arXiv subjects

H. A. Fertig

Publications and source records attributed to H. A. Fertig.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Hall Ferromagnetism in a Cavity Vacuum

We uncover a continuous phase transition in a quantum Hall ferromagnet (QHF) at filling factor $ν=1$, driven by vacuum fluctuations of a cavity. Our analysis starts with a Landau level projection in dipole gauge, where we find the states to be well-represented by a tensor product of the electronic and photonic degrees of freedom. Through analytic spin wave calculations, mean-field theory and density matrix renormalization group (DMRG) simulations, we show that for a spatially antisymmetric cavity field, the uniform QHF state is stable only for weak light-matter coupling and gives way to states of inhomogeneous electron density above a critical coupling. These states involve "flanks" of uniform QHF fluids, separated by a "compact core" of doubly occupied orbitals with the core size being the order parameter, which we dub as "compact-core phases". While the fully spin polarized electronic states are product states, entanglement builds up between the uniform QHF flanks across the compact core in the $S_z=0$ magnetic sector, motivating an ansatz for the compact-core electronic states. The transition boundary is exactly derived for product electronic states in terms of matter and cavity parameters, and numerically confirmed by DMRG. We also study the thin-cylinder limit near the critical point where quantum fluctuations are enhanced, and the many-body excited states in both phases by focusing on the entanglement spectrum degeneracies. Remarkably, the photon number is found to probe the order parameter of the transition, providing a possible experimental signature of the electronic transition and the compact-core states. Our study offers a rare example of a phase of electrons stabilized solely by coupling to the enhanced vacuum fluctuations of a cavity mode.

cond-mat.str-el↗

arXiv2026

Signatures of the Quantum Geometric Dipole of Interlayer Excitons in Counterflow Conductivity

Collective excitations of many-body electron systems can carry internal structure, supporting novel quantum geometric and topological properties. Among these are a quantum geometric dipole (QGD), which for excitons have direct significance as an internal polarization. For interlayer excitons of a bilayer system, this represents an in-plane dipole moment, which can be used to drive them with in-plane electric fields. In this work, we consider counterflow electric currents associated with driven excitons in such a bilayer system as a probe of their QGD structure. As a simple but non-trivial example, we analyze a structure with a one-dimensional periodic potential in a strong perpendicular magnetic field. The resulting magnetoexciton bands host QGD structure that distinguishes it from the exciton QGD of a uniform system. To model exciton transport we adopt a Boltzmann approach that includes inter-band tunneling, allowing us to consider non-equilibrium momentum distributions that result from strong layer-antisymmetric driving fields. We show how linear response to a layer-symmetric component of the driving fields provide information about the QGD, and that the broad QGD structure of the exciton bands can be probed by the varying the layer-antisymmetric field. Our results demonstrate that counterflow conductivity serves as a tunable probe of the internal quantum geometric structure carried by the interlayer excitons, connecting transport to the quantum geometry of many-body excitations.

cond-mat.mes-hall↗

arXiv2026

Quantum simulation of the Haldane phase using open shell molecules

Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the $N=0,J=1/2,F=1$ state is coupled to the $N=1,J=3/2,F=2$ manifold with circularly polarized microwaves, in the presence of a small magnetic field, can lead to spin-1 quantum magnetic Hamiltonians, due to the decoupling between electron spin and orbit, that is unique to the $^2Σ$ ground state molecules. We demonstrate that in one dimension, the phase diagram associated with this Hamiltonian, computed via tensor network methods, hosts the celebrated Haldane phase. We find that the Haldane phase persists even in the presence of SU(3) correction terms that break the SU(2) algebra of the Hamiltonian. We discuss the feasibility of the proposed scheme for $^2Σ$ molecules with large rotational constants such as the directly laser cooled molecule MgF for future experiments.

cond-mat.quant-gas↗

arXiv2025

Quantum Geometric Exciton Drift Velocity

We show that the dipole moment of an exciton is uniquely determined by the quantum geometry of its eigenstates, and demonstrate its intimate connection with a quantity we call the Quantum Geometric Dipole (QGD). The QGD arises naturally in semiclassical dynamics of an exciton in an electric field, contributing to the anomalous velocity differently from the Berry's curvature. In a uniform electric field QGD results in a drift velocity akin to that expected for excitons in crossed electric and magnetic fields, even in the absence of a real magnetic field. We compute the quantities relevant to semiclassical exciton dynamics for several interesting examples of bilayer systems with weak interlayer tunneling and Fermi energy in a gap, where the exciton may be sensibly described as a two-body problem. These quantities include the exciton dispersion, its QGD, and Berry's curvature. For two gapped-graphene layers in a vanishing magnetic field, we find the Quantum Geometric Dipole vanishes if the layers are identical, but may be non-zero when the layers differ. We further analyze examples in the presence of magnetic fields, allowing us to examine cases involving graphene, in which a gap is opened by Landau level splitting. Heterostructures involving TMDs are also considered. In each case the Quantum Geometric Dipole and Berry's curvatures play out differently. In some cases, the lowest energy exciton state is found to reside at finite momentum, with interesting possibilities for Bose condensation. We also find situations in which the QGD increases monotonically with exciton momentum, suggesting that the quantum geometry can be exploited to produce photocurrents from initially bound excitons with electric fields. We speculate on further possible effects of the semiclassical dynamics in geometries where the constituent layers are subject to the same or different electric fields.

cond-mat.mes-hall↗

arXiv2025

Striped Spin Density Wave in a Graphene/Black Phosphorous Heterostructure

A bilayer formed by stacking two distinct materials creates a moiré lattice, which can serve as a platform for novel electronic phases. In this work we study a unique example of such a system: the graphene-black phosphorus heterostructure (G/BP), which has been suggested to have an intricate band structure. Most notably, the valence band hosts a quasi-one-dimensional region in the Brillouin zone of high density of states, suggesting that various many-body electronic phases are likely to emerge. We derive an effective tight-binding model that reproduces this band structure, and explore the emergent broken-symmetry phases when interactions are introduced. Employing a mean-field analysis, we find that the favored ground-state exhibits a striped spin density wave (SDW) order, characterized by either one of two-fold degenerate wave-vectors that are tunable by gating. Further exploring the phase-diagram controlled by gate voltage and the interaction strength, we find that the SDW-ordered state undergoes a metal to insulator transition via an intermediate metallic phase which supports striped SDW correlations. Possible experimental signatures are discussed, in particular a highly anisotropic dispersion of the collective excitations which should be manifested in electric and thermal transport.

cond-mat.str-el↗

arXiv2024

Quantum Band Structure and Topology in One Dimensional Modulated Plasmonic Crystal

Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider topology of plasmons in a two-dimensional metal, subject to a unidirectional periodicity. We show how the plasmon modes and wavefunctions may be computed for such a periodic system, by focusing on the confined, quantized photon degrees of freedom associated with the plasmon modes. At low frequencies the plasmons disperse with wavevector as $\sqrt{q}$; however at higher frequencies one finds a series of bands and gaps in the spectrum. For a unidirectional periodic electron density with inversion symmetry, we show that each band hosts a Zak phase $γ_n$ which may only take the values $0$ or $π$. Each gap has a topological index $ν$ that is determined by the sum of the Zak phases below it. When the system has an interface with the vacuum, one finds in-gap modes for gaps with non-trivial topologies, which are confined to the interface. In addition, interfaces between systems that are the same except for their topologies -- which can be created by a defect in the lattice in which half a unit cell has been removed -- host in-gap, confined states when the topological indices of the relevant gaps are different. We demonstrate these properties numerically by analyzing a Kronig-Penney-type model in graphene, in which the electron density is piecewise constant, modulating between two different densities. In addition, we consider a related plasmon system modeled after the Su-Schrieffer-Heeger (SSH) model. We show that the topological phase diagram of the lowest energy bands is highly analogous to that of the SSH tight-binding system.

cond-mat.mes-hall↗

arXiv2024

Many-Body Quantum Geometric Dipole

Collective excitations of many-body electron systems can carry internal structure, tied to the quantum geometry of the Hilbert space in which they are embedded. This has been shown explicitly for particle-hole-like excitations, which carry a ``quantum geometric dipole'' (QGD) that is essentially an electric dipole moment associated with the state. We demonstrate in this work that this property can be formulated in a generic way, which does not require wavefunctions expressed in terms of single particle-hole states. Our formulation exploits the density matrix associated with a branch of excitations that evolves continuously with its momentum ${\bf K}$, from which one may extract single-particle states allowing a construction of the QGD. We demonstrate the formulation using the single-mode approximation for excited states of two quantum Hall systems: the first for an integrally filled Landau level, and the second for a fractional quantum Hall state at filling factor $ν=1/m$, with $m$ an odd integer. In both cases we obtain the same result for the QGD, which can be attributed to the translational invariance assumed of the system. Our study demonstrates that the QGD is an intrinsic property of collective modes which is valid beyond approximations one might make for their wavefunctions.

cond-mat.mes-hall↗

arXiv2023

Skyrmion stripes in twisted double bilayer graphene

Two dimensional moiré systems have recently emerged as a platform in which the interplay between topology and strong correlations of electrons play out in non-trivial ways. Among these systems, twisted double bilayer graphene (TDBG) is of particular interest as its topological properties may be tuned via both twist angle and applied perpendicular electric field. In this system, energy gaps are observed at half filling of particular bands, which can be associated with correlated spin polarized states. In this work, we investigate the fate of these states as the system is doped away from this filling. We demonstrate that, for a broad range of fractional fillings, the resulting ground state is partially valley polarized, and supports multiple broken symmetries, including a textured spin order indicative of skyrmions, with a novel $\textit{stripe}$ ordering that spontaneously breaks $C_3$ symmetry. Experimental signatures of this state are discussed.

cond-mat.mes-hall↗

arXiv2023

Quantum Plasmons in Double Layer Systems

Plasmons are fundamental excitations of metals which can be described in terms of electron dynamics, or in terms of the electromagnetic fields associated with them. In this work we develop a quantum description of plasmons in a double layer structure, treating them as confined electromagnetic modes of the structure. The structure of the resulting bosonic Hamiltonian indicates the presence of virtual plasmons of the individual layers which appear as quantum fluctuations in the ground state. For momenta smaller than the inverse separation between layers, these modes are in the ultrastrong coupling regime. Coherence terms in the Hamiltonian indicate that modes with equal and opposite momenta are entangled. We consider how in principle these entangled modes might be accessed, by analyzing a situation in which the conductivity of one of the two layers suddenly drops to zero. The resulting density matrix has a large entanglement entropy at small momenta, and modes at $\pm \mathbf{q}$ that are inseparable. More practical routes to releasing and detecting entangled plasmons from this system are considered.

cond-mat.mes-hall↗

arXiv2023

Phase diagram of the $ν= 2$ quantum Hall state in bilayer graphene

Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors $1 < ν\leq 2$ suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric field $D^{*}$. We find the behavior of $D^{*}$ with $ν$ changes markedly as $B$ is reduced. At $ν= 2$, $D^{*}$ may even vanish when $B$ is sufficiently small. We present a theoretical model for lattice-scale interactions which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model we analyze the nature of the $ν= 2$ state as a function of the magnetic and electric fields, and predict that valley-coherence may emerge for $D \sim D^{*}$ in the high $B$ regime. This suggests the system supports Kekule bond-ordering, which could in principle be verified via STM measurements.

cond-mat.mes-hall↗

arXiv2022

Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands

Moiré superlattices engineer band properties and enable observation of fractal energy spectra of Hofstadter butterfly. Recently, correlated-electron physics hosted by flat bands in small-angle moiré systems has been at the foreground. However, the implications of moiré band topology within the single-particle framework are little explored experimentally. An outstanding problem is understanding the effect of band topology on Hofstadter physics, which does not require electron correlations. Our work experimentally studies Chern state switching in the Hofstadter regime using twisted double bilayer graphene (TDBG), which offers electric field tunable topological bands, unlike twisted bilayer graphene. Here we show that the nontrivial topology reflects in the Hofstadter spectra, in particular, by displaying a cascade of Hofstadter gaps that switch their Chern numbers sequentially while varying the perpendicular electric field. Our experiments together with theoretical calculations suggest a crucial role of charge polarization changing concomitantly with topological transitions in this system. Layer polarization is likely to play an important role in the topological states in few-layer twisted systems. Moreover, our work establishes TDBG as a novel Hofstadter platform with nontrivial magnetoelectric coupling.

cond-mat.mes-hall↗

arXiv2022

Broken symmetry and competing orders in Weyl semimetal interfaces

We consider interaction-induced broken symmetry states of two Weyl semimetal surfaces with multiple Fermi-arc (FA) states. In the presence of inter- and intra-surface Coulomb interactions, multiple broken symmetries may emerge which coexist and/or compete with one another. Interlayer exciton condensates involving different FA flavors are shown to form, with amplitudes determined by the strength of interactions and the degree of nesting among the arcs. For FA pairs which are well-separated in momentum with strong nesting, the resulting state is a particle-hole analog of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Intralayer interactions moreover induce charge density wave (CDW) ordering, so that the most general state of the system is a supersolid. These orderings in principle carry signatures in non-linear behavior and narrow band noise in Coulomb drag transport measurements.

cond-mat.mes-hall↗

arXiv2021

Quantum Internal Structure of Plasmons

Plasmons are usually described in terms of macroscopic quantities such as electric fields and currents. However as fundamental excitations of metals they are also quantum objects with internal structure. We demonstrate that this can induce an intrinsic dipole moment which is tied to the quantum geometry of the Hilbert space of plasmon states. This {\it quantum geometric dipole} offers a unique handle for manipulation of plasmon dynamics, via density modulations and electric fields. As a concrete example we demonstrate that scattering of plasmons with non-vanishing quantum geometric dipole from impurities is non-reciprocal, skewing in different directions in a valley-dependent fashion. This internal structure can be used to control plasmon trajectories in two dimensional materials.

cond-mat.mes-hall↗

arXiv2021

Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene

We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moiré reciprocal lattice. The anisotropy of the Dirac cones and a concomitant cascade of saddle points induce a series of topological Lifshitz transitions that can be tuned by the twist angle and perpendicular electric field. We discuss the possibility of direct observation of Dirac magic as well as its consequences for the correlated states of electrons in this moiré system.

cond-mat.mes-hall↗

arXiv2020

Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene

We propose a tunable optical setup to engineer topologically nontrivial flat bands in twisted bilayer graphene under circularly polarized light. Using both analytical and numerical calculations, we demonstrate that nearly flat bands can be engineered at small twist angles near the magic angles of the static system. The flatness and the gaps between these bands can be tuned optically by varying laser frequency and amplitude. We study the effects of interlayer hopping variations on Floquet flat bands and find that lattice relaxation favors their formation. Furthermore, we find that, once formed, the flat bands carry nonzero Chern numbers. We show that at currently known values of parameters, such topological flat bands can be realized using circularly polarized UV laser light. Thus, our work opens the way to creating optically tunable, strongly correlated topological phases of electrons in moiré superlattices.

cond-mat.str-el↗

arXiv2020

Dipolar optical plasmon in thin-film Weyl semimetals

In a slab geometry with large surface-to-bulk ratio, topological surface states such as Fermi arcs for Weyl or Dirac semimetals may dominate their low-energy properties. We investigate the collective charge oscillations in such systems, finding striking differences between Weyl and conventional electronic systems. Our results, obtained analytically and verified numerically, predict that the Weyl semimetal thin-film host a single $ω\propto \sqrt{q}$ plasmon mode, that results from collective, anti-symmetric charge oscillations of between the two surfaces, in stark contrast to conventional 2D bi-layers as well as Dirac semimetals with Fermi arcs, which support anti-symmetric acoustic modes along with a symmetric optical mode. These modes lie in the gap of the particle-hole continuum and are thus spectroscopically observable and potentially useful in plasmonic applications.

cond-mat.mes-hall↗

arXiv2019

RKKY coupling in Weyl semimetal thin films

We consider the effective coupling between impurity spins on surfaces of a thin-film Weyl semimetal within Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory. If the spins are on the same surface, their coupling reflects the anisotropy and the spin-momentum locking of the Fermi arcs. By contrast when the spins are on opposite surfaces, their coupling is mediated by the Fermi arcs as well as by bulk states. In this case the coupling is both surprisingly strong and strongly thickness dependent, with a maximum at an optimum thickness. We demonstrate our results using analytical solutions of states in the thin-film geometry, as well using a two-surface recursive Green's function analysis of the tight-binding model.

cond-mat.mes-hall↗

arXiv2019

RKKY Interactions in Graphene Landau Levels

We study RKKY interactions for magnetic impurities on graphene in situations where the electronic spectrum is in the form of Landau levels. Two such situations are considered: non-uniformly strained graphene, and graphene in a real magnetic field. RKKY interactions are enhanced by the lowest Landau level, which is shown to form electron states binding with the spin impurities and add a strong non-perturbative contribution to pairwise impurity spin interactions when their separation $R$ no more than the magnetic length. Beyond this interactions are found to fall off as $1/R^3$ due to perturbative effects of the negative energy Landau levels. Based on these results, we develop simple mean-field theories for both systems, taking into account the fact that typically the density of states in the lowest Landau level is much smaller than the density of spin impurities. For the strain field case, we find that the system is formally ferrimagnetic, but with very small net moment due to the relatively low density of impurities binding electrons. The transition temperature is nevertheless enhanced by them. For real fields, the system forms a canted antiferromagnet if the field is not so strong as to pin the impurity spins along the field. The possibility that the system in this latter case supports a Kosterlitz-Thouless transition is discussed.

cond-mat.mes-hall↗