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Higher-order topological insulators are an intriguing new family of topological states that host lower-dimensional boundary states. Concurrently, quasiperiodic systems have garnered significant interest due to their complex localization and topological properties. In this work we study the impact of quasiperiodic modulations on the paradigmatic Benalcazar-Bernevig-Hughes model, which hosts topological insulating phases with zero-energy corner modes. We find that the topological properties are not only robust to the quasiperiodic modulation, but can even be enriched. In particular, we unveil the first instance of a quasiperiodic induced second-order topological insulating phase. Furthermore, in contrast with disorder, we find that quasiperiodic modulations can induce multiple reentrant topological transitions, showing an intricate sequence of localization properties. Our results open a promising avenue for exploring the rich interplay between higher-order topology and quasiperiodicity., Comment: 12 pages, 14 figures, typos corrected, references added

Weyl nodal loop semimetals are gapless topological phases that, unlike their insulator counterparts, may be unstable to small perturbations that respect their topology-protecting symmetries. Here, we analyze a clean system perturbed by chiral off-diagonal disorder using numerically exact methods. We establish that the ballistic semimetallic phase is unstable towards the formation of an unconventional topological diffusive metal hosting topological multifractal surface states. Although, as in the clean case, surface states are exponentially localized along the direction perpendicular to the nodal loop, disorder induces a multifractal structure in the remaining directions. Surprisingly, the number of these states also increases with a small amount of disorder. Eventually, as disorder is further increased, the number of surface states starts decreasing. In the strong disordered regime we predict that some types of disorder induce an Anderson transition into an electrically-polarized insulator whose signature may be detected experimentally.

Chiral edge states are the fingerprint of the bulk-edge correspondence in a Chern insulator. Co-propagating edge modes, known as antichiral edge states, have been predicted to occur in the so-called modified Haldane model describing a two-dimensional semi-metal with broken time reversal symmetry. These counterintuitive edge modes are argued to be immune to backscattering and extremely robust against disorder. Here, we investigate the robustness of the antichiral edge states in the presence of Anderson disorder. By analysing different localization parameters, we show that, contrary to the general belief, these edge modes are fragile against disorder, and can be easily localized. Our work provides insights to improve the transport efficiency in the burgeoning fields of antichiral topological photonics and acoustics., Comment: 9 pages, 6 figures

We study the effect of diluting a two-dimensional ferromagnetic insulator hosting a topological phase in the clean limit. By considering the ferromagnetic Heisenberg model in the honeycomb lattice with second nearest-neighbor Dzyanshikii-Moriya interaction, and working in the linear spin-wave approximation, we establish the topological phase diagram as a function of the fraction $p$ of diluted magnetic atoms. The topological phase with Chern number $C=1$ is robust up to a moderate dilution $p_{1}^{*}$, while above a higher dilution $p_{2}^{*}>p_{1}^{*}$ the system becomes trivial. Interestingly, both $p_{1}^{*}$ and $p_{2}^{*}$ are below the classical percolation threshold $p_{c}$ for the honeycomb lattice, which gives physical significance to the obtained phases. In the topological phase for $pp_{2}^{*}$, when all states become localized, the system shows $C=0$ as expected for a trivial phase. Replacing magnetic with non-magnetic atoms in a systems hosting a magnon Chern insulator in the clean limit puts all the three phases within experimental reach., Comment: 10 pages, 6 figures

We unveil a novel mechanism for quasicondensation of hard-core bosons in the presence of quasiperiodicity-induced multifractal single-particle states. The new critical state, here dubbed fractal quasicondensate, is characterized by natural orbitals with multifractal properties and by an occupancy of the lowest natural orbital, {\lambda}0 ~ L{\gamma}, which grows with system size but with a nonuniversal scaling exponent, {\gamma} < 1/2. In contrast to fractal quasicondensates obtained when the chemical potential lies in a region of multifractal single-particle states, placing the chemical potential in regions of localized or delocalized states yields, respectively, no condensation or the usual 1D quasicondensation with {\gamma} = 1/2. Our findings are established by studying one-dimensional hardcore bosons subjected to various quasiperiodic potentials, including the well-known Aubry-Andre model, employing a mapping to non-interacting fermionics that allows for numerically exact results. We discuss how to test our findings in state-of-the-art ultracold atom experiments., Comment: 8 pages (SM included)

We study the fate of two-dimensional quadratic band crossing topological phases under a one-dimensional quasiperiodic modulation. By employing numerically exact methods, we fully characterize the phase diagram of the model in terms of spectral, localization and topological properties. Unlike in the presence of regular disorder, the quadratic band crossing is stable towards the application of the quasiperiodic potential and most of the topological phase transitions occur through a gap closing and reopening mechanism, as in the homogeneous case. With a sufficiently strong quasiperiodic potential, the quadratic band crossing point splits into Dirac cones which enables transitions into gapped phases with Chern numbers $C=\pm1$, absent in the homogeneous limit. This is in sharp contrast with the disordered case, where gapless $C=\pm1$ phases can arise by perturbing the band crossing with any amount of disorder. In the quasiperiodic case, we find that the $C=\pm1$ phases can only become gapless for a very strong potential. Only in this regime, the subsequent quasiperiodic-induced topological transitions into the trivial phase mirror the well-known ``levitation and annihilation'' mechanism in the disordered case., Comment: 11 pages, 4 figures

We analyze the influence of disorder and strong correlations on the topology in two dimensional Chern insulators. A mean field calculation in the half-filled Haldane model with extended Hubbard interactions and Anderson disorder shows that disorder favors topology in the interacting case and extends the topological phase to a larger region of the Hubbard parameters. In the absence of a staggered potential, we find a novel disorder-driven topological phase with Chern number C=1, with co-existence of topology with long range spin and charge orders. More conventional topological Anderson insulating phases are also found in the presence of a finite staggered potential.

We have found the first instance of a third-order topological Anderson insulator (TOTAI). This disorder-induced topological phase is gapped and characterized by a quantized octupole moment and topologically protected corner states, as revealed by a detailed numerically exact analysis. We also find that the disorder-induced transition into the TOTAI phase can be analytically captured with remarkable accuracy using the self-consistent Born approximation. For a larger disorder strength, the TOTAI undergoes a transition to a trivial diffusive metal, that in turn becomes an Anderson insulator at even larger disorder. Our findings show that disorder can induce third-order topological phases in 3D, therefore extending the class of known higher-order topological Anderson insulators.

We demonstrate that quasiperiodicity can radically change the ground state properties of 1D moir\'e systems with respect to their periodic counterparts. By studying an illustrative example we show that while narrow bands play a significant role in enhancing interactions both for commensurate and incommensurate structures, only quasiperiodicity is able to extend the ordered phase down to an infinitesimal interaction strength. In this regime, the quasiperiodic-enabled state has contributions from infinitely many wave vectors. This quasi-factal regime cannot be stabilized in the commensurate case even in the presence of a narrow band. These findings suggest that quasiperiodicity may be a critical factor in stabilizing non-trivial ordered phases in interacting moir\'e structures and signal out multifractal non-interacting phases, recently found in 2D incommensurate moir\'e systems, as particularly promising parent states.

We show that short-range interactions are irrelevant around gapless ground-state delocalization-localization transitions driven by quasiperiodicity in interacting fermionic chains. In the presence of interactions, these transitions separate Luttinger Liquid and Anderson glass phases. Remarkably, close to criticality, we find that excitations become effectively non-interacting. By formulating a many-body generalization of a recently developed method to obtain single-particle localization phase diagrams, we carry out precise calculations of critical points between Luttinger Liquid and Anderson glass phases and find that the correlation length critical exponent takes the value $\nu = 1.001 \pm 0.007$, compatible with $\nu=1$ known exactly at the non-interacting critical point. We also show that other critical exponents, such as the dynamical exponent $z$ and a many-body analog of the fractal dimension are compatible with the exponents obtained at the non-interacting critical point. Noteworthy, we find that the transitions are accompanied by the emergence of a many-body generalization of previously found single-particle hidden dualities. Finally, we show that in the limit of vanishing interaction strength, all finite range interactions are irrelevant at the non-interacting critical point.

We show that incommensurability can enhance superconductivity in one dimensional quasiperiodic systems with s-wave pairing. As a parent model, we use a generalized Aubry-Andr\'e model that includes quasiperiodic modulations both in the potential and in the hoppings. In the absence of interactions, the model contains extended, critical and localized phases for incommensurate modulations. Our results reveal that in a substantial region inside the parent critical phase, there is a significant increase of the superconducting critical temperature compared to the extended phase and the uniform limit without quasiperiodic modulations. We also analyse the results for commensurate modulations with period close to the selected incommensurate one. We find that while in the commensurate case, the scaling of the critical temperature with interaction strength follows the exponentially small weak-coupling BCS prediction for a large enough system size, it scales algebraically in the incommensurate case within the critical and localized parent phases. These qualitatively distinct behaviors lead to a significant incommensurability-induced enhancement of the critical temperature in the weak and intermediate coupling regimes, accompanied by an increase in the superconducting order parameter at zero temperature., Comment: 8 pages, 4 figures

The effect of Anderson diagonal disorder on the topological surface (``drumhead'') states of a Weyl nodal loop semimetal is addressed. Since diagonal disorder breaks chiral symmetry, a winding number cannot be defined. Seen as a perturbation, the weak random potential mixes the clean exponentially localized drumhead states of the semimetal, thereby producing two effects: (i) the algebraic decay of the surface states into the bulk; (ii) a broadening of the low energy density of surface states of the open system due to degeneracy lifting. This behavior persists with increasing disorder, up to the bulk semimetal-to-metal transition at the critical disorder $W_{c}$. Above $W_{c}$, the surface states hybridize with bulk states and become extended into the bulk., Comment: 7 pages, 6 figures

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-Andr\'e model and the models of PRL 114, 146601 and PRL 104, 070601. The analytical treatment follows from recognizing these models as a novel type of fixed-points of the renormalization group procedure recently proposed in arXiv:2206.13549 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and non-trivial mobility edges without the need for the unbounded potentials required by previous proposals., Comment: arXiv admin note: text overlap with arXiv:2206.13549

We develop a renormalization group (RG) description of the localization properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of quasiperiodic systems are characterized by RG fixed points associated with renormalized single-band models. We identify fixed-points that include many previously reported exactly solvable quasiperiodic models. By classifying relevant and irrelevant perturbations, we show that phase boundaries of more generic models can be determined with exponential accuracy in the approximant's unit cell size, and in some cases analytically. Our findings provide a unified understanding of widely different classes of 1D quasiperiodic systems.

Searching for triplet superconductivity has been pursued intensively in a broad field of material science and quantum information for decades. Nevertheless, these novel states remain rare. Within a simplified effective three-orbital model, we reveal a spin triplet pairing in doped MoS$_2$ by employing both the finite temperature determinant quantum Monte Carlo approach and the ground state constrained-phase quantum Monte Carlo method. In a wide filling region of $\avg{n}=0.60-0.80$ around charge neutrality $\avg{n}=2/3$, the $f$-wave pairing dominates over other symmetries. The pairing susceptibility strongly increases as the on-site Coulomb interaction increases, and it is insensitive to spin-orbit coupling., Comment: Accepted for publication as a Regular Article in Physical Review B

Edge magnetism in zigzag transition metal dichalcogenide nanoribbons is studied using a three-band tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic gapped phase at the same edge filling as mean field theory, despite being sign-problematic for other fillings. The obtained results point to edge filling as yet another key ingredient to understand the observed magnetism in nanosheets. Moreover, the filling dependent edge magnetism gives rise to spin-polarized edge currents in zigzag nanoribbons which could be tuned through a back gate voltage, with possible applications to spintronics., Comment: 14 pages, 14 figures

Here we study the instabilities of a quadratic band crossing system to Chern insulating states and uncorrelated disorder. We determined the phase diagram in the plane of topological mass versus disorder strength, characterizing the system with respect to spectral, localization and topological properties. In the clean limit, the system has two gapped Chern insulating phases with Chern numbers C=\pm2, and a trivial phase with C=0. For finite disorder, the quadratic band crossing points are unstable to emergent gapless Chern insulating phases with C=\pm1, not present in the clean limit. These phases occupy a considerable region of the phase diagram for intermediate disorder and show features of topological Anderson insulators: it is possible to reach them through disorder-driven transitions from trivial phases.

We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization as well as density matrix renormalization group, applied to a honeycomb cylinder. The interplay of disorder, interactions and topology gives rise to a rich phase diagram, and in particular highlights the possibility of a disorder-driven trivial-to-topological transition in the presence of finite interactions. That is, the topological Anderson insulator, demonstrated in non-interacting settings, is shown to be stable to the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further perform a finite-size analysis of the transition to the ordered state in the presence of disorder, finding a mixed character of first and second order transitions in finite lattices, tied to specific conditions of disorder realizations and boundary conditions used., Comment: 10 pages, 10 figures; as published

We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-Andr\'e model. These spectral and eigenstate dualities are locally defined near the transition and can, in many cases, be explicitly constructed by considering relatively small commensurate approximants. The construction relies on auxiliary 2D Fermi surfaces obtained as functions of the phase-twisting boundary conditions and of the phase-shifting real-space structure. We show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to obtain mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously studied systems, including generalized Aubry-Andr\'e models and coupled Moir\'e chains. Our findings bring a new perspective to examine quasiperiodicity-induced extended-to-localized transitions in 1D, provide a working criterion for the appearance of mobility edges, and an explicit way to understand the properties of eigenstates close to and at the transition.

We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using an exact-diagonalization, mean-field variational approach, and further complement it with the infinite density matrix renormalization group, applied to an infinite honeycomb cylinder. This model, governed by both on-site and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. Moreover, a third one, a topologically nontrivial insulator with nonlocal order, is also manifest. We test expectations of previous analyses in spinless versions asserting that once a local order parameter is formed, the topological characteristics of the ground state, associated with a finite Chern number, are no longer present, resulting in a topologically trivial wave function. Our study confirms this overall picture, and highlights how finite-size effects may result in misleading conclusions on the coexistence of finite local order parameters and nontrivial topology in this model., Comment: 11 pages, 8 figures

We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance decreases with system size for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.

We study conductance across a twisted bilayer graphene coupled to single-layer graphene leads in two setups: a flake of graphene on top of an infinite graphene ribbon and two overlapping semi-infinite graphene ribbons. We find conductance strongly depends on the angle between the two graphene layers and identify three qualitatively different regimes. For large angles ($\theta \gtrsim 10^{\circ}$) there are strong commensurability effects for incommensurate angles the low energy conductance approaches that of two disconnected layers, while sharp conductance features correlate with commensurate angles with small unit cells. For intermediate angles ($3^{\circ}\lesssim \theta \lesssim 10^{\circ}$), we find a one-to-one correspondence between certain conductance features and the twist-dependent Van Hove singularities arising at low energies, suggesting conductance measurements can be used to determine the twist angle. For small twist angles ($1^{\circ}\lesssim\theta\lesssim 3^{\circ}$), commensurate effects seem to be washed out and the conductance becomes a smooth function of the angle. In this regime, conductance can be used to probe the narrow bands, with vanishing conductance regions corresponding to spectral gaps in the density of states, in agreement with recent experimental findings., Comment: 9 pages, 8 figures

The effect of short-range disorder in nodal line semimetals is studied by numerically exact means. For arbitrary small disorder, a novel semimetallic phase is unveiled for which the momentum-space amplitude of the ground-state wave function is concentrated around the nodal line and follows a multifractal distribution. At a critical disorder strength, a semimetal to compressible metal transition occurs, coinciding with a multi- to single-fractality transition. The universality class of this critical point is characterized by the correlation length and dynamical exponents. At considerably higher disorder, an Anderson metal-insulator transition takes place. Our results show that the nature of the semimetallic phase in non-clean samples is fundamentally different from a clean nodal semimetal.

Van der Waals (vdW) heterostructures ---formed by stacking or growing two-dimensional (2D) crystals on top of each other--- have emerged as a new promising route to tailor and engineer the properties of 2D materials. Twisted bilayer graphene (tBLG), a simple vdW structure where the interference between two misaligned graphene lattices leads to the formation of a moir\'e pattern, is a test bed to study the effects of the interaction and misalignment between layers, key players for determining the electronic properties of these stackings. In this chapter, we present in a pedagogical way the general theory used to describe lattice mismatched and misaligned vdW structures. We apply it to the study of tBLG in the limit of small rotations and see how the coupling between the two layers leads both to an angle dependent renormalization of graphene's Fermi velocity and appearance of low-energy van Hove singularities. The optical response of this system is then addressed by computing the optical conductivity and the dispersion relation of tBLG surface plasmon-polaritons.

We analyze the localization properties of two dimensional systems based on partite lattices with a basis. Contrary to standard results, we find that a band of critical states emerges for systems in the unitary class A preserving spin symmetry when disorder is unevenly distributed over the basis atoms. The critical metal arises when the less disordered sublattice is connected and has time reversal symmetry broken. The unexpected robustness to disorder presented here is an appealing result which can be measured in optical lattices.

The phase diagram of graphene decorated with magnetic adatoms distributed either on a single sublattice, or evenly over the two sublattices, is computed for adatom concentrations as low as $\sim1\%$. Within the framework of the $s$-$d$ interaction, we take into account disorder effects due to the random positioning of the adatoms and/or to the thermal fluctuations in the direction of magnetic moments. Despite the presence of disorder, the magnetic phases are shown to be stable down to the lowest concentration accessed here. This result agrees with several experimental observations where adatom decorated graphene has been shown to have a magnetic response. In particular, the present theory provides a qualitative understanding for the results of Hwang et al. [Sci. Rep. 6, 21460 (2016)], where a ferromagnetic phase has been found below $\sim30\,\text{K}$ for graphene decorated with S-atoms., Comment: 12 pages, 8 figures

The transmission across a graphene bilayer region is calculated for two different types of connections to monolayer leads. A transfer matrix algorithm based on a tight binding model is developed to obtain the ballistic transmission beyond linear response. The two configurations are found to behave similarly when no gate voltage is applied. For a finite gate voltage, both develop a conductance gap characteristic of a biased bilayer, but only one shows a pronounced conductance step at the gap edge. A gate voltage domain wall applied to the bilayer region renders the conductance of the two configurations similar. For a microstructure consisting of equally spaced domain walls, we find a high sensitivity to the domain size. This is attributed to the presence of topologically protected in-gap states localized at domain walls, which hybridize as the domain size becomes of the order of their confining scale. Our results show that transmission through a bilayer region can be manipulated by a gate voltage in ways not previously anticipated., Comment: 10 pages, 8 figures, Font of figures' labels are changed

We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton "gas" that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter wave phononics, in analogy with the electric induced transparency (EIT) effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to $\sim 5$ $\mu$m/s, $\sim 10^3$ times lower than the condensate sound speed. This is a record value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of "stopped-sound" based quantum information protocols., Comment: 10 pages, 8 figures. arXiv admin note: text overlap with arXiv:1801.08169

We present a model for a Chern insulator on the square lattice with complex first and second neighbor hoppings and a sublattice potential which displays an unexpectedly rich physics. Similarly to the celebrated Haldane model, the proposed Chern insulator has two topologically non-trivial phases with Chern numbers $\pm1$. As a distinctive feature of the present model, phase transitions are associated to Dirac points that can move, merge and split in momentum space, at odds with Haldane's Chern insulator where Dirac points are bound to the corners of the hexagonal Brillouin zone. Additionally, the obtained phase diagram reveals a peculiar phase transition line between two distinct topological phases, in contrast to the Haldane model where such transition is reduced to a point with zero sublattice potential. The model is amenable to be simulated in optical lattices, facilitating the study of phase transitions between two distinct topological phases and the experimental analysis of Dirac points merging and wandering.

We show that 1D electron states confined at twin-grain-boundaries in MoSe$_{2}$ can be modeled by a three-orbital tight binding model including a minimum set of phenomenological hopping terms. The confined states are robust to the details of the defect hopping model, which agrees with their experimental ubiquity. Despite a valley Chern number which is finite and opposite on both sides of the defect, there is no topological protection of the confined states. This turns out to be an essential feature to have only one confined electronic band, in agreement with experiments, instead of two, as the bulk-edge correspondence would imply. Modeling the confined state as a 1D interacting electronic system allows us to unveil a mobile quantum impurity type behavior at energy scales beyond the Tomonaga-Luttinger liquid with an interaction range which extends up to the lattice spacing, in excellent agreement with ARPES measurements., Comment: 14 pages, 7 figures

We investigate the phase diagram of the Haldane-Falicov-Kimball model -- a model combining topology, interactions and spontaneous disorder at finite temperatures. Using an unbiased numerical method, we map out the phase diagram on the interaction--temperature plane. Along with known phases, we unveil an \textit{insulating charge ordered state with gapless excitations }and a temperature-driven \textit{gapless topological insulating} phase. Intrinsic -- temperature generated -- disorder, is the key ingredient explaining the unexpected behavior. Our findings support the possibility of having temperature-driven topological phase transitions into gapped and gapless topological insulating phases in systems with a large mass unbalance in fermionic species., Comment: 5 pages, 4 figures

Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate multilayered van der Waals structures for arbitrary lattice mismatch and/or misalignment between different layers. We demonstrate how the developed formalism can be used to model angle-resolved photoemission spectroscopy measurements, and scanning tunnelling spectroscopy which can probe the local and total density of states. The general method is then applied to incommensurate twisted trilayer graphene structures. It is found that the coupling between the three layers can significantly affect the low energy spectral properties, which cannot be simply attributed to the pairwise hybridization between the layers., Comment: 8 pages, 3 figures

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 further characterize the phases according to their gapless or gapped nature by determining the spectral weight at the Fermi level. We find that gapless topological nontrivial phases are supported for both Anderson and binary disorder. In the binary case, we find a reentrant topological phase where, starting from a trivial region, a topological transition occurs for increasing staggered potential $\eta$, followed by a second topological transition to the trivial phase for higher values of $\eta$., Comment: 8 pages, 6 figures

In this work we consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally non-vanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a non-dynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behaviour of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations., Comment: 6 pages; 2 figures

We study the finite time entanglement dynamics between two dark soliton qubits due to quantum fluctuations in a quasi one dimensional Bose-Einstein condensates. Recently, dark solitons are proved to be an appealing platform for qubits due to their appreciably long life time. We explore the entanglement decay for an entangled state of two phonon coherences and the qubits to be in the diagonal basis of so called Dicke states. We observe the collapse and revival of the entanglement, depending critically on the collective damping term but independent of the qubit-qubit interaction for both the initial states. The collective behavior of the dark soliton qubits demonstrate the dependence of entanglement evolution on the interatomic distance., Comment: 8 Pages, 8 Figures

We show that entanglement between two solitary qubits in quasi-one-dimensional Bose-Einstein condensates can be spontaneously generated due to quantum fluctuations. Recently we have shown that dark solitons are an appealing platform for qubits thanks to their appreciable long lifetime. We investigate the spontaneous generation of entanglement between dark-soliton qubits in the dissipative process of spontaneous emission. By driving the qubits with the help of oscillating magnetic field gradients, we observe the formation of long distance steady-state concurrence. Our results suggest that dark-soliton qubits are good candidates for quantum information protocols based purely on matter-wave phononics., Comment: 10 Pages, 8 Figures

Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in atomically thin materials and thus to unlock the much sought-after topological insulating phases in two dimensions. However, the observation of an Anderson topological transition induced by heavy adatoms has proved extremely challenging despite substantial experimental efforts. Here, we present a multi-scale approach combining advanced first-principles methods and accurate single-electron descriptions of adatom-host interactions using graphene as a prototypical system. Our study reveals a surprisingly complex structure in the interactions mediated by random adatoms, including hitherto neglected hopping processes leading to strong valley mixing. We argue that the unexpected intervalley scattering strongly impacts the ground state at low adatom coverage, which would provide a compelling explanation for the absence of a topological gap in recent experimental reports. Our conjecture is confirmed by real-space Chern number calculations and large-scale quantum transport simulations in disordered samples. This resolves an important controversy and suggests that a detectable topological gap can be achieved by engineering the spatial range of spin-orbit interactions., Comment: 6 pages, 3 figures + Supp. Mat. (9 pages, 7 figures). Published in PRB Rapid Communication

We compute the valley/magnetic phase diagram of mono layers of transition metal dichalcogenides in the hole doped region where spin-orbit effects are particularly relevant. Taking into account the moderate to high local electron-electron interactions due to the presence of transition metal atoms, we show that the system is unstable to an itinerant ferromagnetic phase where all charge carriers are spin and valley polarized. This phase shows an anomalous charge Hall and anomalous spin-Hall response, and may thus be detected experimentally., Comment: 5 pages, 3 figures

Graphene nanoribbons with armchair edges are studied for externally enhanced, but realistic parameter values: enhanced Rashba spin-orbit coupling due to proximity to a transition metal dichalcogenide like WS$_{2}$, and enhanced Zeeman field due to exchange coupling with a magnetic insulator like EuS under applied magnetic field. The presence of s--wave superconductivity, induced either by proximity or by decoration with alkali metal atoms like Ca or Li, leads to a topological superconducting phase with Majorana end modes. The topological phase is highly sensitive to the application of uniaxial strain, with a transition to the trivial state above a critical strain well below $0.1\%$. This sensitivity allows for real space manipulation of Majorana fermions by applying non-uniform strain profiles. Similar manipulation is also possible by applying inhomogeneous Zeeman field or chemical potential., Comment: 5 pages, 5 figures; references added

We study the Haldane model under strain using a tight-binding approach, and compare the obtained results with the continuum-limit approximation. As in graphene, nonuniform strain leads to a time-reversal preserving pseudo-magnetic field that induces (pseudo) Landau levels. Unlike a real magnetic field, strain lifts the degeneracy of the zeroth pseudo Landau levels at different valleys. Moreover, for the zigzag edge under uniaxial strain, strain removes the degeneracy within the pseudo-Landau levels by inducing a tilt in their energy dispersion. The latter arises from next-to-leading order corrections to the continuum-limit Hamiltonian, which are absent for a real magnetic field. We show that, for the lowest pseudo-Landau levels in the Haldane model, the dominant contribution to the tilt is different from graphene. In addition, although strain does not strongly modify the dispersion of the edge states, their interplay with the pseudo-Landau levels is different for the armchair and zigzag ribbons. Finally, we study the effect of strain in the band structure of the Haldane model at the critical point of the topological transition, thus shedding light on the interplay between non-trivial topology and strain in quantum anomalous Hall systems.

It is known that in two dimensional relativistic Dirac systems, the Landau levels can collapse in the presence of a critical in plane electric field. We extend this mechanism to the three dimensional Weyl semimetals and analyze the physical consequences for the cases of both, real and pseudo Landau levels arising form strain induced elastic magnetic fields., Comment: New version as published in PRB (R)

We study the possibility of using dark soliton in quasi one dimensional Bose Einstein condensates to produce two level system (qubits) by exploiting the intrinsic nonlinear and the coherent nature of the matter waves. We calculate the soliton spectrum and the conditions for a qubit to exist. We also compute the coupling between the phonons and the soliton and investigate the emission rate of the qubits in that case. Remarkably, the qubit lifetime is estimated to be of the order of a few seconds, being by the dark soliton "death" due to quantum evaporation., Comment: Bose Einstein condensates, Qubit, Dark Soliton

Lattice deformations couple to the low energy electronic excitations of graphene as vector fields similar to the electromagnetic potential \cite{SA02b,VKG10}. The suggestion that certain strain configurations would be able to induce pseudo landau levels in the spectrum of graphene \cite{GKG10,GGKN10}, and the subsequent experimental observation of these \cite{LBetal10} has been one of the most exciting events in an already fascinating field. It opened a new field of research "straintronics" linked to new applications, and had a strong influence on the physics of the new Dirac materials in two and three dimensions \cite{Amorim16}. The experimental observation of pseudo landau levels with scanning tunnel microscopy presents nevertheless some ambiguities. Similar strain patterns show different images sometimes difficult to interpret. In this work we strain the analogy of the pseudo versus real electromagnetic fields, as well as the fact that graphene has a relativistic behavior and show that, for some strain configurations, the deformation potential acts like a parallel electric field able to destabilize the Landau level structure via a mechanism identical to that described in \cite{LSB07,PC07} for real electromagnetic fields. The underlying physics is the combination of Maxwell electrodynamics and special relativity implying that different reference frames observe different electromagnetic fields \cite{LSB07}. The mechanism applies equally if the electric field has an external origin, which opens the door to an electric control of the giant pseudomagnetic fields in graphene., Comment: 5 pages, 2 figures

The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced superconductivity is studied using a minimal 3-band tight-binding model. The unstrained system shows a topological phase with Majorana zero modes localized at the boundaries of the one-dimensional (1D) zigzag edges. By direct inspection of the spectrum and wave functions we examine the evolution of the topological phase as an in-plane, uniaxial deformation is imposed. It is found that strain shifts the energy of 1D edge states, thus causing a topological phase transition which eliminates the Majorana modes. For realistic parameter values, we show that the effect of strain can be changed from completely destructive -- in which case a small built in strain is enough to destroy the topological phase -- to a situation where strain becomes an effective tuning parameter which can be used to manipulate Majorana zero modes. These two regimes are accessible by increasing the value of the applied Zeeman field within realistic values. We also study how strain effects are affected by the chemical potential, showing in particular how unwanted effects can be minimized. Finally, as a cross-check of the obtained results, we reveal the connection between 1D Majorana zero modes in the zigzag edge and the multi-band Berry phase, which serves as a topological invariant of this system., Comment: 8 pages, 5 figures

Topological matter is a trending topic in condensed matter: From a fundamental point of view it has introduced new phenomena and tools, and for technological applications, it holds the promise of basic stable quantum computing. Similarly, the physics of localization by disorder, an old paradigm of obvious technological importance in the field, continues revealing surprises when new properties of matter appear. This work deals with the localization behavior of electronic systems based on partite lattices with special attention to the role of topology. We find an unexpected result from the point of view of localization properties: A robust topological metallic state characterized by a non--quantized Hall conductivity arises from strong disorder in class A (time reversal symmetry broken) insulators. The key issue is the nature of the disorder realization: selective disorder in only one sublattice in systems based on bipartite lattices. The generality of the result is based on the partite nature of most recent 2D materials as graphene or transition metal dichalcogenides, and the possibility of the physical realization of the particular disorder demonstrated in ref. 1. An anomalous Hall metal arises also when the original clean insulator is topologically trivial.

The functionalized graphene with induced superconductivity, Zeeman coupling, and finite Rashba spin-orbit coupling is proposed to display topological superconducting phases with Majorana end modes. We obtain the phase diagram of bulk graphene and nanoribbon by calculating the Chern number, band structure and wavefunction. The electron doping in graphene, magnetic field and strain-induced pseudomagnetic field can result in the topological phase transition. Moreover, it is interested to note that strain has negative influence on the stability of topological nontrivial phase either uniform or nonuniform, destroying the existence of Majorana fermion, which provides a new way to transfer, create and fuse Majorana fermions. Some experimental schemes are also introduced to tailor functionalized graphene, generating various devices applied in topological quantum computation.

Majorana fermions in some model semiconductor nanowires proximity coupled with \emph{s}-wave superconductor have been investigated, as well as other intragap bound states in topological phase of a Rashba nanowire with non-uniform spin-orbit interaction (SOI). Various sources of disorder, such as disorder in semiconductor nanowire, bulk superconductor and semiconductor-superconductor interface, are included to characterize their effects on the stability of the topological phase. In the case of multiband semiconducting nanowires, the phase diagram of the system as a function of the chemical potential and magnetic field have been calculated. In two-band wire or two coupled single band wire, the phase of one band can be controlled through the other band, and these properties is critical to build multiband quantum device. When the SOI vector or magnetic field in semiconductor nanowire rapidly rotates by the angle $\pi $, changes its sign, a topological $\pi $ junction forms at the junction between two wire sections characterized by different directions of the SOI vectors or magnetic field. In this case, some fermionic bound states (FBS) can emerge inside the proximity gap, which localize at the topological $\pi $ junction, and coexist with Majorana bound states localized at the nanowire ends. Changing the position of the topological $\pi $ junction from one end to the other, the zero-energy FBS moves and can be used as mediator to transfer quantum information between two distance MFs. Meanwhile, the Andreev spectrum of the junction is qualitatively phase shift by $\pi $ compared to usual Majorana weak links. The FBS can act as quasiparticle traps and serve as an effective mediator of hybridization between two distant Majorana bound states (MBSs)., Comment: text overlap with arXiv:1408.3366, arXiv:1106.3078 by other authors

We analyse the topological transition and localization evolution of disordered two dimensional systems with non trivial topology based on bipartite lattices. Chern insulators with broken time reversal symmetry show non standard behavior for disorder realizations selectively distributed on only one of the sublattices. The Chern number survives to a much stronger disorder strength (one order of magnitude higher) than in the equally distributed disordered case and the final state in the strongly disordered case is metallic., Comment: Minor changes. Published version

The effect of a magnetic field on a two-dimensional Chern band insulator is discussed. It is shown that, unlike the trivial insulator, an anomalous Hall insulator with Chern number $C$ becomes a metal when a magnetic field is applied at constant particle density, for any $C>0$. For a time reversal invariant topological insulator with a spin Chern resolved number, $C_\uparrow= - C_\downarrow=C$, the magnetic field induces a spin polarized spin Hall insulator. We consider also the effect of a superlattice potential and extend previous results for the quantization of the Hall conductance of filled Hofstadter bands to this problem., Comment: 7 pages, 5 figures

We investigate the fate of interaction driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest and next nearest neighbour interactions. We find evidence for a charge density wave phase, a Kekul\'e bond order and a sublattice charge modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground state degeneracy and by calculating charge order and bond order correlation functions., Comment: 7 pages, 6 figures, updated references