arXiv subjects

Karyn Le Hur

Publications and source records attributed to Karyn Le Hur.

At least 19 recordsLinked to original sources

arXiv2026

Free Majorana Fermions with Superconducting Quantum Wires and a Magnetic Impurity

Through the two-channel Kondo model, I address a magnetic spin-1/2 impurity interacting with a bound state of spin origin at the edge in a Luther-Emery liquid showing a spin gap in the bulk. The system presents two zero-energy Majorana fermions of magnetic origin, one on the impurity site and one at the edge. I derive the wavefunction at the edge for the produced zero-energy Majorana fermion bound state within the same formalism as topological interfaces. I present alternative versions of the quantum field theory revealing the specific pairing of the Majorana fermions in the bulk. I address local physical responses. I develop the idea that this model can be realized with a magnetic impurity bridging the gap between two s-wave superconducting wires. I show the protection of the zero-energy Majorana fermions that will be referred to as free Majorana fermions.

cond-mat.str-el↗

arXiv2026

Spin Response of a Magnetic Monopole and Quantum Hall Response in Topological Lattice Models through Local Invariants and Light

Here, we elaborate on and develop the geometrical approach introduced in K. Le Hur, Physics Reports 1104 1-42 (2025) between the magnetic monopole created from a radial field, quantum physics and topological lattice models through quantum phase transitions. We introduce an effective magnetic moment for a monopole when applying an additional source field along z-direction which also mediates the quantum phase transition. We present its relation with the transverse pumped quantum Hall current. The magnetic susceptibility can be introduced as a measure of the topological invariant i.e. it remains quantized within the topological phase until the transition. We show the relation with two-dimensional topological lattice models such as a honeycomb Haldane model in real space. We develop the theory and present a numerical analysis between local invariants in momentum space introduced from Dirac points, correlation functions and the responses to circularly polarized light. We develop the formalism for coupled-planes materials including the possibility of quantum spin Hall effect and address a relation between the Ramanujan infinite alternating series and an interface in real space with a topological number one-half.

cond-mat.mes-hall↗

arXiv2026

Geometrical approach and topological electron density in the $p_x + ip_y$ superconductor

We present an analysis on the geometrical and physical nature of the $p_x + ip_y$ superconductor on the square lattice, with an emphasis on the topological phase transition at half-filling. We develop a local topological marker from specific Dirac points within the Brillouin zone, which is introduced via the addition of two one-dimensional (1D) $\mathbb{Z}$ $(\mathbb{Z}_2$) invariants defined on the Bloch sphere. We relate this topological marker to the electron spectral function integrated on frequency through the local momentum-resolved electron density, which may be measured via Angle Resolved Photoemission Spectroscopy (ARPES), and show that it remains well-protected including temperature effects. Integrating on a small area around a specific point in momentum space associated to the measure uncertainty, this also reveals the Van Hove logarithmic profile of the density of states in the derivative of the local marker while preserving the topological information. Topological transitions correspond to a protected semi-metal. We analyse the real space representation of this topological marker from correlation functions. We present physical responses such as the topological superfluid density.

cond-mat.str-el↗

arXiv2026

Theory of local orbital magnetization: local Berry curvature

We develop a thermodynamic theory of local orbital magnetization based on a perturbative expansion of the magnetic-field-dependent local density of states. Applicable to periodic crystals, finite systems with open boundaries, and ribbons alike, the formalism resolves orbital magnetic textures at the sublattice scale. It further reveals a previously unidentified local Berry curvature that captures the magnetic-field-induced redistribution of electronic weight in real space. We establish the consistency of the theory across geometries, identify orbital ferro-, antiferro-, and ferrimagnetic phases in both topological and trivial insulators, and demonstrate that the local Berry curvature provides a bulk description of topology in finite systems.

cond-mat.mes-hall↗

arXiv2026

Spin qubit gates via phonon buses in electron nanowires

Scalable architectures for quantum computing using semiconductor quantum dots require interactions between qubits beyond adjacent quantum dots. Here, we propose using nanowires of electrons to mediate the interaction between two quantum dots. Virtual phonons in the linear chain of electrons can mediate an interaction that gives rise to effective spin-spin coupling of the electrons in distant quantum dots. We find coupling strengths of more than 30 MHz for experimentally realisable parameters in GaAs quantum dots.

cond-mat.mes-hall↗

arXiv2026

Bipartite Fluctuations and Charge Fractionalization in Quantum Wires

We introduce a quantum information method for measuring fractional charges in ballistic quantum wires generalizing bipartite fluctuations to the chiral quasiparticles in Luttinger liquids, i.e. analyzing and summing charge and current fluctuations in a region of the wire. Bipartite fluctuations at equilibrium are characterized through a logarithmic scaling with distance encoding the entangled nature of these fractional charges in one-dimensional (1D) fluids. This approach clarifies the physical meaning of the dephasing factor of electronic interferences in a ballistic ring geometry at zero temperature, as a result of charge fractionalization. We formulate an analogy towards ground-state energetics. We show how bipartite current fluctuations represent a useful tool to locate quantum phase transitions associated to Mott physics. We address a spin chain equivalence and verify the fractional charges through an algorithm such as Density Matrix Renormalization Group (DMRG). Adding a potential difference between the two sides (parties) of the wire, bipartite fluctuations can detect a bound state localized at the interface through the Jackiw-Rebbi model coexisting with fractional charges.

cond-mat.mes-hall↗

arXiv2025

Topological Signatures of Magnetic Phase Transitions with Majorana Fermions through Local Observables and Quantum Information

The one-dimensional (1D) $J_1-J_2$ quantum spin model can be viewed as a strong-coupling analogue of the Schrieffer-Su-Heeger model with two inequivalent alternating Ising couplings along the wire, associated to the physics of resonating valence bonds. Similar to the quantum Ising model, which differently presents a long-range N\' eel ordered phase, this model also maps onto a p-wave superconducting wire which shows a topological phase transition with the emergence of low-energy Majorana fermions. We show how signatures of the topological phase transition for the p-wave superconducting wire, i.e. a half Skyrmion, are revealed through local (short-range) spin observables and their derivatives related to the capacitance of the pairing fermion model. Then, we present an edge correspondence through the edge spin susceptibility in the $J_1-J_2$ model revealing that the topological phase transition is a metal of Majorana fermions. We justify that the spin magnetization at an edge at very small transverse magnetic field is a good marker of the topological invariant and of Majorana zero modes. We identify a correspondence between the quantum information of resonating valence bonds and the charge fluctuations in a p-wave superconductor through our method "the bipartite fluctuations". Physical properties of this 1D model are in fact robust when including additional interactions, which is optimistic for practical applications e.g. in quantum circuits.

cond-mat.str-el↗

arXiv2025

A Model for Topological p-wave Superconducting Wires with Disorder and Interactions

We present a comprehensive theoretical study of interacting and disordered topological phases of coupled Kitaev wires, which may support further realistic applications of Majorana fermions. We develop a variety of analytical, mathematical and numerical methods for one and two-coupled wires, associated with a topological marker accessible from real-space correlation functions on the wire(s). We verify the stability of the topological superconducting phase and quantify disorder effects close to the quantum phase transitions, e.g. through two-point correlation functions or using a renormalization group (RG) analysis of disorder. We show for the first time that the double critical Ising (DCI) phase -- a fractional Majorana liquid characterized by a pair of half central charges and topological numbers -- is stabilized by strong interactions against disorder which respects the inversion symmetry between the wires (ie. parity conservation on each wire). In the presence of an inter-wire hopping term, the DCI phase turns into a protected topological phase with a bulk gap. We study the localization physics developing along the critical line for weaker interactions.

cond-mat.supr-con↗

arXiv2025

Topological Quantum Spin Hall Semimetals with Light

We introduce a quantum spin Hall semimetal or Fermi liquid characterized with a Z2 topological invariant, measurable through circularly polarized light. We propose its engineering through two topological metallic band structures in crystals on the honeycomb lattice, with spin-orbit interaction, realizable through the interplay of a charge or spin density wave substrate and Zeeman effects, in between a quantum spin Hall and a quantum anomalous Hall insulator. These systems show topologically protected helical edge or photo-induced currents.

cond-mat.mes-hall↗

arXiv2024

Quantum Hall and Light Responses in a 2D Topological Semimetal

We have recently identified a protected topological semimetal in graphene which presents a zero-energy edge mode robust to disorder and interactions. Here, we address the characteristics of this semimetal and show that the $\mathbb{Z}$ topological invariant of the Hall conductivity associated to the lowest energy band can be equivalently measured from the resonant response to circularly polarized light resolved at the Dirac points. The (non-quantized) conductivity responses of the intermediate energy bands, including the Fermi surface, also give rise to a $\mathbb{Z}_2$ invariant. We emphasize on the bulk-edge correspondence as a protected topological half metal, i.e. one spin-population polarized in the plane is in the insulating phase related to the robust edge mode while the other is in the metallic regime. The quantized transport at the edges is equivalent to a $\frac{1}{2}-\frac{1}{2}$ conductance for spin polarizations along $z$ direction. We also build a parallel between the topological Hall response and a pair of half numbers (half Skyrmions) through the light response locally resolved in momentum space and on the sphere.

cond-mat.mes-hall↗

arXiv2024

Topological signatures of a p-wave superconducting wire through light

We show how the $\mathbb{Z}_{2}$ topological index of a one-dimensional topological p-wave superconductor can be revealed when driving with a classical vector potential i.e. an electromagnetic wave, through the light-induced transition probabilities and the profile of the induced quasiparticles population. As a function of driving frequency $ω$, it is possible to obtain a measure of this topological invariant from the resonance envelope classifying the two distinct topological phases of the short-range Kitaev wire. We propose to probe the topological phase transition in the model through the responses of the global capacitance in the presence of the light field and through the Josephson current between the wire and the proximity coupled bulk superconductor. The system may also be implemented on the Bloch sphere allowing alternative ways to measure the $\mathbb{Z}$ and $\mathbb{Z}_2$ topological invariants through circuit or cavity quantum electrodynamics.

cond-mat.supr-con↗

arXiv2024

Majorana fermions and quantum information with fractional topology and disorder

The quest to identify and observe Majorana fermions in physics and condensed-matter systems remains an important challenge. Here, we introduce a qubit (spin-$1/2$) from the occurrence of two delocalized zero-energy Majorana fermions in a model of two spins-$1/2$ on the Bloch sphere within the fractional one-half topological state. We address specific protocols in time with circularly polarized light and the protection of this delocalized spin-$1/2$ state related to quantum information protocols. We also show how disorder can play a positive and important role allowing singlet-triplet transitions and resulting in an additional elongated region for the fractional phase, demonstrating the potential of this platform related to applications in topologically protected quantum information. We generalize our approach with an array and Majorana fermions at the edges in a ring geometry.

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↗

arXiv2024

One-Half Topological Number in Entangled Quantum Physics

A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing an hedgehog structure as a result of a radial magnetic field. We elaborate on a relation between the formation of an entangled wavefunction at one pole, in a two-spins model, and an interesting pair of one-half topological numbers. Similar to Cooper pairs in superconductors, the Einstein-Podolsky-Rosen pair or Bell state produces a half flux quantization, which here refers to the halved flux of the Berry curvature on the surface. These 1/2-numbers also reveal the presence of a free Majorana fermion at a pole. The topological responses can be measured when driving from north to south and also from a circularly polarized field at the poles revealing the quantized or half-quantized nature of the protected transverse currents. We show applications of entangled wavefunctions in band structures, introducing a local topological marker in momentum space, to characterize the topological response of two-dimensional semimetals in bilayer geometries.

cond-mat.mes-hall↗

arXiv2023

Topological Matter and Fractional Entangled Quantum Geometry through Light

Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2 particle acquires an integer topological charge in the presence of a radial magnetic field. We show that global topological properties are encoded from the poles of the surface allowing a correspondence between smooth fields, metric and quantum distance with the square of the topological number. The information is transported from each pole to the equatorial plane on a thin Dirac string. We develop the theory, "quantum topometry" in space and time, and present applications on transport from a Newtonian approach, on a quantized photo-electric effect from circular dichroism of light towards topological band structures of crystals. Edge modes related to topological lattice models are resolved analytically when deforming the sphere or ellipse onto a cylinder. Topological properties of the quantum Hall effect, quantum anomalous Hall effect and quantum spin Hall effect on the honeycomb lattice can be measured locally in the Brillouin zone from light-matter coupling. The formalism allows us to include interaction effects from the momentum space. Interactions may also result in fractional entangled geometry within the curved space. We develop a relation between entangled wavefunction in quantum mechanics, coherent superposition of geometries, a way to one-half topological numbers and Majorana fermions. We show realizations in topological matter. We present a link between axion electrodynamics, topological insulators on a surface of a cube and the two-spheres' model via merons.

cond-mat.mes-hall↗

arXiv2023

Fractional Topology in Interacting 1D Superconductors

We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and propose topological markers directly measurable from ground state correlation functions. These quantities remain powerful tools in the presence of couplings and interactions. We show with the density matrix renormalization group that the double critical Ising (DCI) phase discovered in [1] is a fractional topological phase with gapless Majorana modes in the bulk, and a one-half topological invariant per wire. Using both numerics and quantum field theoretical methods, we show that the phase diagram remains stable in the presence of an inter-wire hopping amplitude $t_{\bot}$ at length scales below $\sim 1/t_{\bot}$. A large inter-wire hopping amplitude results in the emergence of two integer topological phases, stable also at large interactions. They host one edge mode per boundary shared between both wires. At large interactions, the two wires are described by Mott physics, with the $t_{\bot}$ hopping amplitude resulting in a paramagnetic order.

cond-mat.str-el↗

arXiv2022

A topologically protected quantum dynamo effect in a driven spin-boson model

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of Faraday's law of induction, justifying the term 'quantum dynamo effect'. For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, the effect thus corresponds to a work-to-work conversion and allows to interpret this transmitted energy into the bath as work. We study this effect, its performance and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.

quant-ph↗

arXiv2022

Protected Topological Nodal Ring Semimetal in Graphene

Graphene is a two-dimensional Dirac semimetal showing interesting properties as a result of its dispersion relation with both quasiparticles and quasiholes or matter and anti-matter. We introduce a topological nodal ring semimetal in graphene with a quantized quantum Hall response, a robust one-dimensional chiral edge mode and a quadratic Fermi-liquid spectrum for the quasiparticles and quasiholes in the bulk. The bulk band degeneracy at the Fermi energy is protected through a Z2 symmetry related to the two spin polarizations of an electron and a double-orthogonality structure in the sublattice and spin quantum numbers of the two crossing eigenstates. The system may have applications in nano-electronics and in quantum mechanical entanglement applied to band theory.

cond-mat.mes-hall↗