arXiv subjects

Karyn Le Hur

Publications and source records attributed to Karyn Le Hur.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2022

Topological superconductivity on the honeycomb lattice: Effect of normal state topology

The search for topological superconductors is one of the most pressing and challenging questions in condensed matter and material research. Despite some early suggestions that doping a topological insulator might be a successful recipe to find topological superconductors, until today there is no general understanding of the relationship of the topology of the superconductor and the topology of its underlying normal state system. One of the major obstacles is the strong effect of the Fermi surface and its subsequent pairing tendencies within the Hubbard model framework, usually preventing a detailed comparison between different topological superconducting systems. Here we present an analysis of doped insulators - topological and trivial - where the dominant Fermi surface effects have been equalized. Our approach allows us to study and compare superconducting instabilities of different normal state systems and present rigorous results about the influence of the normal state system's topology.

cond-mat.supr-con↗

arXiv2021

Global and Local Topological Quantized Responses from Geometry, Light and Time

To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square ($C^2$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this $C^2$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the $\mathbb{Z}_2$ topological number robust to interactions can be measured locally from a correspondence between the pfaffian and light. We address a relation with a spin pump and the quantum spin Hall conductance. The analogy between light and magnetic nuclear resonance may be applied for imaging, among other applications.

cond-mat.mes-hall↗

arXiv2021

Localization Dynamics from Static and Mobile Impurities

We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a $\mathbb{U}(1)$ gauge field or a uniform magnetic field. Impurities are described through two-state systems which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a classical Ising symmetry for static and mobile impurities associated to the inversion symmetry of the two legs of the ladder. From the decoupled rungs limit, we also identify a local $\mathbb{Z}_2$ gauge theory for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we study the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a N\' eel state.

cond-mat.str-el↗

arXiv2021

Analytical approach for the Mott transition in the Kane-Mele-Hubbard model

The description of interactions in strongly-correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We find that the Mott transition of the Kane-Mele-Hubbard model may be described by the variational principle with one equation. We present different views of this equation from the electron Green's function, the free-energy and the Hellmann-Feynman theorem. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the $x-y$ plane. The interacting topological phase is described through a $\mathbb{Z}_2$ number related to helical edge modes. Our results then show that improving stochastic approaches can give further insight on the understanding of interacting phases of matter.

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↗

arXiv2021

Quantum Entangled Fractional Topology and Curvatures

We propose a two-spin quantum-mechanical model with applied magnetic fields acting on the Poincaré-Bloch sphere, to reveal a new class of topological energy bands with Chern number one half for each spin-1/2. The mechanism behind this fractional topology is a two-spin product state at the north pole and a maximally entangled state close to the south pole. The fractional Chern number of each spin can be measured through the magnetizations at the poles. We study a precise protocol where the spin dynamics in time reflects the Landau-Zener physics associated with energy band crossing effects. We show a correspondence between the two-spin system and topological bilayer models on a honeycomb lattice. These models describe semimetals with a nodal ring surrounding the region of entanglement.

cond-mat.mes-hall↗

arXiv2021

Quantum system dynamics with a weakly nonlinear Josephson junction bath

We investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.

quant-ph↗

arXiv2020

Interacting Stochastic Topology and Mott Transition from Light Response

We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field variational approach, supported by density matrix renormalization group results and Ginzburg-Landau arguments. From the Bloch sphere, we make predictions for circular dichroism of light related to the quantum Hall conductivity on the lattice and in the presence of interactions. This analysis shows that the topological number can be measured from the light response at the Dirac points. Electron-electron interactions can also produce a substantial number of particle-hole pairs above the band gap, which leads us to propose a "stochastic Chern number" as an interacting measure of the topology. The stochastic Chern number can describe disordered situations with a fluctuating staggered potential and we build an analogy between interaction-induced particle-hole pairs and temperature effects. Our stochastic approach is physically intuitive, easy to implement and leads the way to further studies of interaction effects.

cond-mat.str-el↗

arXiv2020

Phase-Coherent Dynamics of Quantum Devices With Local Interactions

This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aiming at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data, by showing clear interaction effects in the dynamics of mesoscopic capacitors.

cond-mat.mes-hall↗

arXiv2020

Kondo induced π-phase shift of microwave photons in a circuit quantum electrodynamics architecture

Mesoscopic systems constitute appealing platforms to study many-body physics with light and matter degrees of freedom. The Kondo effect refers to the screening of a spin-1/2 impurity by a cloud of conduction electrons, then forming a many-body Fermi liquid ground state. The Kondo resonance produces a phase shift in the transmitted electronic wave packet which depends on the symmetry and nature of the many-body ground state. Theoretical calculations suggest that the Kondo resonance can interact with the irradiation photon field and should give rise to a π-phase shift of the photon signal in the case where the ground state is a Fermi liquid. This π-phase shift of microwave photon is driven from the Korringa-Shiba relation of quantum impurity Fermi-liquid ground states. We report the first observation of such a π-phase shift in a graphene double quantum dot within a circuit quantum electrodynamics architecture where the microwave photons couple to the pseudo-spin or charge degrees of freedom. The observed Kondo temperature TK ~ 550 mK is in agreement with DC conductance measurements. All our results support the formation of a Kondo resonance located above the Fermi level of the electronic reservoirs and the occurrence of an SU(4) Fermi-liquid ground state. We finally study how the Kondo-photon interactions can be tuned by inter-dot electron tunnel coupling strengths. Our experimental achievements may contribute to a better understanding of many-body physics in hybrid circuit systems, and open up new applications in atomic thin materials from the light-matter interaction.

cond-mat.mes-hall↗

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↗

arXiv2020

Fluctuating Forces Induced by Non Equilibrium and Coherent Light Flow

Casimir physics covers a wealth of phenomena where forces between macroscopic objects are induced by long range fluctuations of either classical or quantum origin. Fluctuations of the quantum electrodynamic vacuum epitomize this type of physics, but such fluctuation induced forces arise in a wide range of systems. Here we present a surprisingly never anticipated example of fluctuation induced radiation forces, stemming from spatially long ranged mesoscopic coherent fluctuations of light propagating in random media. Quite remarkably, spatially coherent light fluctuations can be thoroughly described by a hydrodynamic Langevin approach, where a properly tailored noise accounts for mesoscopic coherent effects. The light flow depends on two parameters only, the diffusion coefficient $D$ and the mobility $σ$, otherwise related by a Einstein relation. The mapping we present between coherent light flow and out of equilibrium hydrodynamics is easily generalisable to a large class of quantum or classical wave problems. A clear asset of this type of approach is in its dependence upon two parameters only thus making it a candidate to efficient machine learning algorithms. Moreover, the strength of these coherent fluctuating forces depends on a single and easily tunable dimensionless conductance $g$ -- analog of electronic conductance -- which encapsulates both the geometry and the scattering properties of the random medium. Hence coherent multiple light scattering offers setups where fluctuation induced forces are significantly enhanced compared to other known situations. The scarcity of measurable non equilibrium phenomena makes the present proposal particularly relevant to experimental inspections and applications, e.g. a wide variety of sensors in soft condensed matter, biophysics and quantum technologies.

cond-mat.mes-hall↗

arXiv2020

From Topological Superconductivity to Quantum Hall States in Coupled Wires

We present a theoretical study of the interplay between topological p-wave superconductivity, orbital magnetic fields and quantum Hall phases in coupled wire systems. First, we calculate the phase diagram and physical observables of a fermionic ladder made of two coupled Kitaev chains, and discuss the presence of two and four Majorana zero modes. Second, we analyze hybrid systems consisting of a Kitaev chain coupled to a Luttinger liquid. By tuning the magnetic field and the carrier density, we identify quantum Hall and charge density wave phases, as well as regimes in which superconductivity is induced in the second chain by proximity effect. Finally, we consider two-dimensional systems made of weakly coupled ladders. There, we engineer a $p+ip$ superconductor and describe a generalization of the $ν=1/2$ fractional quantum Hall phase. These phases might be realized in solid-state or cold-atom nanowires.

cond-mat.str-el↗

arXiv2019

Valence bond fluctuations in the Kitaev spin model

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and their entanglement properties. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogues. We also show how these valence bond fluctuations can locate quantum phase transitions between the three gapped and the gapless Majorana semi-metal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the 111 direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions towards the three gapped phases. The linear scaling behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Neel magnetic state.

cond-mat.str-el↗

arXiv2019

Quench-induced dynamical phase transitions and $π$-synchronization in the Bose-Hubbard Model

We investigate the non-equilibrium behavior of a fully-connected (or all-to-all coupled) Bose-Hubbard model after a Mott to superfluid quench, in the limit of large boson densities and for an arbitrary number $V$ of lattice sites, with potential relevance in experiments ranging from cold atoms to superconducting qubits. By means of the truncated Wigner approximation, we predict that crossing a critical quench strength the system undergoes a dynamical phase transition between two regimes that are characterized at long times either by an inhomogeneous population of the lattice (i.e. macroscopical self-trapping) or by the tendency of the mean-field bosonic variables to split into two groups with phase difference $π$, that we refer to as $π$-synchronization. We show the latter process to be intimately connected to the presence, only for $V \ge 4$, of a manifold of infinitely many fixed points of the dynamical equations. Finally, we show that no fine-tuning of the model parameters is needed for the emergence of such $π$-synchronization, that is in fact found to vanish smoothly in presence of an increasing site-dependent disorder, in what we call a synchronization crossover.

cond-mat.mes-hall↗

arXiv2019

Topological proximity effects in a Haldane-graphene bilayer system

We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

cond-mat.mes-hall↗

arXiv2019

Real-Time Ramsey Interferometry in Fractional Quantum Hall States

We study the time-dependent dynamical phase of fractional quasiparticles in quantum Hall states using Ramsey interferometry. A Ramsey two-pulse voltage modulation generates an interference term in the current noise of a quantum point contact oscillating with the dynamical phase. We show that the interference pattern probes the Green's function of the fractional quasi-particles in the time domain and reveals the fractional charge. We address both the case of a point-like tunnel junction and the case of momentum-resolved tunneling which also provides information on the speed of those quasiparticles propagating along the edge. For the 5/2 fractional quantum Hall case, the Ramsey signal can differentiate between the Pfaffian and anti-Pfaffian states.

cond-mat.str-el↗