We study the topological edge states of the Haldane's graphene model with zigzag/armchair lattice edges. The Harper equation for solving the energies of the edge states is derived. The results show that there are two edge states in the bulk energy gap, corresponding to the two zero points of the Bloch function on the complex-energy Riemann surface. The edge-state energy loops move around the hole of the Riemann surface in appropriate system parameter regimes. The quantized Hall conductance can be expressed by the winding numbers of the edge states, which reflects the topological feature of the Haldane model.
We present a functional renormalization group approach to interacting topological Green function invariants with a focus on the nature of transitions. The method is applied to chiral symmetric fermion chains in the Mott limit that can be driven into a Haldane phase. We explicitly show that the transition to this phase is accompanied by a zero of the fermion Green function. Our results for the phase boundary are quantitatively benchmarked against DMRG data.
We study the topological properties of the two-body bound states in an interacting Haldane model as a function of interparticle interactions. In particular, we identify topological phases where the two-body edge states have either the same or the opposite chirality as compared to single-particle edge states. We highlight that in the moderately interacting regime, which is relevant for the experimental realization with ultracold atoms, the topological transition is affected by the internal structure of the bound state, and the phase boundaries are consequently deformed.
Supersymmetry and supergravity were invented in the 1970s to solve fundamental problems in high-energy physics. Even though neither of these ideas has yet been confirmed in high-energy and cosmology experiments, they have been beneficial in constructing numerous theoretical models, including superstring theory. Despite the absence of supersymmetry in particle physics, it can potentially emerge in exotic phases of strongly correlated condensed matter systems. In this paper, we propose a supergravity model that describes the low-energy physics of the Haldane-Rezayi state, a gapless quantum Hall …
Topological insulators have attracted abundant attention for a variety of reasons -- notably, the possibility for lossless energy transport through edge states `protected' against disorder. Topological effects like the Quantum Hall state can be induced through a gauge field, which is however hard to create in practice, especially for charge-neutral particles. One way to induce an effective gauge potential is through a dynamic, time-periodic modulation of the lattice confining such particles. In this way, the Haldane Quantum Hall effect was recently observed in a cold atom system. Here, we show…
We study the half-filled Haldane model with Anderson and binary disorder and determine its phase diagram, as a function of the Haldane flux and staggered sub-lattice potential, for increasing disorder strength. We establish that disorder stabilizes topologically nontrivial phases in regions of the phase diagram where the clean limit is topologically trivial. At small disorder strength, our results agree with analytical predictions obtained using a first order self-consistent Born approximation, and extend to the intermediate and large disorder values where this perturbative approach fails. We …
We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes wi…
We study the interplay between a uniaxial strain and the topology of the Haldane and the modified Haldane models which, respectively, exhibit chiral and antichiral edge modes. The latter were, recently, predicted by Colomés and Franz (Phys. Rev. Lett. {\bf 120}, 086603 (2018)) and expected to take place in the transition metal dichalcogenides. Using the continuum approximation and a tight-binding approach, we investigate the effect of the strain on the topological phases and the corresponding edge modes. We show that the strain could induce transitions between topological phases with opposite …
We consider a periodically $δ$-kicked Haldane type Chern insulator with the kicking applied in the $\hat{z}$ direction. This is known to behave as an inversion symmetry breaking perturbation, since it introduces a time-dependent staggered sub-lattice potential. We study here the effects of such driving on the topological phase diagram of the original Haldane model of a Hall effect in the absence of a net magnetic field. The resultant Floquet band topology is again that of a Chern insulator with the driving parameters, frequency and amplitude, influencing the inversion breaking mass $M$ of the …
Photonic topological materials with a broken time reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge states when enclosed by an opaque type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed matter systems, as it unveiled that a broken time reversal is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of th…
We explore topological properties of a modulated Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor terms is made unequal and the three-fold rotational symmetry $\mathcal{C}_3$ is broken by introducing a trimerization term ($|t_{1w(2w)}|< t_{1s(2s)}$) in the Hamiltonian. Using the parameter $η={t_{1w}}/{t_{1s}}= t_{2w}/t_{2s}$, we show that the MHM supports a transition from the quantum anomalous Hall insulator (QAHI) to a HOTI phase at $η=\pm 0.5$. The MHM also hosts a zero-energy corner mode on a nano-disk that can transition to a trivial insulator wi…
In this Letter we present a comprehensive study of topological magnon bands and thermal Hall effect in non-collinear antiferromagnetic systems on the honeycomb lattice with an intrinsic Dzyaloshinskii-Moriya interaction. We theoretically show that the system possesses topological magnon bands with Chern number protected edge modes accompanied by a nonzero thermal magnon Hall effect. These features result from non-collinearity of the magnetic moments due to an applied out-of-plane magnetic field. Our results provide an experimental clue towards the realization of topological magnon transports i…
Based on a quasi-one-dimensional limit of quantum Hall states on a thin torus, we construct a model of interaction-induced topological pumping which mimics the Hall response of the bosonic integer quantum Hall (BIQH) state. The quasi-one-dimensional counterpart of the BIQH state is identified as the Haldane phase composed of two-component bosons which form effective spin-$1$ degrees of freedom. An adiabatic change between the Haldane phase and trivial Mott insulators constitute {\it off-diagonal} topological pumping in which the translation of the lattice potential for one component induces a …
Interlayer Coupling and Floquet-Driven Topological Phases in Bilayer Haldane Lattices
Zhejiang Normal University（浙江师范大学）；Khazar University（哈扎尔大学）；Quaid-I Azam University Islamabad（巴基斯坦奎德-阿扎姆大学伊斯兰堡分校）；Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究院）
Institute of Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）；Laboratoire d’Acoustique de l’Université du Mans, Unite Mixte de Recherche 6613, Centre National de la Recherche Scientifique（勒芒大学声学实验室，联合研究单位6613，法国国家科学研究中心）
Topological magnetotransport in modified-Haldane systems
National Centre for physics（国家物理中心）；Department of Physics, Quaid-I-Azam University（真纳大学物理系）；Department of Physics, Zhejiang Normal University（浙江师范大学物理系）；Zhejiang Institute of Photoelectronics（浙江光电子研究所）
Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in non-Hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. Here, we present the first study on the emergence of topological edge states in two-dimensional Haldane lattices exhibiting balanced gain and loss. In line with recent studies on other Chern insulator models, we show that edge states can be observed in the so-ca…
The Chern insulator displays a quantized Hall effect without Landau levels. In a landmark paper in 1988, Haldane showed that a Chern insulator could be realized through complex next-nearest-neighbor hopping in a honeycomb lattice. Despite its profound impact on the field of topological physics and recent implementation in cold-atom experiments, the Haldane model has remained elusive in solid-state materials. Here, we report the experimental realization of a Haldane Chern insulator in AB-stacked MoTe2/WSe2 moiré bilayers, which form a honeycomb moiré lattice with two sublattices residing in dif…
We propose the model of layered materials, in which each layer is described by the conventional Haldane model, while the inter - layer hopping parameter corresponds to the ABC stacking. We calculate the topological invariant $N_3$ for the resulting model, which is responsible for the conductivity of intrinsic quantum Hall effect. It has been shown that in a certain range of the values of interlayer hopping parameter, the value of $N_3$ is equal to the number of layers multiplied by the topological invariant of each layer. At the same time this value may be calculated using the low energy effec…
We present an ab initio analysis of a continuous Hamiltonian that maps into the celebrated Haldane model. The tunnelling coefficients of the tight-binding model are computed by means of two independent methods - one based on the maximally localized Wannier functions, the other through analytic expressions in terms of gauge-invariant properties of the spectrum - that provide a remarkable agreement and allow to accurately reproduce the exact spectrum of the continuous Hamiltonian. By combining these results with the numerical calculation of the Chern number, we are able to draw the phase diagram…
We propose a protocol to locally detect the Berry curvature of a three terminal Josephson junction with a quantum dot based on a synchronic detection when an AC modulation is applied in the device. This local gauge invariant quantity is expressed in terms of the instantaneous Green function of the Bogoliubov-de Gennes Hamiltonian. We analyze the contribution to the Berry curvature from both the quasi-particle excitations and the Andreev bound state levels by introducing an effective low-energy model. In addition, we propose to induce topological properties in the junction by breaking time-reve…
We study the role of the edges in determining the features of the topological phase in a quasicrystalline higher order topological insulator. We consider a specific model consisting of two stacked Haldane models with opposite Chern number and a $30^\circ$ twist, whose structure is crystallographically equivalent to that of the graphene quasicrystal. We find that the gap-opening in the low energy spectrum of the higher order topological insulator occurs at different energies when different kinds of edges are considered. Crucially, bearded bonds appear to be necessary for the gap to appear close…
We consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary non-relativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current …
We develop a framework to analyze one-dimensional topological superconductors with charge conservation. In particular, we consider models with $N$ flavors of fermions and $(\mathbb{Z}_2)^N$ symmetry, associated with the conservation of the fermionic parity of each flavor. For a single flavor, we recover the result that a distinct topological phase with exponentially localized zero modes does not exist due to absence of a gap to single particles in the bulk. For $N>1$, however, we show that the ends of the system can host low-energy, exponentially-localized modes. The analysis can readily be ge…
The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z)^2$, and the rhombic-type, $E[(S^x)^2-(S^y)^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the $\mathbb{Z}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on …
We propose a Haldane-like model of dice lattice analogous to graphene and explore its topological properties within the tight-binding formalism. The topological phase boundary of the system is identical to that of Haldane model of graphene but the phase diagram is richer than the latter due to existence of a distorted flat band. The system supports phases which have a "gapped-out" valence (conduction) band and an indirect overlap between the conduction (valence) band and the distorted flat band. The overlap of bands imparts metallic character to the system. These phases may be further divided …
We study the topological properties of a Haldane model on a band deformed dice lattice, which has three atoms per unit cell (call them as A, B and C) and the spectrum comprises of three bands, including a flat band. The bands are systematically deformed with an aim to study the evolution of topology and the transport properties. The deformations are induced through hopping anisotropies and are achieved in two distinct ways. In one of them, the hopping amplitudes between the sites of B and C sublattices and those between A and B sublattices are varied along a particular direction, and in the ot…
