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Doping carriers into a correlated quantum ground state offers a promising route to generate new quantum states. The recent advent of moir\'{e} superlattices provided a versatile platform with great tunability to explore doping physics in systems with strong interplay between strong correlation and nontrivial topology. Here we study the effect of electron doping in the quantum anomalous Hall insulator realized in TMD moir\'{e} superlatice at filling $\nu=1$, which can be described by the canonical Kane-Mele-Hubbard model. By solving the Kane-Mele-Hubbard model using an unrestricted real-space Hartree-Fock method, we find that doping generates quantum anomalous Hall crystals (QAHC) and topological domain walls. In the QAHC, the doping induces skyrmion spin textures, which hosts one or two electrons in each skyrmion as in-gap states. The skyrmions crystallize into a lattice, with the lattice parameter being tunable by the density of doped electrons. Remarkably, we find that the QAHC can survive even in the limit of vanishing Kane-Mele topological gap for a significant range of fillings. Furthermore, doping can also induce domain walls separating topologically distinct domains with different electron densities, hosting chiral localized modes.

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.

The surgical removal of head and neck tumors requires safe margins, which are usually confirmed intraoperatively by means of frozen sections. This method is, in itself, an oversampling procedure, which has a relatively low sensitivity compared to the definitive tissue analysis on paraffin-embedded sections. Confocal laser endomicroscopy (CLE) is an in-vivo imaging technique that has shown its potential in the live optical biopsy of tissue. An automated analysis of this notoriously difficult to interpret modality would help surgeons. However, the images of CLE show a wide variability of patterns, caused both by individual factors but also, and most strongly, by the anatomical structures of the imaged tissue, making it a challenging pattern recognition task. In this work, we evaluate four popular few shot learning (FSL) methods towards their capability of generalizing to unseen anatomical domains in CLE images. We evaluate this on images of sinunasal tumors (SNT) from five patients and on images of the vocal folds (VF) from 11 patients using a cross-validation scheme. The best respective approach reached a median accuracy of 79.6% on the rather homogeneous VF dataset, but only of 61.6% for the highly diverse SNT dataset. Our results indicate that FSL on CLE images is viable, but strongly affected by the number of patients, as well as the diversity of anatomical patterns., Comment: 6 pages

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 scaling of the entanglement entropy in different classes of one-dimensional fermionic quasiperiodic systems with and without pairing, focusing on multifractal critical points/phases. We find that the entanglement entropy scales logarithmically with the subsystem size $N_{A}$ with a proportionality coefficient $\mathcal{C}$, as in homogeneous critical points, apart from possible additional small oscillations. In the absence of pairing, we find that the entanglement entropy coefficient $\mathcal{C}$ is non-universal and depends significantly and non-trivially both on the model parameters and electron filling, in multifractal critical points. In some of these points, $\mathcal{C}$ can take values close to the homogeneous (or ballistic) system, although it typically takes smaller values. We find a close relation between the behaviour of the entanglement entropy and the small-$q$ (long-wavelength) dependence of the momentum structure factor $\mathcal{S}(q)$. $\mathcal{S}(q)$ increases linearly with q as in the homogeneous case, with a slope that grows with $\mathcal{C}$. In the presence of pairing, we find that even the addition of small anomalous terms affects very significantly the scaling of the entanglement entropy compared to the unpaired case. In particular, we focused on topological phase transitions for which the gap closes with either extended or critical multifractal states. In the former case, the scaling of the entanglement entropy mirrors the behaviour observed at the critical points of the homogeneous Kitaev chain, while in the latter, it shows only slight deviations arising at small length scales. In contrast with the unpaired case, we always observe $\mathcal{C}\approx1/6$ for different critical points, the known value for the homogeneous Kitaev chain with periodic boundary conditions.

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

Quasiperiodic systems in one dimension can host non-ergodic states, e.g. localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e. spatially localized or ballistic. However, periodic quenches across these two non-ergodic phases were thought to produce ergodic diffusive-like states even for non-interacting particles. We show that this expectation is not met at the thermodynamic limit where the system always attains a non-ergodic state. We find that ergodicity may be recovered by scaling the Floquet quenching period with system size and determine the corresponding scaling function. Our results suggest that while the fraction of spatially localized or ballistic states depends on the model's details, all Floquet eigenstates belong to one of these non-ergodic categories. Our findings demonstrate that quasiperiodicity hinders ergodicity and thermalization, even in driven systems where these phenomena are commonly expected.

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

In this paper we explore the effects of quasiperiodicity in paradigmatic models of Chern insulators. We identify a plethora of topological phase transitions and characterize them based on spectral and localization properties. Contrary to uncorrelated disorder, gap closing and reopening topological transitions can be induced by quasiperiodicity. These can separate widely different phases, including (i) trivial and Chern insulators, both with ballistic states near the gap edges; (ii) Chern insulators with critical states around the gap edges or (iii) Chern and trivial insulators respectively with ballistic and localized gap-edge states. Transition (i) is similar to clean-limit topological transitions due to the ballistic character of the gap-edge states, but at the same time resembles (quasi)disorder driven topological Anderson insulator phenomena. On the other hand, transitions (ii) and (iii) have no clean-limit counterpart. Additionally, quasiperiodicity can also induce topological transitions into a trivial state for which the gap closes and does not reopen, a scenario that resembles more what is observed with uncorrelated disorder. However, we found that such transitions can also be non-conventional in that they can be accompanied by the emergence of intermediate metallic and critical phases where the Chern number is not quantized. Our results show that a rich variety of topological phase transitions, not previously realized experimentally nor predicted theoretically can be attained when applying quasiperiodic modulations to simple Chern insulators. Such models have previously been realized experimentally in widely different platforms, including in optical lattices and photonic or acoustic media, where quasiperiodicity effects can be incorporated. The unveiled topological phase transitions can in principle be observed experimentally with state-of-the-art techniques., Comment: Preliminary work 10 pages, 7 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.

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 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 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.

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.

Squamous Cell Carcinoma (SCC) is the most common cancer type of the epithelium and is often detected at a late stage. Besides invasive diagnosis of SCC by means of biopsy and histo-pathologic assessment, Confocal Laser Endomicroscopy (CLE) has emerged as noninvasive method that was successfully used to diagnose SCC in vivo. For interpretation of CLE images, however, extensive training is required, which limits its applicability and use in clinical practice of the method. To aid diagnosis of SCC in a broader scope, automatic detection methods have been proposed. This work compares two methods with regard to their applicability in a transfer learning sense, i.e. training on one tissue type (from one clinical team) and applying the learnt classification system to another entity (different anatomy, different clinical team). Besides a previously proposed, patch-based method based on convolutional neural networks, a novel classification method on image level (based on a pre-trained Inception V.3 network with dedicated preprocessing and interpretation of class activation maps) is proposed and evaluated. The newly presented approach improves recognition performance, yielding accuracies of 91.63% on the first data set (oral cavity) and 92.63% on a joint data set. The generalization from oral cavity to the second data set (vocal folds) lead to similar area-under-the-ROC curve values than a direct training on the vocal folds data set, indicating good generalization., Comment: Erratum for version 1, correcting the number of CLE image sequences used in one data set

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 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

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

Deep learning technologies such as convolutional neural networks (CNN) provide powerful methods for image recognition and have recently been employed in the field of automated carcinoma detection in confocal laser endomicroscopy (CLE) images. CLE is a (sub-)surface microscopic imaging technique that reaches magnifications of up to 1000x and is thus suitable for in vivo structural tissue analysis. In this work, we aim to evaluate the prospects of a priorly developed deep learning-based algorithm targeted at the identification of oral squamous cell carcinoma with regard to its generalization to further anatomic locations of squamous cell carcinomas in the area of head and neck. We applied the algorithm on images acquired from the vocal fold area of five patients with histologically verified squamous cell carcinoma and presumably healthy control images of the clinically normal contra-lateral vocal cord. We find that the network trained on the oral cavity data reaches an accuracy of 89.45% and an area-under-the-curve (AUC) value of 0.955, when applied on the vocal cords data. Compared to the state of the art, we achieve very similar results, yet with an algorithm that was trained on a completely disjunct data set. Concatenating both data sets yielded further improvements in cross-validation with an accuracy of 90.81% and AUC of 0.970. In this study, for the first time to our knowledge, a deep learning mechanism for the identification of oral carcinomas using CLE Images could be applied to other disciplines in the area of head and neck. This study shows the prospect of the algorithmic approach to generalize well on other malignant entities of the head and neck, regardless of the anatomical location and furthermore in an examiner-independent manner., Comment: Erratum: In the previous version, the number of CLE sequences in the vocal folds data set was inadequately reported