surface that can be tuned by the doping level. Tight binding calculations identify their origin as Fermi level pinning by trap states at the surface. Magnetically doped topological insulators enable the quantum anomalous Hall effect (QAHE) which provide quantized edge states for lossless charge transport applications. The edge states are hosted by a magnetic energy gap at the Dirac point which has not been experimentally observed to date. Our low temperature ARPES studies unambiguously reveal the magnetic gap of Mn-doped Bi2Te3. Our analysis shows a five times larger gap size below the Tc than theoretically predicted. We assign this enhancement to a remarkable structure modification induced by Mn doping. Instead of a disordered impurity system, a self-organized alternating sequence of MnBi2Te4 septuple and Bi2Te3quintuple layers is formed. This enhances the wave-function overlap and gives rise to a large magnetic gap. Mn-doped Bi2Se3 forms similar heterostructure, but only a nonmagnetic gap is observed in this system. This correlates with the difference in magnetic anisotropy due to the much larger spin-orbit interaction in Bi2Te3 compared to Bi2Se3. These findings provide crucial insights for pushing lossless transport in topological insulators towards room-temperature applications.

<sec> The discovery of topological materials – condensed matter systems that have nontrivial topological invariants – marked the commencement of a new era in condensed matter physics and materials science. Three dimensional topological insulators (3D TIs) are one of the first discovered and the most studied among all topological materials. The bulk material of the TIs have the characteristics of the insulator, having a complete energy gap. Their surface electronic states, on the other hand, have the characteristics of a conductor, with energy band passes continuously through the Fermi surface. The conductivity of this topological surface state (TSS) is protected by the time reversal symmetry of the bulk material. The TSS is highly spin-polarized and form a special spin-helical configuration that allows electrons with specific spin to migrate only in a specific direction on the surface. By this means, surface electrons in TIs can " bypass” the influence of local impurities, achieving a lossless transmission of spin-polarized current. The existence of TIs directly leads to a variety of novel transport, magnetic, electrical, and optical phenomena, such as non-local quantum transport, quantum spin Hall effect, etc., promising wide application prospects. Recently, several research groups have searched all 230 non-magnetic crystal space groups, exhausting all the found or undiscovered strong/weak TIs, topological crystalline insulators (TCI), and topological semimetals. This series of work marks that theoretical understanding of non-magnetic topological materials has gone through a period of one-by-one prediction and verification, and entered the stage of the large-area material screening and optimization.</sec><sec> Parallel to non-magnetic TIs, magnetic topological materials constructed by ferromagnetic or antiferromagnetic long range orders in topological systems have always been an important direction attracting theoretical and experimental efforts. In magnetic TIs, the lack of time reversal symmetry brings about new physical phenomena. For example, when a ferromagnetic order is introduced into a three-dimensional TI, the Dirac TSS that originally intersected at one point will open a magnetic gap. When the Fermi surface is placed just in the gap, the quantum anomalous Hall effect can be implemented. At present, the research on magnetic topology systems is still in the ascendant. It is foreseeable that these systems will be the main focus and breakthrough point of topology material research in the next few years. </sec><sec> Angle-resolved photoemission spectroscopy (ARPES) is one of the most successful experimental methods of solid state physics. Its unique <i>k</i>-space-resolved single-electron detection capability and simple and easy-to-read data format make it a popular choice for both theoretists and experimentalists. In the field of topological materials, ARPES has always been an important experimetnal technique. It is able to directly observe the bulk and surface band structure of crystalline materials, and in a very intuitive way. With ARPES, it is incontrovertible to conclude whether a material is topological, and which type of topological material it belongs to.</sec><sec> This paper reviews the progress of ARPES research on TIs since 2008, focusing on the experimental energy band characteristics of each series of TIs and the general method of using ARPES to study this series of materials. Due to space limitations, this paper only discusses the research progress of ARPES for strong 3D TIs (focusing on the Bi<sub>2</sub>Se<sub>3</sub> series) and magnetic TIs (focusing on the MnBi<sub>2</sub>Te<sub>4</sub> series). Researches involving TCIs, topological Kondo insulators, weak 3D TIs, topological superconductors and heterostructures based on topological insulators will not be discussed. This paper assumes that the reader has the basic knowledge of ARPES, so the basic principles and system components of ARPES are not discussed.</sec>

Understanding the superconducting proximity effect on the surface of a topological insulator is of critical importance in realizing topological superconductivity and Majorana fermions in solid state settings. We fabricate delicate heterostructure samples between topological insulator (TI) Bi2Se3 thin film and high temperature superconductor Bi2Sr2CaCu2O8+ (Tc ~ 91 K). Using angle-resolved photoemission spectroscopy, we probe the electronic structure and the possible existence of superconducting gap on the top surface of Bi2Se3 thin films. Our systematic data show no significant proximity-induced superconducting gap in the topological surface states with sample temperature down to 10 K (<<91 K) and with a confidence level of sub 5 meV, much smaller than what have been claimed previously, which indicates the near absence of the proximity-induced superconductivity on the TI surface. Our momentum space imaging provides evidence for the coexistence of two crystalline phases in Bi2Se3/Bi2Sr2CaCu2O8+ samples, which we argue to be due to the strong mismatch of lattice crystalline symmetries. Our data identify the major contributors in reducing the proximity-induced superconducting gap below the meV range, including the lack of momentum space overlap between the Bi2Se3 and Bi2Sr2CaCu2O8+ Fermi surfaces, the strong mismatch of lattice crystalline symmetries and superconducting pairing symmetries, as well as the very short superconducting coherence length in Bi2Sr2CaCu2O8+. Our ARPES studies not only provide critical momentum space insights into the Bi2Se3/Bi2Sr2CaCu2O8+ heterostructure, but also set an upper bound on the proximity induced gap for realizing a Majorana fermion condition in this system, which may be further destabilized by the d-wave nodes dominated in a cuprate superconductor.

Twisted bilayer graphene (TBG), which has drawn much attention in recent years, arises from van der Waals materials gathering each component together via van der Waals force. It is composed of two sheets of graphene rotated relatively to each other. Moiré potential, resulting from misorientation between layers, plays an essential role in determining the band structure of TBG, which directly relies on the twist angle. Once the twist angle approaches a certain critical value, flat bands will show up, indicating the suppression of kinetic energy, which significantly enhances the importance of Coulomb interaction between electrons. As a result, correlated states like correlated insulators emerge from TBG. Surprisingly, superconductivity in TBG is also reported in many experiments, which drags researchers into thinking about the underlying mechanism. Recently, the interest in the atomic reconstruction of TBG at small twist angles comes up and reinforces further understandings of properties of TBG. In addition, twisted multilayer graphene receives more and more attention, as they could likely outperform TBG although they are more difficult to handle experimentally. In this review, we mainly introduce theoretical and experimental progress on TBG. Besides the basic knowledge of TBG, we emphasize the essential role of atomic reconstruction in both experimental and theoretical investigations. The consideration of atomic reconstruction in small-twist situations can provide us with another aspect to have an insight into physical mechanism in TBG. In addition, we cover the recent hot topic, twisted multilayer graphene. While the bilayer situation can be relatively easy to resolve, multilayer situations can be really complicated, which could foster more unique and novel properties. Therefore, in the end of the review, we look forward to future development of twisted multilayer graphene.

Growing twisted bilayer graphene at small angles

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors. The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity. This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction. As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means. Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Topological insulators are electronic materials that have a conventional energy gap as an insulator or semiconductor in the bulk, but possess gapless conducting states around their boundary. They are novel topological states of quantum matters and exhibit a series of exotic physics, such as quantum spin Hall effect, single valley Dirac fermions, Majorana fermions, topological magnetoelectric effect, etc. The conducting edge and surface states have topological origin of the electron band structure, and are protected by time-reversal symmetry such that they are robust or immune against local perturbation. In this dissertation, an effective continuous model for surface states is established from the three-dimensional modified Dirac model, and a theory of ultrathin film for topological insulators is developed. The established electronic model helps us explore spin physics of massive Dirac fermions. The theory has been successfully applied to explain an energy gap opening of the surface states in Bi2Se3 thin film in the measurement of angle-resolved photoemission spectroscopy (ARPES). In-gap bound states are also considered due to vacancy and impurity in topological insulators. It is found that a vacancy can always induce in-gap bound states in both two- and threedimensional topological insulators, and a half quantum magnetic flux inside the vacancy can result in helical Dirac zero modes. Finally the effect of random impurities on the surface transport in topological insulators is investigated, particularly the weak anti-localization of surface electrons in the quantum diffusion regime. It is found that the spin-orbit scattering may suppress the weak localization behaviors of massive Dirac fermions, which suggests an experiment to detect the weak localization in the topological insulator thin film.

Condensed matter physics is a vibrant branch of physics, which addresses a very broad spectrum of issues related to electronic, magnetic, thermal, structural and optical proper- ties of condensed phases of matter. The interplay between structural and magnetic phases, interactions between different components of a material, spin-orbit coupling (SOC) and other effects, make condensed matter physics a rich and colorful field. In this thesis I will focus on topological materials, excitonic insulators and atomically thin films, which are being explored intensely both theoretically and experimentally. Specifically, topological materials, including topological (crystalline) insulators and topological Weyl semimetals are covered in Chapters 2 to 4. Chapter 5 is mainly concerned about the excitonic in- sulator (EI) phase in 'slow graphene'. The electronic structure of atomically thin MoS2 films will be discussed in Chapter 6. 3D Topological insulators (TIs), known as quantum spin Hall insulators in 2D, are in- sulating in the bulk while conducting on the surface in sharp contrast with conventional insulators. In Chapter 2, by using first-principles and tight-binding model calculations, we identify a 2-ML (monolayer) Bi(110) thin film as a candidate quantum-spin-Hall in- sulator. In the absence of spin-orbit coupling, 2-ML Bi(110) thin films have two types of Dirac cones in the Brillouin zone (BZ). The Dirac cones, carrying non-zero winding numbers, serve as the starting or ending points of the edge bands in the ribbon spectrum. After the inclusion of the SOC, all Dirac nodes are gapped out. Correspondingly, a Dirac cone formed by the gapless edge states was found at the boundary of the ribbon reflecting the topologically nontrivial nature of the system. In Chapter 3, we present our work on the topological Weyl semimetal phase in the transi- tion metal monopnictide TaAs. A topological Weyl semimetal is a new kind of topological phase, which shows exotic properties in the bulk and on the surface. In the bulk, the valence and conduction bands touch each other at discrete K points, termed as Weyl points or Weyl nodes. On the surface, the Weyl nodes can induce Fermi arcs which are non-closed surface states connecting Weyl nodes with opposite chiralities. TaAs breaks the inversion symmetry and therefore it can be a possible system to host the topologi- cal Weyl semimetal phase. Our first-principles and tight-binding model calculations find that there are 24 Weyl points in the Brillouin zone. The Fermi arcs on (001) surface are identified by surface-state calculations and observed in angle-resolved photoemission experiments (ARPES). Topological crystalline insulators (TCIs) are new kind of topological insulators, which are protected by the crystal symmetries instead of time-reversal symmetry. In Chapter 4, we consider a rotational symmetry protected topological crystalline phase in TaAs2 family of materials. The TaAs2 class crystalizes in a monoclinic structure with space group No. 12. By checking the parity eigenvalues of the occupied bands at time reversal invariant momenta (TRIM), the topological invariants (symmetry indicators) of TaAs2 are found to be (Z2Z2Z2; Z4) = (111; 2), suggesting that TaAs2 can host two Dirac cones on the (010) surface protected by C2 rotational symmetry. Our surface state calculation identified two clear Dirac cones on the (010) surface with the bulk band gap as large as 300 meV. An excitonic insulator instability can arise in narrow gap semiconductors and semimetals when the binding energy of an electron-hole pair exceeds the band gap. Although many experiments have shown some signs of an excitonic insulator state in various systems, conclusive experimental evidence still remains elusive. In Chapter 5 we discuss the ex- citonic instability in 'slow graphene'. We approach the EI transition from two different directions. First, we apply a commonly used mean-field approach that can give us the overall phase diagram of the EI transition. In another approach, we solve the Bethe- Salpeter equation (BSE) and follow the evolution of the lowest excitons. Since graphene is gapless, the presence of an excitonic state at negative energy signals an instability of the assumed ground state. By studying properties of the exciton, we can infer properties of the resulting EI phase, finding overall consistency between the two approaches. Finally, in Chapter 6, we consider the electronic structure of few-layer MoS2. Transition metal dichalcogenides are a family of layered materials, which exhibit metal to semicon- ductor transitions and many other interesting properties as a function of the number of layers. For example, bulk MoS2 is a semiconductor with indirect gap, while monolayer MoS2 has a direct gap at the K-point. I will investigate the evolution of the electronic structure and related properties of MoS2 films as the number of layers is increased within the first-principles density functional theory (DFT) framework. Wannier-function based tight-binding models will be used to gain insight into the first-principles results. I will summarize my thesis in Chapter 7.

Moiré superlattices of 2D materials with a small twist angle are thought to exhibit appreciable flexoelectric effect, though unambiguous confirmation of their flexoelectricity is challenging due to artifacts associated with commonly used piezoresponse force microscopy (PFM). For example, unexpectedly small phase contrast (≈8°) between opposite flexoelectric polarizations is reported in twisted bilayer graphene (tBG), though theoretically predicted value is 180°. Here a methodology is developed to extract intrinsic moiré flexoelectricity using twisted double bilayer graphene (tDBG) as a model system, probed by lateral PFM. For small twist angle samples, it is found that a vectorial decomposition is essential to recover the small intrinsic flexoelectric response at domain walls from a large background signal. The obtained threefold symmetry of commensurate domains with significant flexoelectric response at domain walls is fully consistent with the theoretical calculations. Incommensurate domains in tDBG with relatively large twist angles can also be observed by this technique. A general strategy is provided here for unraveling intrinsic flexoelectricity in van der Waals moiré superlattices while providing insights into engineered symmetry breaking in centrosymmetric materials.

Controlling the balance between piezoelectric and flexoelectric effects is crucial for tailoring the electromechanical responses of a material. In twisted graphene, it is found that the electromechanical response near the domain walls (DWs) is dominated by either the flexoelectric effect as in twisted bilayer graphene (tBLG) or the piezoelectric effect as in twisted monolayer–bilayer graphene (tMBG). The codominance of both effects in a single system is rare. Here, utilizing lateral piezoresponse force microscopy (LPFM), we show that piezoelectric and flexoelectric effects can coexist and are equally important in twisted double bilayer graphene (tDBG), termed as the piezo-flexoelectric effect. Unlike tBLG and tMBG, distinctive two-step LPFM spatial profiles are captured across the moiré DWs of tDBG. By decomposing the LPFM signal into axisymmetric and antisymmetric components, we find that the angular dependence of both components satisfies sinusoidal relations. Quantitatively, the in-plane piezoelectric coefficient of DWs in tDBG is determined to be 0.15 pm/V by dual AC resonance tracking (DART) LPFM measurement. The conclusion is further supported by continuum mechanics simulations. Our results demonstrate that the stacking configuration serves as a powerful tuning knob for modulating the electromechanical responses of twisted van der Waals materials.

Topological insulators (TIs) are a new quantum state of matter discovered in recent years. They are beyond the spontaneous symmetry‐breaking description by Landau and are instead characterized by topological invariants, and described by topological field theory. Their topological nature is similar to the quantum Hall effect, a major discovery of condensed‐matter physics in 1980s (Klaus von Klitzing, Nobel Prize in Physics, 1985). The manifestation of the topological effect is the existence of robust gapless surface states inside the bulk energy gap. The topological surface states exhibit Dirac‐cone‐like energy dispersion with strong spin‐momentum locking. Potential future applications cover areas such as spintronics, thermoelectrics, quantum computing and beyond.It is remarkable that TIs have been realized in many common materials, without the requirement of extreme conditions such as high magnetic field and low temperature. The first TI was predicted in 2006 and experimentally realized in 2007 in HgTe quantum wells. Soon afterwards, three traditionally well‐known binary chalcogenides, Bi2Se3, Bi2Te3 and Sb2Te3, were predicted and observed to be TIs with a large bulk gap and a metallic surface state consisting of a single Dirac cone. The discovery of these topological materials opened up the exciting field of topological insulators. Extensive experimental and theoretical efforts are devoted to synthesizing and optimizing samples, characterizing the topological states by surface sensitive spectroscopy, transport measurements, device fabrications, and searching for new material candidates.The field of TIs is now expanding at a rapid pace in the communities of physics, chemistry and materials science. In this Focus Issue, we intend to present a high‐quality snapshot of the materials and applications aspect of this field.We present ten Review papers from both experiment and theory aspects. Five experimental papers [1–5] overview recent status and challenges of TI nanostructures [1], magnetotransport and induced superconductivity [2], chemistry of Bi‐based TI materials [3], molecular beam epitaxial growth of TI thin films [4], and angle‐resolved photoemission spectroscopy (ARPES) with circular dichroism [5]. On the other hand, five theoretical papers [6–10] report the progress from different perspectives: materials design by first‐principles calculations [6, 7], the relations between TIs and thermoelectric materials [8], Floquet TIs [9], and the classification of topological states [10].We present ten Letters that cover various aspects, ranging from ARPES, transport measurement and devices, thin film growth to first‐principles simulations and fundamental theory. Letters on ARPES [11–14] report the surface states of HgTe [11], Bi2Se3 [12, 13] and Bi2Te3 [11, 14], in which the surface modification, defect doping and electron–phonon coupling are discussed; a paper on transport experiments [15] demonstrates the coexistence of electron‐ and hole‐type charge carriers in devices of Sb2Te3/Bi2Te3 heterostructures; the growth of YPtSb thin film is reported [16], which is a Heusler compound near the boundary of topological trivial–nontrivial transition. Corresponding to the ARPES experiments, a Letter of band structure calculations [17] also reveals the effect of vacancy defects on Bi2Se3 surface states; another paper [18] shows the dependence of edge state dispersion on edge geometry of graphene. Last but not the least, two papers on phenomenological models [19, 20] report the maximally localized flat‐band Hamiltonians and the spectra flow for Aharonov–Bohm rings, respectively.We hope that this Focus Issue will be helpful for your research and stimulate more activity in the exciting field of topological insulators (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Realization and design of topological insulators emerging from electron correlations, called topological Mott insulators (TMIs), is pursued by using mean-field approximations as well as multi-variable variational Monte Carlo (MVMC) methods for Dirac electrons on honeycomb lattices. The topological insulator phases predicted in the previous studies by the mean-field approximation for an extended Hubbard model on the honeycomb lattice turn out to disappear, when we consider the possibility of a long-period charge-density-wave (CDW) order taking over the TMI phase. Nevertheless, we further show that the TMI phase is still stabilized when we are able to tune the Fermi velocity of the Dirac point of the electron band. Beyond the limitation of the mean-field calculation, we apply the newly developed MVMC to make accurate predictions after including the many-body and quantum fluctuations. By taking the extrapolation to the thermodynamic and weak external field limit, we present realistic criteria for the emergence of the topological insulator caused by the electron correlations. By suppressing the Fermi velocity to a tenth of that of the original honeycomb lattice, the topological insulator emerges in an extended region as a spontaneous symmetry breaking surviving competitions with other orders. We discuss experimental ways to realize it in a bilayer graphenesystem.