arXiv subjects

Niels R. Walet

Publications and source records attributed to Niels R. Walet.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Theory Angular Momentum; Electronic version 2026

This is an electronic version of the open source book "Quantum Theory of Angular Momentum" by D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, original copyright \c{opyright} 1988 by World Scientific Publishing Co. Pte. Ltd, with the CC-BY 4.0 open source ebook funded by SCOAP. We have made appropriate modifications for the modern age--such as python-based symbolic manipulators to replace algebraic and numeric the tables. The new version contains a number of small modification, even though it is close to the original, with additional indices, hyperlinking, redrawing of figures. There has been a substantial check of the results presented, supported by the use of AI, even though all mistakes are the author's responsibility. All material is available from the book's github site (https://github.com/nwalet/Varshalovich/), where new updated versions will also be presented.

nucl-th↗

arXiv2026

Topological phases of a generalised tripartite Haldane model

We present a generalised tripartite Haldane model with a complex nearest neighbour hopping parameter. The total magnetic flux through the primitive unit cell, which consists of three hexagonal unit cells is zero, and thus the model has the structure of a loop-current model. We calculate topological phase diagrams of the Chern numbers as a function of the phases of the nearest and next-nearest neighbour hopping parameters for a fixed ratio of the magnitude of the hopping parameters. We show that, unlike the Haldane model, the topological phase diagram of this model is very complex, but some aspects can still be dealt with analytically. Furthermore, the Chern numbers of the topological phases are as large as $7$ in absolute value. The analysis is supported by explicit expressions for energy bands crossing at high symmetry points in the Brillouin zone, which show as linear phase boundaries in the phase diagram. We show that such lines explain many features in the topological phase diagrams. Finally, we analyse a few representative examples of the nature of level crossings away from high symmetry and their evolution with model parameters.

cond-mat.mes-hall↗

arXiv2026

Extended Coupled Cluster approach to Twisted Graphene Layers

A study of correlation effects in twisted bilayer graphene, using the extended coupled cluster method, is presented. This approach considers both self-consistent mean-field and beyond mean-field contributions, and can describe phase transitions in such strongly correlated systems, without further inputs or assumptions. Detailed expressions and a suitable implementation for the method are developed. Combining modern tensor contraction techniques with singular value decomposition, the correlation effects are successfully described in a qualitative manner, including contributions from the short-range and long-range parts of the Coulomb interaction. The superconducting gap is found to be maximal at a twist angle of $θ_c = 1.00 °$ with a roughly equal combination of s-wave and f-wave components. Using BCS theory, the size of the gap corresponds to a critical temperature value of $T_\text{c}^\text{BCS} = 0.5$K. This matches qualitatively with experimental data. Within the limitation of the numerical truncations used, a novel candidate for the mechanism behind superconductive phases in twisted bilayer graphene is proposed.

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arXiv2023

Calculation of Dynamical Response Functions Using a Bound-state Method

We investigate a method to extract response functions (dynamical polarisabilities) directly from a bound-state approach applied to calculations of perturbation-induced reactions. The use of a square-integrable basis leads to a response in the form of a sum of $δ$ functions. We integrate this over energy and fit a smooth function to the resulting stepwise-continuous one. Its derivative gives the final approximation to the physical response function. We show that the method reproduces analytical results where known, and analyse the details for a variety of models. We apply it to some simple models, using the Stochastic Variational Method as the numerical method. Although we find that this approach, and other numerical techniques, have some difficulties with the threshold behaviour in coupled-channel problems with multiple thresholds, its stochastic nature allows us to extract robust results even for such cases.

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arXiv2023

Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model

We analyze a special separable and chiral-symmetric model with a quantized quadrupole moment, extending the Benalcazar-Bernevig-Hughes model [Science 357, 61 (2017)]. Using nested-Wilson loop formalism, we give an exact expression for Wannier centers, sector polarizations, and quadrupole moments. These are connected to the winding numbers of the constitutive one-dimensional chains. We prove that these winding numbers can characterize the model's Wannier topology as a $\mathbb{Z}\times\mathbb{Z}$ set. These results clearly show that the quantization of the quadrupole moment can arise without additional spatial symmetry (except for translation symmetry) for the bulk. By switching from the Wannier representation to the Bloch representation, we derive an alternative expression for the bulk quadrupole moment and obtain its exact value. Combining the bulk quadrupole and edge polarizations, we analytically calculate the corner charge in a large square system and make the bulk-boundary correspondence explicit in an edge-consistent gauge. Our work reveals the relationship between zero-energy states at the boundary, charge localization, and the bulk quadrupole of the extended model.

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arXiv2022

Rotating Majorana Zero Modes in a disk geometry

We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor in order to understand their use as a building block for topological quantum computers. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied, and calculate their dynamical evolution when rotating the magnetic field, with special emphasis on non-adiabatic effects. We characterize the phase transition between high-frequency and near-adiabatic evolution using Floquet analysis. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states, which we have quantified numerically and analytically. These results show that controlling the rotation frequency can be a simple method to avoid the non-adiabatic errors originated from this coupling and thus increase the robustness of topological quantum computation.

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arXiv2021

Electrostatic interactions in twisted bilayer graphene

The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sublattice symmetry, or both.

cond-mat.mes-hall↗

arXiv2021

Narrow bands, electrostatic interactions and band topology in graphene stacks

The occurrence of superconducting and insulating phases is well-established in twisted graphene bilayers, and they have also been reported in other arrangements of graphene layers. We investigate three such arrangements: untwisted AB bilayer graphene on an hBN substrate, two graphene bilayers twisted with respect to each other, and a single ABC stacked graphene trilayer on an hBN substrate. Narrow bands with different topology occur in all cases, producing a high density of states which enhances the role of interactions. We investigate the effect of the long range Coulomb interaction, treated within the self consistent Hartree-Fock approximation. We find that the on-site part of the Fock potential strongly modifies the band structure at charge neutrality. The Hartree part does not significantly modify the shape and width of the bands in the three cases considered here, in contrast to the effect that such a potential has in twisted bilayer graphene.

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arXiv2020

Flat bands, strains, and charge distribution in twisted-bilayer hBN

We study the effect of twisting on bilayer graphene. The effect of lattice relaxation is included; we look at the electronic structure, piezo-electric charges and spontaneous polarisation. We show that the electronic structure without lattice relaxation shows a set of extremely flat in-gap states similar to Landau-levels, where the spacing scales with twist angle. With lattice relaxation we still have flat bands, but now the spectrum becomes independent of twist angle for sufficiently small angles. We describe in detail the nature of the bands, and study appropriate continuum models, at the same time explaining the spectrum We find that even though the spectra for both parallel an anti-parallel alignment are very similar, the spontaneous polarisation effects only occur for parallel alignment. We argue that this suggests a large interlayer hopping between boron and nitrogen.

cond-mat.mes-hall↗

arXiv2019

Tuneable terahertz oscillation arising from Bloch-point dynamics in chiral magnets

Skyrmionic textures are being extensively investigated due to the occurrence of novel topological magnetic phenomena and their promising applications in a new generation of spintronic devices that take advantage of the robust topological stability of their spin structures. The development of practical devices relies on a detailed understanding of how skyrmionic structures can be formed, transferred, detected and annihilated. In this work, our considerations go beyond static skyrmions and theoretically show that the formation/annihilation of both skyrmions and antiskyrmions is enabled by the transient creation and propagation of topological singularities (magnetic monopole-like Bloch points). Critically, during the winding/unwinding of skyrmionic textures, our results predict that the Bloch-point propagation will give rise to an emergent electric field in a terahertz frequency range and with substantial amplitude. We also demonstrate ways for controlling Bloch-point dynamics, which directly enable the tuneability on both frequency and amplitude of this signal. Our studies provide a concept of directly exploiting topological singularities for terahertz skyrmion-based electronic devices.

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arXiv2019

Twists and The Electronic Structure of Graphitic Materials

We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a fixed angle, two pieces of semi-infinite graphite rotated with respect to each other, and finally a single layer of graphene rotated with respect to a graphite surface. In all three cases we find a rich structure, with sharp resonances and flat bands for small twist angles. The method used can be easily generalized to more complex arrangements and stacking sequences.

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arXiv2019

Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach

The emergence of flat bands in twisted bilayer graphene leads to an enhancement of interaction effects, and thus to insulating and superconducting phases at low temperatures, even though the exact mechanism is still widely debated. The position and splitting of the flat bands is also very sensitive to the residual interactions. Moreover, the low energy bands of twisted graphene bilayers show a rich structure of singularities in the density of states, van Hove singularities, which can enhance further the role of interactions. We study the effect of the long-range interactions on the band structure and the van Hove singularities of the low energy bands of twisted graphene bilayers. Reasonable values of the long-range electrostatic interaction lead to a band dispersion with a significant dependence on the filling. The change of the shape and position of the bands with electronic filling implies that the van Hove singularities remain close to the Fermi energy for a broad range of fillings. This result can be described as an effective pinning of the Fermi energy at the singularity. The sensitivity of the band structure to screening by the environment may open new ways of manipulating the system.

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arXiv2019

Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action

The functional renormalization group for the effective action is used to construct an effective hydrodynamic description of weakly interacting Bose gases. We employ a scale-dependent parametrization of the boson fields developed previously to start the renormalization evolution in a Cartesian representation at high momenta and interpolate to an amplitude-phase one in the low-momentum regime. This technique is applied to Bose gases in one, two and three dimensions, where we study thermodynamic quantities such as the pressure and energy per particle. The interpolation leads to a very natural description of the Goldstone modes in the physical limit, and compares well to analytic and Monte-Carlo simulations at zero temperature. The results show that our method improves aspects of the description of low-dimensional systems, with stable results for the superfluid phase in two dimensions and even in one dimension.

cond-mat.quant-gas↗

arXiv2019

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

We generalize the continuum model for Moiré structures made from twisted graphene layers, in order to include lattice relaxation and the formation of channels at very small (marginal) twist angles. We show that a precise description of the electronic structure at such small angles can be achieved by i) calculating first the relaxed atomic structure, ii) projecting the interlayer electronic hopping parameters using a suitable basis of Bloch states, and iii) increasing the number of harmonics in the continuum approximation to interlayer hopping. The results show a complex structure of quasi one dimensional states when a finite bias is applied.

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arXiv2019

Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter

We analyze a description of twisted graphene bilayers, that incorporates deformation of the layers due to the nature modern interlayer potentials, and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrisation. We shall show that flat bands result in all cases, but that their nature can be rather different. We will show how to construct a more general reduction to a continuum model, and show that even though such a model can be constructed, its complexity increases, requiring more coupling parameters to be included, and the full in-layer dispersion to be taken into account. We conclude that the combination of all these effects will have a large impact on the wave functions of the flat bands, and that changes in the detail of the underlying models can lead to significant changes. A robust conclusion is that the natural strength of the interlayer couplings is higher than usually assumed, which causes additional Dirac points to appear for the standard magic angles. This gives rise to a degeneracy at the $Γ$ point. Since the appearance of a gap at the $Γ$ point is crucial for the construction of the Wannier states which are used in the standard descriptions of superconductivity, such an approach not be robust.

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arXiv2019

Lattice Deformation, Low Energy Models and Flat Bands in Twisted Graphene Bilayers

Twisted graphene bilayers show a complex electronic structure, further modified by interaction effects. The main features can be obtained from effective models, which make use a few phenomenological parameters. We analyze the influence of effects at the atomic scale, such as interlayer hopping and lattice relaxation, on the electronic bands. We assume that the twist angle and the size of the Moiré pattern is fixed, as it is usually the case in experiments. We obtain a strong dependence of the electronic structure on details of the models at the atomic scale. We discuss how to incorporate this dependence on effective models

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arXiv2018

Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers

Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in the regions of the Moiré pattern with $AA$ stacking. The resulting electrostatic potential gives rise to the dominant contribution to the electron-electron interaction within this low energy band, which becomes significantly distorted. The changes in the band structure are described by new local interactions, and lead to an assisted electron-hopping process. These couplings favor superconductivity at certain fillings.

cond-mat.mes-hall↗

arXiv2018

Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations

We study weakly interacting Bose gases using the functional renormalization group with a hydrodynamic effective action. We use a scale-dependent parametrization of the boson fields that interpolates between a Cartesian representation at high momenta and an amplitude-phase one for low momenta. We apply this to Bose gases in two and three dimensions near the superfluid phase transition where they can be described by statistical O(2) models. We are able to give consistent physical descriptions of the infrared regime in both two and three dimensions. In particular, and in contrast to previous studies using the functional renormalization group, we find a stable superfluid phase at finite temperatures in two dimensions. We compare our results for the superfluid and boson densities with Monte-Carlo simulations, and we find they are in reasonable agreement.

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