arXiv subjects

Cécile Repellin

Publications and source records attributed to Cécile Repellin.

17 recordsLinked to original sources

arXiv2024

Absence of gapless Majorana edge modes in few-leg bosonic flux ladders

The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor $ν=1$, similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive DMRG simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems.

cond-mat.quant-gas↗

arXiv2023

Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit

We explore the quasi one-dimensional (thin torus, or TT) limit of fractional Chern insulators (FCIs) as a starting point for their adiabatic preparation in quantum simulators. Our approach is based on tuning the hopping amplitude in one direction as an experimentally amenable knob to dynamically change the effective aspect ratio of the system. Similar to the TT limit of fractional quantum Hall (FQH) systems in the continuum, we find that the hopping-induced TT limit adiabatically connects the FCI state to a trivial charge density wave (CDW) ground state. This adiabatic path may be harnessed for state preparation schemes relying on the initialization of a CDW state followed by the adiabatic decrease of a hopping anisotropy. Our findings are based on the calculation of the excitation gap in a number of FCI models, both on a lattice and consisting of coupled wires. By analytical calculation of the gap in the limit of strongly anisotropic hopping, we show that its scaling is compatible with the preparation of large size FCIs for sufficiently large hopping anisotropy. Our numerical simulations in the framework of exact diagonalization explore the full anisotropy range to corroborate these results.

cond-mat.quant-gas↗

arXiv2023

Amorphous and polycrystalline routes towards a chiral spin liquid

We show that a chiral spin liquid spontaneously emerges in partially amorphous, polycrystalline, or ion-irradiated Kitaev materials. In these systems, time-reversal symmetry is broken spontaneously due to a non-zero density of plaquettes with an odd number of edges, $n_{odd}$. This mechanism opens a sizeable gap, at small $n_{odd}$ compatible with that of typical amorphous materials and polycrystals, and which can alternatively be induced by ion-irradiation. We find that the gap is proportional to $n_{odd}$, saturating at $n_{odd}\sim 40\%$. Using exact diagonalization, we find that the chiral spin liquid is approximately as stable to Heisenberg interactions as Kitaev's honeycomb spin liquid model. Our results open up a significant number of non-crystalline systems where chiral spin liquids can emerge without external magnetic fields.

cond-mat.str-el↗

arXiv2023

Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line

We show that pressure applied to twisted WSe$_2$ can enhance the many-body gap and region of stability of a fractional Chern insulator at filling $ν= 1/3$. Our results are based on exact diagonalization of a continuum model, whose pressure-dependence is obtained through {\it ab initio} methods. We interpret our results in terms of a {\it magic line} in the pressure-{\it vs}-twist angle phase diagram: along the magic line, the bandwidth of the topmost moiré valence band is minimized while simultaneously its quantum geometry nearly resembles that of an ideal Chern band. We expect our results to generalize to other twisted transition metal dichalcogenide homobilayers.

cond-mat.str-el↗

arXiv2023

Absence of edge reconstruction for quantum Hall edge channels in graphene devices

Electronic edge states in topological insulators have become a major paradigm in physics. The oldest and primary example is that of quantum Hall (QH) edge channels that propagate along the periphery of two-dimensional electron gases (2DEGs) under perpendicular magnetic field. Yet, despite 40 years of intensive studies using a variety of transport and scanning probe techniques, imaging the real-space structure of QH edge channels has proven difficult, mainly due to the buried nature of most 2DEGs in semiconductors. Here, we show that QH edge states in graphene are confined to a few magnetic lengths at the crystal edges by performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride. These findings indicate that QH edge states are defined by boundary conditions of vanishing electronic wavefunctions at the crystal edges, resulting in ideal one-dimensional chiral channels, free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, contrasting with conjectures on the existence of non-topological upstream modes. The absence of electrostatic reconstruction of quantum Hall edge states has profound implications for the universality of electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

cond-mat.mes-hall↗

arXiv2022

Realization of a fractional quantum Hall state with ultracold atoms

Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement, and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light, preparing fractional quantum Hall states in engineered systems remains elusive. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic $ν=1/2$ Laughlin state with two particles on sixteen sites. This minimal system already captures many hallmark features of Laughlin-type FQH states: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations, and we measure a fractional Hall conductivity of $σ_\text{H}/σ_0= 0.6(2)$ via the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field we map out the transition point between the normal and the FQH regime through a spectroscopic probe of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms.

cond-mat.quant-gas↗

arXiv2022

Imaging tunable quantum Hall broken-symmetry orders in graphene

When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy. The zeroth Landau level of graphene under magnetic field is a particularly interesting strongly interacting flat band because inter-electron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders. Evidence for these stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy or by dielectric screening of the Coulomb interaction. However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders. Here, we image three distinct broken-symmetry phases in graphene using scanning tunneling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low or high dielectric constant environment, and with a magnetic field. In the unscreened case, we unveil a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz-Thouless transition. Under dielectric screening, a sublattice-unpolarized ground state emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

cond-mat.mes-hall↗

arXiv2019

Chern bands of twisted bilayer graphene: fractional Chern insulators and spin phase transition

When one of the graphene layers of Magic Angle Twisted Bilayer Graphene is nearly aligned with its hexagonal boron nitride substrate (a configuration dubbed TBG/hBN), the active electronic bands are nearly flat, and have a Chern number $C=\pm1$. Recent experiments demonstrated a quantum anomalous Hall effect and spontaneous valley polarization at integer filling $ν_T=3$ of the conduction band in this system. Motivated by this discovery, we ask whether fractional quantum anomalous Hall states (FQAH) could also emerge in TBG/hBN. We focus on the range of filling fractions where valley ferromagnetism was observed experimentally. Using exact diagonalization, we find that the ground states at $ν_T = \frac{10}{3}$ and $ν_T=\frac{17}{5}$ are fractional Chern insulator states in the flat band limit (in the hole picture, these are the fractional quantum Hall fractions $\frac{2}{3}$ and $\frac{3}{5}$). The ground state is either spin polarized or a spin singlet depending sensitively on band parameters. For nominally realistic band parameters, spin polarization is favored. Flattening the Berry curvature by changing a band parameter gives way to the spin singlet phase. Our estimation of the charge gap in the flat band limit shows that the FQAH state may be seen at accessible temperatures in experiments. We also study the effect of a non-zero bandwidth and show that there is a reasonable range of parameters in which the FQAH state is the ground state.

cond-mat.str-el↗

arXiv2019

Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker

The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn$_2$As$_2$, and cold atomic realizations.

cond-mat.mes-hall↗

arXiv2019

Ferromagnetism in narrow bands of moiré superlattices

Many graphene moiré superlattices host narrow bands with non-zero valley Chern numbers. We provide analytical and numerical evidence for a robust spin and/or valley polarized insulator at total integer band filling in nearly flat bands of several different moiré materials. In the limit of a perfectly flat band, we present analytical arguments in favor of the ferromagnetic state substantiated by numerical calculations. Further, we numerically evaluate its stability for a finite bandwidth. We provide exact diagonalization results for models appropriate for ABC trilayer graphene aligned with hBN, twisted double bilayer graphene, and twisted bilayer graphene aligned with hBN. We also provide DMRG results for a honeycomb lattice with a quasi-flat band and non-zero Chern number, which extend our results to larger system sizes. We find a maximally spin and valley polarized insulator at all integer fillings when the band is sufficiently flat. We also show that interactions may induce effective dispersive terms strong enough to destabilize this state. These results still hold in the case of zero valley Chern number (for example, trivial side of TLG/hBN). We give an intuitive picture based on extended Wannier orbitals, and emphasize the role of the quantum geometry of the band, whose microscopic details may enhance or weaken ferromagnetism in moiré materials.

cond-mat.str-el↗

arXiv2019

Detecting fractional Chern insulators through circular dichroism

Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning inter-particle interactions, suggest that strongly-correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number, and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Our scheme offers a practical tool for the detection of topologically-ordered states in quantum-engineered systems, with potential applications in solid state.

cond-mat.quant-gas↗

arXiv2018

Dynamics and level statistics of interacting fermions in the Lowest Landau Level

We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g. in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian Orthogonal Ensemble) can appear in many cases despite the lack of time-reversal symmetry.

cond-mat.str-el↗

arXiv2017

Stability of the spin-$1/2$ kagome ground state with breathing anisotropy

We numerically study the spin-$1/2$ breathing kagome lattice. In this variation of the kagome Heisenberg antiferromagnet, the spins belonging to upward and downward facing triangles have different coupling strengths. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that the kagome antiferromagnet spin liquid is extremely robust to this anisotropy. Materials featuring this anisotropy -- and especially the recently studied vanadium compound $[{\mathrm{NH}}_{4}{]}_{2}[{\mathbf{C}}_{7}{\mathbf{H}}_{14}\mathbf{N}][{\mathbf{V}}_{7}{\mathbf{O}}_{6}{\mathbf{F}}_{18}]$ (DQVOF) -- may thus be very good candidates to realize the much studied kagome spin liquid. Further, we closely examine the limit of strong breathing anisotropy and find indications of a transition to a nematic phase.

cond-mat.str-el↗

arXiv2016

Creating a bosonic fractional quantum Hall state by pairing fermions

We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the entanglement spectra shows that the gapped ground state is the bosonic $1/2$ Laughlin state. Our work therefore provides compelling evidence of a topological phase transition from the fermionic quantum Hall state at unity filling to the bosonic Laughlin state at a critical attraction strength.

cond-mat.str-el↗

arXiv2015

Phase diagram of $ν=\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $ν=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is $SU(2)$ symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.

cond-mat.str-el↗

arXiv2015

Triplet FFLO Superconductivity in the doped Kitaev-Heisenberg Honeycomb Model

We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. This picture is also supported by exact diagonalizations on finite clusters.

cond-mat.str-el↗

arXiv2015

Projective construction of the $\mathbb{Z}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.

cond-mat.str-el↗