arXiv subjects

Valentin Crépel

Publications and source records attributed to Valentin Crépel.

35 records · Page 2Linked to original sources

arXiv2024

Sublattice structure and topology in spontaneously crystallized electronic states

The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. In this Letter, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective `time-reversal symmetry' and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.

cond-mat.str-el↗

arXiv2023

Probing the fractional quantum Hall phases in valley-layer locked bilayer MoS$_{2}$

Semiconducting transition-metal dichalcogenides (TMDs) exhibit high mobility, strong spin-orbit coupling, and large effective masses, which simultaneously leads to a rich wealth of Landau quantizations and inherently strong electronic interactions. However, in spite of their extensively explored Landau levels (LL) structure, probing electron correlations in the fractionally filled LL regime has not been possible due to the difficulty of reaching the quantum limit. Here, we report evidence for fractional quantum Hall (FQH) states at filling fractions 4/5 and 2/5 in the lowest LL of bilayer MoS$_{2}$, manifested in fractionally quantized transverse conductance plateaus accompanied by longitudinal resistance minima. We further show that the observed FQH states sensitively depend on the dielectric and gate screening of the Coulomb interactions. Our findings establish a new FQH experimental platform which are a scarce resource: an intrinsic semiconducting high mobility electron gas, whose electronic interactions in the FQH regime are in principle tunable by Coulomb-screening engineering, and as such, could be the missing link between atomically thin graphene and semiconducting quantum wells.

cond-mat.mes-hall↗

arXiv2023

Geometric squeezing of rotating quantum gases into the lowest Landau level

The simulation of quantum Hall physics with rotating quantum gases is witnessing a revival due to recent experimental advances that enabled the observation of a Bose-Einstein condensate entirely contained in its lowest kinetic energy state, i.e. the lowest Landau level. We theoretically describe this experimental result, and show that it can be interpreted as a squeezing of the geometric degree of freedom of the problem, the guiding center metric. This "geometric squeezing" offers an unprecedented experimental control over the quantum geometry in Landau-level analogues, and at the same time opens a realistic path towards achieving correlated quantum phases akin to quantum Hall states with neutral atoms.

cond-mat.quant-gas↗

arXiv2023

Chiral model of twisted bilayer graphene realized in a monolayer

We demonstrate that a single layer of graphene subject to a superlattice potential nearly commensurate to a $\sqrt{3} \times \sqrt{3}$ supercell exactly maps to the chiral model of twisted bilayer graphene, albeit with half as many degrees of freedom. We comprehensively review the properties of this ``half-chiral model,'' including the interacting phases stabilized at integer fillings and the effects of substrate-induced symmetry breaking. We list candidate substrates that could produce a superlattice potential on graphene with the correct periodicity to access the flat band limit. Experimental measurements on a half-chiral moire heterostructure, in which valley-skyrmions cannot form, could yield insights on the physics they mediate in twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2023

Topological superconductivity in doped magnetic moiré semiconductors

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moiré band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tuanble strength, which may be large. Together with the low moiré carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.

cond-mat.supr-con↗

arXiv2022

Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation

We show that the quantum dimer state on the Kagome lattice, which was recently realized with high fidelity in a Rydberg quantum simulator [Semeghini et al., Science 374, 6572 (2021)], offers a sufficient resource for universal measurement-based quantum computations. In particular, we provide an efficient encoding of logical qubits in this state, and give explicit measurement sequences that implement a universal set of gates on these qubits. Since the building blocks of the proposed measurements have already been experimentally implemented, our work highlights one possible path towards promoting Rydberg simulators to universal quantum computers relying on the measurement-based model of quantum computation with currently existing technology.

quant-ph↗

arXiv2022

Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides

We predict robust Ising ferromagnetism driven by Coulomb interaction in the metallic phase of twisted transition metal dichalcogenides homobilayers for a range of small twist angles. Due to the presence of spin-valley locking and Chern band, the completely spin polarized state -- a half metal -- has a spin gap and exhibits anomalous Hall effect. We also find that near a magic angle where the Chern band is predicted to be exceptionally flat, the anomalous Hall metal at $1/3$ filling may become unstable at low temperature to a $\sqrt{3}\times\sqrt{3}$ charge density wave, or a fractional Chern insulator.

cond-mat.str-el↗

arXiv2021

Unconventional superconductivity due to interband polarization

We analyze in detail the superconductivity that arises in an extended Hubbard model describing a multiband system with repulsive interactions. We show that virtual interband processes induce an effective attractive interaction for small momentum transfers, a situation not found in most models of superconductivity from repulsion. This attraction can be traced back, in real space, to the presence of correlated hopping terms induced by interband polarization. We reveal this physics with both strong-coupling expansion and many-body perturbation theory, supplemented by numerical calculations. Finally, we point out interesting similarities with the problem of interacting electrons in twisted bilayer graphene, suggesting the importance of interband contribution to superconductivity.

cond-mat.supr-con↗

arXiv2021

Magic in twisted transition metal dichalcogenide bilayers

The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, we predict the realization of a generalized Kane-Mele model with a topological flat band, interaction-driven Haldane insulator, and Mott insulators at the filling of one hole per moiré unit cell. The combination of flat dispersion and uniformity of Berry curvature near the magic angle holds promise for realizing fractional quantum anomalous Hall effect at fractional filling. We also identify twist angles favorable for quantum spin Hall insulators and interaction-induced quantum anomalous Hall insulators at other integer fillings.

cond-mat.mes-hall↗

arXiv2021

Spin-triplet superconductivity from interband effect in doped insulators

Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a general mechanism for spin-triplet superconductivity in multi-band systems, where a non-retarded pairing interaction between conduction electrons is produced by their electronic repulsion to a third-electron undergoing a virtual interband transition. Our theory is analytically controlled by an interband hybridization parameter, and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. In light of this theory, we propose that recently discovered dilute superconductors such as ZrNCl and WTe$_2$ are spin-triplet, and compare the expected consequences of our theory with experimental data.

cond-mat.supr-con↗

arXiv2021

Geometric squeezing into the lowest Landau level

The equivalence between neutral particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. In their quantum descriptions, translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. Here, we exploit the ability to squeeze non-commuting variables to dynamically create a Bose-Einstein condensate occupying a single Landau gauge wavefunction in the lowest Landau level. We directly resolve the extent of the zero-point cyclotron orbits, and demonstrate geometric squeezing of the orbits' guiding centers by more than ${7}~$dB below the standard quantum limit. The condensate attains an angular momentum of more than ${1000}\,{\hbar}$ per particle, and an interatomic distance comparable to the size of the cyclotron orbits. This offers a new route towards strongly correlated fluids and bosonic quantum Hall states.

cond-mat.quant-gas↗

arXiv2021

Crystallization of Bosonic Quantum Hall States

The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level (LLL). We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.

cond-mat.quant-gas↗

arXiv2021

Universal signatures of Dirac fermions in entanglement and charge fluctuations

We investigate the entanglement entropy (EE) and charge fluctuations in models where the low energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, \emph{i.e.}, independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and number of Dirac cones, and either for strictly two-dimensional models or for gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides non-universal, geometry dependent results.

cond-mat.mes-hall↗

arXiv2021

New mechanism and exact theory of superconductivity from strong repulsive interaction

We introduce a new and general mechanism for superconductivity in Fermi systems with strong repulsive interaction. Because kinetic terms are small compared to the bare repulsion, the dynamic of charge carriers is constrained by the the presence of other nearby carriers. By treating kinetic terms as a perturbation around the atomic limit, we show that pairing can be induced by correlated multi-particle tunneling processes that favor two itinerant carriers to be close together. Our analytically-controlled theory provides a quantitative formula relating $T_c$ to microscopic parameters, with maximum $T_c$ reaching about 10% of the Fermi temperature. Our work demonstrates a powerful method for studying strong coupling superconductivity with unconventional pairing symmetry. It also offers a realistic new route to realizing finite angular momentum superfluidity of spin-polarized fermions in optical lattice.

cond-mat.supr-con↗

arXiv2020

Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices

Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the low-energy and strong coupling limits, which impose severe constraints on the physical systems where they could be realized. We investigate the microscopic relevance of a class of coupled-wire models and their possible experimental realization in cold-atom experiments. We connect with earlier results and prove the emergence of fractional quantum Hall states in the limit of strong inter-wire tunneling. Contrary to previous studies relying on renormalization group arguments, our microscopic approach exposes the connection between coupled-wire constructions and model wavefunctions in continuum Landau levels. Then, we use exact diagonalization methods to investigate the appearance of these fractional quantum Hall states in more realistic settings. We examine the parameter regimes where these strongly correlated phases arise, and provide a way to detect their appearance in cold-atom experiments through standard time-of-flight measurements. Motivated by this experimental probe, we finally propose a realization of our model with cold-atom in spin-dependent optical lattices. Our estimates show that the previous fractional quantum Hall phases lie within experimentally accessible parameter regimes, giving a viable route towards their experimental study.

cond-mat.str-el↗

arXiv2019

Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $ν= 1/2 + 1/2$ Bilayers

We propose a one-parameter variational ansatz to describe the tunneling-driven Abelian to non-Abelian transition in bosonic $ν=1/2+1/2$ fractional quantum Hall bilayers. This ansatz, based on exact matrix product states, captures the low-energy physics all along the transition and allows to probe its characteristic features. The transition is continuous, characterized by the decoupling of antisymmetric degrees of freedom. We futhermore determine the tunneling strength above which non-Abelian statistics should be observed experimentally. Finally, we propose to engineer the inter-layer tunneling to create an interface trapping a neutral chiral Majorana. We microscopically characterize such an interface using a slightly modified model wavefunction.

cond-mat.str-el↗

arXiv2017

Creation of a Bose-condensed gas of rubidium 87 by laser cooling

We demonstrate direct laser cooling of a gas of rubidium 87 atoms to quantum degeneracy. The method does not involve evaporative cooling, is fast, and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of cloud compression to increase the density, followed by degenerate Raman sideband cooling to decrease the temperature. Light-induced loss at high atomic density is substantially reduced by using far red detuned optical pumping light. Starting with 2000 atoms, we prepare 1400 atoms in 300 ms at quantum degeneracy, as confirmed by the appearance of a bimodal velocity distribution as the system crosses over from a classical gas to a Bose-condensed, interacting one-dimensional gas with a macroscopic population of the quantum ground state. The method should be broadly applicable to many bosonic and fermionic species, and to systems where evaporative cooling is not possible.

physics.atom-ph↗