arXiv subjects

Julian Legendre

Publications and source records attributed to Julian Legendre.

8 recordsLinked to original sources

arXiv2025

Optimizing proximitized magnetic topological insulator nanoribbons for Majorana bound states

Heterostructures comprised of a magnetic topological insulator (MTI) placed in the proximity of an $s$-wave superconductor have emerged as a platform for the practical realization of Majorana bound states (MBSs). More specifically, it has been theoretically predicted that MBS can appear in proximitized MTI nanoribbons (PNRs) in the quantum anomalous Hall regime. As with all MBS platforms, disorder and device imperfections can be detrimental to the formation of robust and well-separated MBSs that are suitable for fusion and braiding experiments. Here, we identify the optimal conditions for obtaining a topological superconducting gap that is robust against disorder, with spatially separated stable MBSs in PNRs, and introduce a figure of merit that encompasses these conditions. Particular attention is given to the thin-film limit of magnetic topological insulators (MTIs), where the hybridization of the surface states cannot be neglected, and to the role of electron-hole asymmetry in the low-energy physics of the system. Based on our numerical results, we find that (1) MTI thin films that are normal (rather than quantum spin Hall) insulators for zero magnetization are favorable, (2) strong electron-hole asymmetry causes the stability and robustness of MBS to be very different for chemical potentials above or below the Dirac point, and (3) the magnetization strength should preferably be comparable to the hybridization or confinement energy of the surface states, whichever is largest.

cond-mat.mes-hall↗

arXiv2024

Topological properties of finite-size heterostructures of magnetic topological insulators and superconductors

Heterostructures of magnetic topological insulators (MTIs) and superconductors (SCs) in two-dimensional (2D) slab and one-dimensional (1D) nanoribbon geometries have been predicted to host, respectively, chiral Majorana edge states (CMESs) and Majorana bound states (MBSs). We study the topological properties of such MTI/SC heterostructures upon variation of the geometry from wide slabs to quasi-1D nanoribbon systems and as a function of the chemical potential, the magnetic doping, and the induced superconducting pairing potential. To do so, we construct effective symmetry-constrained low-energy Hamiltonians accounting for the real-space confinement. For a nanoribbon geometry with finite width and length, we observe different phases characterized by CMESs, MBSs, as well as coexisting CMESs and MBSs, as the chemical potential, the magnetic doping and/or the width are varied.

cond-mat.mes-hall↗

arXiv2024

Low-energy modeling of three-dimensional topological insulator nanostructures

We develop an accurate nanoelectronic modeling approach for realistic three-dimensional topological insulator nanostructures and investigate their low-energy surface-state spectrum. Starting from the commonly considered four-band $\boldsymbol{\mathrm{k\cdot p}}$ bulk model Hamiltonian for the Bi$_2$Se$_3$ family of topological insulators, we derive new parameter sets for Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$. We consider a fitting strategy applied to \emph{ab initio} band structures around the $Γ$ point that ensures a quantitatively accurate description of the low-energy bulk and surface states, while avoiding the appearance of unphysical low-energy states at higher momenta, something that is not guaranteed by the commonly considered perturbative approach. We analyze the effects that arise in the low-energy spectrum of topological surface states due to band anisotropy and electron-hole asymmetry, yielding Dirac surface states that naturally localize on different side facets. In the thin-film limit, when surface states hybridize through the bulk, we resort to a thin-film model and derive thickness-dependent model parameters from \emph{ab initio} calculations that show good agreement with experimentally resolved band structures, unlike the bulk model that neglects relevant many-body effects in this regime. Our versatile modeling approach offers a reliable starting point for accurate simulations of realistic topological material-based nanoelectronic devices.

cond-mat.mes-hall↗

arXiv2024

Spectroscopy and topological properties of a Haldane light system

We introduce a local spectroscopic method in real space to probe the topological properties of a circuit quantum electrodynamics (cQED) array generalizing previous approaches from one to two dimensions in the plane. As an application, we develop the theory of microwave light propagating in the local probe capacitively coupled to the cQED array associated to a bosonic Haldane model. Interestingly, we show that the measured reflection coefficient, resolved in frequency through the resonance, reveals the geometrical properties of the model and the topological phase transition. We discuss the role of physical parameters such as the lifetime of the light modes and stability towards local disorder related to further realizations.

cond-mat.mes-hall↗

arXiv2023

Conductance asymmetry in proximitized magnetic topological insulator junctions with Majorana modes

We theoretically discuss electronic transport via Majorana states in magnetic topological insulator-superconductor junctions with an asymmetric split of the applied bias voltage. We study normal-superconductor-normal (NSN) junctions made of narrow (wire-like) or wide (film-like) magnetic topological insulator slabs with a central proximitized superconducting sector. The occurrence of charge non-conserving Andreev processes entails a nonzero conductance related to an electric current flowing to ground from the proximitized sector of the NSN junction. We show that topologically-protected Majorana modes require an antisymmetry of this conductance with respect to the point of equally split bias voltage across the junction.

cond-mat.mes-hall↗

arXiv2022

Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling

We study the Hubbard model with time-reversal invariant flux and spin-orbit coupling and position-dependent onsite energies on the kagome lattice, using numerical and analytical methods. In particular, we perform calculations using real space dynamical mean-field theory (R-DMFT). To study the topological properties of the system, we use the topological Hamiltonian approach. We obtain a rich phase diagram: for weak and intermediate interactions, depending on the model parameters, the system is in the band insulator, topological insulator, or metallic phase, while for strong interactions the system is in the Mott insulator phase. We also investigate the magnetic phases that occur in this system. For this purpose, in addition to R-DMFT, we also use two analytical methods: perturbation theory for large interactions and onsite energies, and stochastic mean-field theory.

cond-mat.str-el↗

arXiv2021

Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry

We study the topological properties of a spin-orbit coupled Hofstadter model on the Kagome lattice. The model is time-reversal invariant and realizes a $\mathbb{Z}_2$ topological insulator as a result of artificial gauge fields. We develop topological arguments to describe this system showing three inequivalent sites in a unit cell and a flat band in its energy spectrum in addition to the topological dispersive energy bands. We show the stability of the topological phase towards spin-flip processes and different types of on-site potentials. In particular, we also address the situation where on-site energies may differ inside a unit cell. Moreover, a staggered potential on the lattice may realize topological phases for the half-filled situation. Another interesting result is the occurrence of a topological phase for large on-site energies. To describe topological properties of the system we use a numerical approach based on the twisted boundary conditions and we develop a mathematical approach, related to smooth fields.

cond-mat.str-el↗

arXiv2020

Magnetic Topological Kagome Systems

The recently discovered material Co$_3$Sn$_2$S$_2$ shows an impressive behavior of the quantum anomalous Hall (QAH) conductivity driven by the interplay between ferromagnetism in the $z$ direction and antiferromagnetism in the $xy$ plane. Motivated by these facts, first we build and study a spin-1/2 model to describe the magnetism of Co-atoms on the Kagome planes. Then, we include conduction electrons which are coupled to the spins-1/2 through a strong Hund's coupling. The spin-orbit coupling results in topological low-energy bands. For 2/3 on-site occupancy, we find a topological transition from a QAH ferromagnetic insulating phase with Chern number one to a quantum spin Hall (QSH) antiferromagnetic phase. The QAH phase is metallic when slightly changing the on-site occupancy. To account for temperature effects, we include fluctuations in the direction of the Hund's coupling. We show how the Hall conductivity can now smoothly evolve when spins develop a $120^o$ antiferromagnetism in the $xy$ plane and can synchronize with the ferromagnetic fraction.

cond-mat.str-el↗