Berry phase effect on the exciton transport and on the exciton Bose-Einstein condensate

Geometric Stiffness in Interlayer Exciton Condensates

Recent experiments have confirmed the presence of interlayer excitons in the ground state of transition metal dichalcogenide bilayers. The interlayer excitons are expected to show remarkable transport properties when they undergo Bose condensation. In this Letter, we demonstrate that quantum geometry of Bloch wave functions plays an important role in the phase stiffness of the interlayer exciton condensate. Notably, we identify a geometric contribution that amplifies the stiffness, leading to the formation of a robust condensate with an increased Berezinskii-Kosterlitz-Thouless temperature. Our results have direct implications for the ongoing experimental efforts on interlayer excitons in materials that have nontrivial quantum geometry. We provide estimates for the geometric contribution in transition metal dichalcogenide bilayers through a realistic continuum model with gated Coulomb interaction, and find that the substantially increased stiffness may allow an interlayer exciton condensate to be realized at amenable experimental conditions.

Observation of chiral and slow plasmons in twisted bilayer graphene

Moiré superlattices have led to observations of exotic emergent electronic properties such as superconductivity and strong correlated states in small-rotation-angle twisted bilayer graphene (tBLG)^1,2. Recently, these findings have inspired the search for new properties in moiré plasmons. Although plasmon propagation in the tBLG basal plane has been studied by near-field nano-imaging techniques^3-7, the general electromagnetic character and properties of these plasmons remain elusive. Here we report the direct observation of two new plasmon modes in macroscopic tBLG with a highly ordered moiré superlattice. Using spiral structured nanoribbons of tBLG, we identify signatures of chiral plasmons that arise owing to the uncompensated Berry flux of the electron gas under optical pumping. The salient features of these chiral plasmons are shown through their dependence on optical pumping intensity and electron fillings, in conjunction with distinct resonance splitting and Faraday rotation coinciding with the spectral window of maximal Berry flux. Moreover, we also identify a slow plasmonic mode around 0.4 electronvolts, which stems from the interband transitions between the nested subbands in lattice-relaxed AB-stacked domains. This mode may open up opportunities for strong light-matter interactions within the highly sought after mid-wave infrared spectral window⁸. Our results unveil the new electromagnetic dynamics of small-angle tBLG and exemplify it as a unique quantum optical platform.

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 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 a nonvanishing quantum geometric dipole from impurities is nonreciprocal, skewing in different directions in a valley-dependent fashion. This internal structure can be used to control plasmon trajectories in two dimensional materials.

Exciton Band Topology in Spontaneous Quantum Anomalous Hall Insulators: Applications to Twisted Bilayer Graphene

We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite nonzero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently reported broken-symmetry spontaneous QAH insulators in substrate aligned magic-angle twisted bilayer graphene.

Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals

Exciton valley Hall effect is the spatial separation of the valley-tagged excitons by a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering. We develop a microscopic theory of the exciton valley Hall effect in the presence of a synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current also demonstrating the cancellation of the anomalous velocity. The sensitivity of the effect to the origin of the drag force and to the scattering processes is shown. We extend the drift-diffusion model to account for the valley Hall effect and calculate the exciton density and valley polarization profiles.

Tunable Flux Vortices in Two-Dimensional Dirac Superconductors

The nontrivial geometry encoded in the quantum mechanical wave function has important consequences for both noninteracting and interacting systems. Yet, our understanding of the relationship between geometrical effects in noninteracting systems and their interacting counterparts is far from complete. Here, we demonstrate how the single-particle Berry curvature associated with the normal phase in two dimensions modifies the fluxoid quantization of a Bardeen-Cooper-Schrieffer superconductor. A discussion of the experimental scenarios where this anomalous quantization is expected is provided. Our work demonstrates the importance of variational Ansätze in making a clear connection between the Berry phases of single-particle and many-body wave functions.

Robust Room Temperature Valley Hall Effect of Interlayer Excitons

The Berry curvature in the band structure of transition metal dichalcogenides (TMDs) introduces a valley-dependent effective magnetic field, which induces the valley Hall effect (VHE). Similar to the ordinary Hall effect, the VHE spatially separates carriers or excitons, depending on their valley index, and accumulates them at opposite sample edges. The VHE can play a key role in valleytronic devices, but previous observations of the VHE have been limited to cryogenic temperatures. Here, we report a demonstration of the VHE of interlayer excitons in a MoS₂/WSe₂ heterostructure at room temperature. We monitored the in-plane propagation of interlayer excitons through photoluminescence mapping and observed their spatial separation into two opposite transverse directions that depended on the valley index of the excitons. Our theoretical simulations reproduced the salient features of these observations. Our demonstration of the robust interlayer exciton VHE at room temperature, enabled by their intrinsically long lifetimes, will open up realistic possibilities for the development of opto-valleytronic devices based on TMD heterostructures.

Polariton Anomalous Hall Effect in Transition-Metal Dichalcogenides

We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling, we unveil novel, highly tunable features of the spectrum that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhances the Berry phase of polaritons well beyond that of its elementary constituents, paving the way to achieve a polariton anomalous Hall effect.

Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides

Using the quasiclassical concept of Berry curvature we demonstrate that a Dirac exciton-a pair of Dirac quasiparticles bound by Coulomb interactions-inevitably possesses an intrinsic angular momentum making the exciton effectively self-rotating. The model is applied to excitons in two-dimensional transition metal dichalcogenides, in which the charge carriers are known to be described by a Dirac-like Hamiltonian. We show that the topological self-rotation strongly modifies the exciton spectrum and, as a consequence, resolves the puzzle of the overestimated two-dimensional polarizability employed to fit earlier spectroscopic measurements.

Exciton Hall effect in monolayer MoS2

The spontaneous Hall effect driven by the quantum Berry phase (which serves as an internal magnetic flux in momentum space) manifests the topological nature of quasiparticles and can be used to control the information flow, such as spin and valley. We report a Hall effect of excitons (fundamental composite particles of electrons and holes that dominate optical responses in semiconductors). By polarization-resolved photoluminescence mapping, we directly observed the Hall effect of excitons in monolayer MoS₂ and valley-selective spatial transport of excitons on a micrometre scale. The Hall angle of excitons is found to be much larger than that of single electrons in monolayer MoS₂ (ref. ), implying that the quantum transport of the composite particles is significantly affected by their internal structures. The present result not only poses a fundamental problem of the Hall effect in composite particles, but also offers a route to explore exciton-based valleytronics in two-dimensional materials.

Detection of the Anomalous Velocity with Subpicosecond Time Resolution in Semiconductor Nanostructures

We report on the time-resolved detection of the anomalous velocity, constituting charge carriers moving perpendicular to an electric driving field, in undoped GaAs quantum wells. For this we optically excite the quantum wells with circularly polarized femtosecond laser pulses, thereby creating a state which breaks time-inversion symmetry. We then employ a quasi-single-cycle terahertz pulse as an electric driving field to induce the anomalous velocity. The electromagnetic radiation emitted from the anomalous velocity is studied with a subpicosecond time resolution and reveals intriguing results. We are able to distinguish between intrinsic (linked to the Berry curvature) and extrinsic (linked to scattering) contributions to the anomalous velocity both originating from the valence band and observe local energy space dependence of the anomalous velocity. Our results thus constitute a significant step towards noninvasive probing of the anomalous velocity locally in the full energy-momentum space and enable the investigation of many popular physical effects such as the anomalous Hall effect and spin Hall effect on ultrafast time scales.

Anomalous Light Cones and Valley Optical Selection Rules of Interlayer Excitons in Twisted Heterobilayers

We show that, because of the inevitable twist and lattice mismatch in heterobilayers of transition metal dichalcogenides, interlayer excitons have sixfold degenerate light cones anomalously located at finite velocities on the parabolic energy dispersion. The photon emissions at each light cone are elliptically polarized, with the major axis locked to the direction of exciton velocity, and helicity specified by the valley indices of the electron and the hole. These finite-velocity light cones allow unprecedented possibilities for optically injecting valley polarization and valley current, and the observation of both direct and inverse valley Hall effects, by exciting interlayer excitons. Our findings suggest potential excitonic circuits with valley functionalities, and unique opportunities to study exciton dynamics and condensation phenomena in semiconducting 2D heterostructures.

Berry Phase Modification to the Energy Spectrum of Excitons

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and it highlights the importance of the Berry curvature in the effective mass approximation.

Valley excitons in two-dimensional semiconductors

Monolayer group-VIB transition-metal dichalcogenides have recently emerged as a new class of semiconductors in the two-dimensional limit. The attractive properties include the visible range direct band gap ideal for exploring optoelectronic applications; the intriguing physics associated with spin and valley pseudospin of carriers which implies potentials for novel electronics based on these internal degrees of freedom; the exceptionally strong Coulomb interaction due to the two-dimensional geometry and the large effective masses. The physics of excitons, the bound states of electrons and holes, has been one of the most actively studied topics on these two-dimensional semiconductors, where the excitons exhibit remarkably new features due to the strong Coulomb binding, the valley degeneracy of the band edges and the valley-dependent optical selection rules for interband transitions. Here, we give a brief overview of the experimental and theoretical findings on excitons in two-dimensional transition-metal dichalcogenides, with focus on the novel properties associated with their valley degrees of freedom.

Kondo metal and ferrimagnetic insulator on the triangular kagome lattice

We obtain the rich phase diagrams in the Hubbard model on the triangular kagome lattice as a function of interaction, temperature, and asymmetry by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. The phase diagrams show the asymmetry separates the critical points in the Mott transition of two sublattices on the triangular kagome lattice and produces two novel phases called plaquette insulator with a clearly visible gap and a gapless Kondo metal. When the Coulomb interaction is stronger than the critical value U(c), a short range paramagnetic insulating state, which is a candidate for the short rang resonating valence-bond spin liquid, emerges before the ferrimagnetic order is formed independent of asymmetry. Furthermore, we discuss how to measure these phases in future experiments.

Proposal for a mesoscopic optical berry-phase interferometer

We propose a novel spin-optronic device based on the interference of polaritonic waves traveling in opposite directions and gaining topological Berry phase. It is governed by the ratio of the TE-TM and Zeeman splittings, which can be used to control the output intensity. Because of the peculiar orientation of the TE-TM effective magnetic field for polaritons, there is no analogue of the Aharonov-Casher phase shift existing for electrons.