arXiv subjects

Tobias Wolf

Publications and source records attributed to Tobias Wolf.

9 recordsLinked to original sources

arXiv2026

Coexisting Charge Density Wave and Superconducting Order in Quantizing Magnetic Fields

Charge density wave (CDW) and superconductivity are both common in strongly interacting electron systems. While CDW order is ubiquitous in both quantum Hall systems and unconventional superconductors, superconductivity is generally suppressed by the strong magnetic fields required for Landau quantization. Here we investigate the intertwined CDW and superconducting phases of rhombohedral hexalayer graphene (R6G) in a large displacement field, which generates tunable flat band edges, and a strong magnetic field, which generates a manifold of nearly degenerate Landau levels. We find a series of integer quantum Hall effects with Hall conductance quantum numbers that deviate from nearby integer filling factors, an observation that can be explained only by CDW order that mixes many Landau levels. We also find a nearby superconducting phase stabilized by perpendicular magnetic fields and persists deep within the quantum Hall regime. This intertwinement provides new insight into superconductivity in R6G at zero magnetic field.

cond-mat.mes-hall↗

arXiv2026

Physics Matters in PnP: Recovery Guarantees with the MMSE and NN Denoisers

We investigate the forward-backward-splitting version of the Plug and Play (PnP) method for linear ill-posed problems with MMSE estimators as denoisers. In contrast to existing literature, we consider estimators which are specialized for (degenerate) Gaussian noise with possibly non-diagonal covariance matrices. We further deviate from the classical iteration by replacing parts of the descent step with a linear operator that relates the observation noise to that of the MMSE estimator. Under mild assumptions, we derive several properties of the denoiser and prove recovery guarantees of the iteration both pointwise and in the Wasserstein distance of the underlying probability distributions. Crucially, our analysis shows that the denoiser cannot be chosen in a physics-agnostic way, that is, independently of the forward model. We extend our results to the case where the MMSE denoiser is parametrized by a neural network and derive the corresponding recovery bounds.

math.OC↗

arXiv2025

Applications of multiscale hierarchical decomposition to blind deconvolution

The blind image deconvolution is a challenging, highly ill-posed nonlinear inverse problem. We introduce a Multiscale Hierarchical Decomposition Method (MHDM) that is iteratively solving variational problems with adaptive data and regularization parameters, towards obtaining finer and finer details of the unknown kernel and image. We establish convergence of the residual in the noise-free data case, and then in the noisy data case when the algorithm is stopped early by means of a discrepancy principle. Fractional Sobolev norms are employed as regularizers for both kernel and image, with the advantage of computing the minimizers explicitly in a pointwise manner. In order to break the notorious symmetry occurring during each minimization step, we enforce a positivity constraint on the Fourier transform of the kernels. Numerical comparisons with a single-step variational method and a non-blind MHDM show that our approach produces comparable results, while less laborious parameter tuning is necessary at the price of more computations. Additionally, the scale decomposition of both reconstructed kernel and image provides a meaningful interpretation of the involved iteration steps.

math.NA↗

arXiv2025

Nested Bregman Iterations for Decomposition Problems

We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a variational approach with an infimal convolution of appropriate functions as a regularizer. Especially for noise corrupted observations, incorporating these functionals into the classical method of Bregman iterations provides a robust method for obtaining an overall good approximation of the true image, by stopping early the iteration according to a discrepancy principle. However, crucially, the quality of the separate components depends further on the proper choice of the regularization weights associated to the infimally convoluted functionals. Here, we propose the method of Nested Bregman iterations to improve a decomposition in a structured way. This allows to transform the task of choosing the weights into the problem of stopping the iteration according to a meaningful criterion based on normalized cross-correlation. We discuss the well-definedness and the convergence behavior of the proposed method, and illustrate its strength numerically with various image decomposition tasks employing infimal convolution functionals.

math.NA↗

arXiv2024

Magnetism in the Dilute Electron Gas of Rhombohedral Multilayer Graphene

Lightly-doped rhombohedral multilayer graphene has recently emerged as one of the most promising material platforms for exploring electronic phases driven by strong Coulomb interactions and non-trivial band topology. This review highlights recent advancements in experimental techniques that deepen our understanding of the electronic properties of these systems, especially through the application of weak-field magnetic oscillations for studying phase transitions and Fermiology. Theoretically, we advocate modeling these systems using an electron gas framework, influenced primarily by two major energy scales: the long-range Coulomb potential and band energy. The interplay between these energies drives transitions between paramagnetic and ferromagnetic states, while smaller energy scales like spin-orbit coupling and sublattice-valley-dependent interactions at the atomic lattice scale shape the (magnetic anisotropic energy) differences between distinct symmetry-broken states. We provide first-principles estimates of lattice-scale coupling constants for Bernal bilayer graphene under strong displacement field, identifying the on-site inter-valley scattering repulsion, with a strength of $g_{\perp \perp}=269\text{meV nm}^2$ as the most significant short-range interaction. The mean-field phase diagram is analyzed and compared with experimental phase diagrams. New results on spin and valley paramagnons are presented, highlighting enhanced paramagnetic susceptibility at finite wavevectors and predicting valley and spin density-wave instabilities. The interplay between superconductivity and magnetism, particularly under the influence of spin-orbit coupling, is critically assessed. The review concludes with a summary of key findings and potential directions for future research.

cond-mat.str-el↗

arXiv2023

Multiscale hierarchical decomposition methods for ill-posed problems

The Multiscale Hierarchical Decomposition Method (MHDM) was introduced as an iterative method for total variation regularization, with the aim of recovering details at various scales from images corrupted by additive or multiplicative noise. Given its success beyond image restoration, we extend the MHDM iterates in order to solve larger classes of linear ill-posed problems in Banach spaces. Thus, we define the MHDM for more general convex or even non-convex penalties, and provide convergence results for the data fidelity term. We also propose a flexible version of the method using adaptive convex functionals for regularization, and show an interesting multiscale decomposition of the data. This decomposition result is highlighted for the Bregman iteration method that can be expressed as an adaptive MHDM. Furthermore, we state necessary and sufficient conditions when the MHDM iteration agrees with the variational Tikhonov regularization, which is the case, for instance, for one-dimensional total variation denoising. Finally, we investigate several particular instances and perform numerical experiments that point out the robust behavior of the MHDM.

math.NA↗

arXiv2023

Partial condensation of mobile excitons in graphene multilayers

At a large displacement field, in rhomboedral and Bernal-stacked graphene a normal paramagnetic state transitions to a correlated state. Recent experiments showed that such systems have several phase transitions as a function of the carrier density. The phase adjacent to a paramagnetic state has anomalously high resistance and reduced degeneracy of the Fermi sea. We show that both phenomena can be explained through a concept of partial intervalley exciton condensation: a fraction of particles condenses into excitons, and another forms an intervalley coherent Fermi liquid. The exciton part of the system do not contribute to the electrical current thus increasing the resistance. Within this paradigm, the increase in the resistance has entirely geometrical origin. We check validity of the phenomenological theory through numerical calculations. We also show that the quantum oscillation data should not be very different between the partial excitonic state and the intervalley coherent states suggested by other authors. Further, we suggest STM/AFM or Raman spectroscopy to have a conclusive evidence for the occurrence of the partial exciton condensation that we suggest in this paper.

cond-mat.mes-hall↗

arXiv2023

Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene

We employ a functional renormalization group approach to ascertain the pairing mechanism and symmetry of the superconducting phase observed in rhombohedral trilayer graphene. Superconductivity in this system occurs in a regime of carrier density and displacement field with a weakly distorted annular Fermi sea. We find that repulsive Coulomb interactions can induce electron pairing on the Fermi surface by taking advantage of momentum-space structure associated with the finite width of the Fermi sea annulus. The degeneracy between spin-singlet and spin-triplet pairing is lifted by valley-exchange interactions that strengthen under the RG flow and develop nontrivial momentum-space structure. We find that the leading pairing instability is $d$-wave-like and spin-singlet, and that the theoretical phase diagram versus carrier density and displacement field agrees qualitatively with experiment.

cond-mat.supr-con↗

arXiv2022

Spin and Orbital Metallic Magnetism in Rhombohedral Trilayer Graphene

We provide a complete theoretical interpretation of the metallic broken spin/valley symmetry states recently discovered in ABC trilayer graphene (ABC) perturbed by a large transverse displacement field. Our conclusions combine insights from ABC trilayer graphene electronic structure models and mean field theory, and are guided by precise magneto-oscillation Fermi-surface-area measurements. We conclude that the physics of ABC trilayer graphene is shaped by the principle of momentum-space condensation, which favors Fermi surface reconstructions enabled by broken spin/valley flavor symmetries when the single-particle bands imply thin annular Fermi seas. We find one large outer Fermi surface enclosed majority-flavor states and one or more small inner hole-like Fermi surfaces enclosed minority-flavor states that are primarily responsible for nematic order. The smaller surfaces can rotate along a ring of van-Hove singularities or reconstruct into multiple Fermi surfaces with little cost in energy. We propose that the latter property is responsible for the quantum oscillation frequency fractionalization seen experimentally in some regions of the carrier-density/displacement-field phase diagram.

cond-mat.mes-hall↗