Coulomb Interaction Of Electrons Research Articles

Correlated insulators and charge density wave states in chirally twisted triple bilayer graphene

Motivated by recent experimental observations of displacement-field-tuned correlated insulators at integer and half-integer fillings in chirally twisted triple bilayer graphene (CTTBG) [Phys.Rev.Lett.132.246501], we study the single-particle and interacting physics of CTTBG. We find that there are two inequivalent stacking orders, i.e., AB-AB-BC and AB-AB-AB, and both exhibit flat bands with nontrivial topology. We then use the Hartree–Fock approximation to calculate the rich phase diagram of CTTBG at all integer and half-integer fillings in both stacking orders and under the vertical displacement field. Under a small displacement field, the groundstates are flavor polarized states for AB-AB-BC stacking order and intervalley coherent states for AB-AB-AB stacking order at all integer and half-integer fillings. A larger displacement field will turn them into layer-polarized states. At half-integer fillings, the groundstates also exhibit charge density wave (CDW) order. For AB-AB-AB stacking, the groundstates at half-integer fillings are always 2 × 1 stripe state among a range of displacement fields. For AB-AB-BC stacking, the groundstates at half-integer fillings are also 2 × 1 stripe states under a small displacement field and a larger displacement will possibly favor further translation-symmetry-breaking, depending on filling and the direction of the displacement field. We demonstrate that the CDW states observed in the experiment can originate from the strong Coulomb interaction of the flat band electrons.

The Computation and Application of Electron Correlation in Solids

Correlated materials are often identified from the strength of the electronic Coulomb interactions. In this brief report, we present a method to quantify the electron interaction in a correlated system, and discuss a few representative examples which actively utilize Coulomb interactions to obtain specific material properties.

Ultralow Auger-Assisted Interlayer Exciton Annihilation in WS2/WSe2 Moiré Heterobilayers.

Transition metal dichalcogenide (TMD) heterobilayers have emerged as a promising platform for exploring solid-state quantum simulators and many-body quantum phenomena. Their type II band alignment, combined with the moiré superlattice, inevitably leads to nontrivial exciton interactions and dynamics. Here, we unveil the distinct Auger annihilation processes for delocalized interlayer excitons in WS2/WSe2 moiré heterobilayers. By fitting the characteristic efficiency droop and bimolecular recombination rate, we quantitatively determine an ultralow Auger coefficient of 1.3 × 10-5 cm2 s-1, which is >100-fold smaller than that of excitons in TMD monolayers. In addition, we reveal selective exciton upconversion into the WSe2 layer, which highlights the significance of intralayer electron Coulomb interactions in dictating the microscopic scattering pathways. The distinct Auger processes arising from spatial electron-hole separation have important implications for TMD heterobilayers while endowing interlayer excitons and their strongly correlated states with unique layer degrees of freedom.

The Role of Plasmasphere in the Formation of Electron Heat Fluxes

AbstractPlasmasphere plays an important role in the magnetospheric physics, defining many important inputs to the ionosphere from the middle to the auroral latitudes. Among them are electron thermal heat fluxes resulting from the Coulomb interaction of superthermal electrons (SE) and cold plasmaspheric electrons. These fluxes define the electron temperature at the upper ionospheric altitudes and are the input to the global ionospheric modeling networks. As was previously found from the calculation of lower energy SE and thermal heat fluxes, the knowledge of field‐aligned cold plasma distribution in the plasmasphere is a very sensitive parameter that introduces the most uncertainties in the calculation of these values. To verify the previously used SuperThermal Electron Transport code assumptions regarding plasmaspheric field‐aligned density structure ∼[B(s)/Bo]a, we used the latest version of 3D plasmaspheric model developed by Pierrard, Botek, and Darrouzet (2021, https://doi.org/10.3389/fspas.2021.681401). Such an assumption is found to be very reasonable in the calculations of electron thermal heat fluxes entering upper ionospheric altitudes and the associated electron temperature formation for the two selected dayside and nightside electron precipitation events driven by whistler‐mode wave activity.

Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies

We present a theoretical investigation of electron heat current in asymmetrical length armchair graphene nanoribbon (AGNR) heterostructures with vacancies, focusing on the topological states (TSs). In particular, we examine the 9-7-9 AGNR heterostructures where the TSs are well-isolated from the conduction and valence subbands. This isolation effectively mitigates thermal noise of subbands arising from temperature fluctuations during charge transport. Moreover, when the TSs exhibit an orbital off-set, intriguing electron heat rectification phenomena are observed, primarily attributed to inter-TS electron Coulomb interactions. To enhance the heat rectification ratio (η Q ), we manipulate the coupling strengths between the heat sources and the TSs by introducing asymmetrical lengths in the 9-AGNRs. This approach offers control over the rectification properties, enabling significant enhancements. Additionally, we introduce vacancies strategically positioned between the heat sources and the TSs to suppress phonon heat current. This arrangement effectively reduces the overall phonon heat current, while leaving the TSs unaffected. Our findings provide valuable insights into the behavior of electron heat current in AGNR heterostructures, highlighting the role of topological states, inter-TS electron Coulomb interactions, and the impact of structural modifications such as asymmetrical lengths and vacancy positioning. These results pave the way for the design and optimization of graphene-based devices with improved thermal management and efficient control of electron heat transport.

Effects of Coulomb Blockade on the Charge Transport through the Topological States of Finite Armchair Graphene Nanoribbons and Heterostructures.

In this study, we investigate the charge transport properties of semiconducting armchair graphene nanoribbons (AGNRs) and heterostructures through their topological states (TSs), with a specific focus on the Coulomb blockade region. Our approach employs a two-site Hubbard model that takes into account both intra- and inter-site Coulomb interactions. Using this model, we calculate the electron thermoelectric coefficients and tunneling currents of serially coupled TSs (SCTSs). In the linear response regime, we analyze the electrical conductance (Ge), Seebeck coefficient (S), and electron thermal conductance (κe) of finite AGNRs. Our results reveal that at low temperatures, the Seebeck coefficient is more sensitive to many-body spectra than electrical conductance. Furthermore, we observe that the optimized S at high temperatures is less sensitive to electron Coulomb interactions than Ge and κe. In the nonlinear response regime, we observe a tunneling current with negative differential conductance through the SCTSs of finite AGNRs. This current is generated by electron inter-site Coulomb interactions rather than intra-site Coulomb interactions. Additionally, we observe current rectification behavior in asymmetrical junction systems of SCTSs of AGNRs. Notably, we also uncover the remarkable current rectification behavior of SCTSs of 9-7-9 AGNR heterostructure in the Pauli spin blockade configuration. Overall, our study provides valuable insights into the charge transport properties of TSs in finite AGNRs and heterostructures. We emphasize the importance of considering electron-electron interactions in understanding the behavior of these materials.

Second Landau level projection of antiholomorphic Pfaffian wave functions

We propose a new state described by the second Landau level (SLL) projection of a generalized Moore-Read Pfaffian wavefunction with an antiholomorphic pairing component. Unlike the PH-Pfaffian state which is described by the lowest Landau level (LLL) projection of the same antiholomorphic Pfaffian wavefunction, we find the proposed state, which we call the SLL PH-Pfaffian, represents a gapped, incompressible phase, and provides an excellent description for the exact ground state of finite-size SLL Coulomb-interacting electrons over a range of the short distance interaction strength. We also find the SLL PH-Pfaffian, when mapped to the LLL, has a very large overlap and the same low-energy orbital entanglement spectrum structures with the anti-Pfaffian state. We discuss possible interpretations of our results on the nature of the topological order of both states.

Theory of coherent optical nonlinearities of intersubband transitions in semiconductor quantum wells

We theoretically study the coherent nonlinear response of electrons confined in semiconductor quantum wells under the effect of an electromagnetic radiation close to resonance with an intersubband transition. Our approach is based on the time-dependent Schr\"odinger-Poisson equation stemming from a Hartree description of Coulomb-interacting electrons. This equation is solved by standard numerical tools and the results are interpreted in terms of approximated analytical formulas. For growing intensity, we observe a redshift of the effective resonance frequency due to the reduction of the electric dipole moment and the corresponding suppression of the depolarization shift. The competition between coherent nonlinearities and incoherent saturation effects is discussed. The strength of the resulting optical nonlinearity is estimated across different frequency ranges from mid-IR to THz with an eye to ongoing experiments on Bose-Einstein condensation of intersubband polaritons and to the speculative exploration of quantum optical phenomena such as single-photon emission in the mid-IR and THz windows.

Evidence of the Coulomb gap in the density of states of MoS2

${\mathrm{MoS}}_{2}$ is an emergent van der Waals material that shows promising prospects in semiconductor industry and optoelectronic applications. However, its electronic properties are not yet fully understood. In particular, the nature of the insulating state at low carrier density deserves further investigation, as it is important for fundamental research and applications. In this study we investigate the insulating state of a dual-gated exfoliated bilayer ${\mathrm{MoS}}_{2}$ field-effect transistor by performing magnetotransport experiments. We observe a positive and nonsaturating magnetoresistance, in a regime where only one band contributes to electron transport. At low electron density ($\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$) and a perpendicular magnetic field of 7 Tesla the resistance exceeds by more than one order of magnitude the zero field resistance and exponentially drops with increasing temperature. We attribute this observation to strong electron localization. Both temperature and magnetic field dependence can, at least qualitatively, be described by the Efros-Shklovskii law, predicting the formation of a Coulomb gap in the density of states due to Coulomb interactions. However, the localization length obtained from fitting the temperature dependence exceeds by more than one order of magnitude the one obtained from the magnetic field dependence. We attribute this discrepancy to the presence of a nearby metallic gate, which provides electrostatic screening and thus reduces long-range Coulomb interactions. The result of our study suggests that the insulating state of ${\mathrm{MoS}}_{2}$ originates from a combination of disorder-driven electron localization and Coulomb interactions.

Electron–hole interaction in cylindrical quantum dots

The Coulomb interaction of electron and hole in a cylindrical quantum dot in the frame of the first perturbation theory and the effective mass approximation is studied. The analogue of Brus’s equation for Coulomb interaction of electron–hole pair in a spherical quantum dot is obtained for a cylindrical nanocrystal and an expression for the energy band gap shift is derived, which can be used for explaining of some experimental results obtained for MoS2 and 3C-SiC nanocrystals.

The density–temperature range of exchange–correlation exciton existence by the fermionic path integral Monte Carlo method

A recently developed fermionic path integral Monte Carlo approach [Filinov et al., Phys. Rev. E 102, 033203 (2020) and Filinov et al., J. Phys. A 55, 035001 (2021)] has been applied for the estimation of the density–temperature range of exchange–correlation exciton existence in a strongly coupled degenerate uniform electron gas. The approach allows us to reduce the “fermionic sign problem” taking into account the interference effects of the Coulomb and exchange interaction of electrons in the basic Monte Carlo cell and its periodic images. Our results for radial distribution functions demonstrate the formation and decay of a short-range quantum ordering of electrons associated with exchange–correlation excitons in the literature. Such excitons have never been observed earlier in standard path integral Monte Carlo simulations.

Spectral response of a microresonator containing a double quantum dot modified by Coulomb interaction of localized electrons

A theoretical model of a semiconductor nanostructure consisting of a single-mode microresonator containing two quantum dots is considered. It is shown that the Coulomb interaction between electrons localized in the quantum dots modifies a spectral response of the system to an external laser field. The possibility of its use for detecting an elementary charge in the third (optically inactive) quantum dot is discussed. The influence of both diagonal (Stark effect) and non-diagonal (Foerster effect) Coulomb matrix elements of the Hamiltonian on the detection accuracy is studied. The dependences of a measuring contrast on the parameters of the resonator and the quantum dots are calculated. The existence of such structural configurations for which the contrast retains an optimal value even at large distances to the measured dot is established. Keywords: quantum dots, microresonators, nanophotonics, semiconductors, laser, measurement

Correlated half-semimetal state in heavy fermion systems

An ideal half-semimetal is characterized by a single spin-polarized electronic relativistic band across the Fermi energy. Realizing such state in the correlated electron systems depends not only on the way the time reversal symmetry breaks, but also on the electron filling and electron correlations. Here we investigate a honeycomb Anderson lattice model in the strong $f$ electron Coulomb interaction limit and with an additional $f$ electron ferromagnetic coupling. A generic phase diagram is presented showing the successive first-order phase transitions from the decoupled local ferromagnetic phase to the heavy fermion ferromagnetic and paramagnetic phases. In particular, the magnetic heavy fermion phase emerges in the intermediate region but with two magnetic states, identified as the ground state or metastable state with small or large spin magnetization, respectively. When the total electron filling is fixed at 3/8, the band crossing of the spin-down polarized channel in the small spin magnetization state locates at the Fermi energy, without the existence of other Fermi surfaces. Such ideal half-semimetal feature is protected by the Kondo gap in the spin-up polarized channel.

Monte Carlo simulations of the electron short-range quantum ordering in Coulomb systems and the ‘fermionic sign problem’

To account for the interference effects of the Coulomb and exchange interactions of electrons the new path integral representation of the density matrix has been developed in the canonical ensemble at finite temperatures. The developed representation allows to reduce the notorious ‘fermionic sign problem’ in the path integral Monte Carlo simulations of fermionic systems. The obtained results for pair distribution functions in plasma and uniform electron gas demonstrate the short-range quantum ordering of electrons associated in literature with exchange-correlation excitons. The charge estimations show the excitonic electric neutrality. Comparison of the internal energy with available ones in the literature demonstrates that the short range ordering does not give noticeable contributions to integral thermodynamic characteristics. This fine physical effect was not observed earlier in the standard path integral Monte Carlo simulations.

Orbital Isotropy of Magnetic Fluctuations in Correlated Electron Materials Induced by Hund's Exchange Coupling.

Characterizing nonlocal magnetic fluctuations in materials with strong electronic Coulomb interactions remains one of the major outstanding challenges of modern condensed matter theory. In this Letter, we address the spatial symmetry and orbital structure of magnetic fluctuations in perovskite materials. To this aim, we develop a consistent multiorbital diagrammatic extension of dynamical mean-field theory, which we apply to an anisotropic three-orbital model of cubic t_{2g} symmetry. We find that the form of spatial spin fluctuations is governed by the local Hund's coupling. For small values of the coupling, magnetic fluctuations are anisotropic in orbital space, which reflects the symmetry of the considered t_{2g} model. Large Hund's coupling enhances collective spin excitations, which mixes orbital and spatial degrees of freedom, and magnetic fluctuations become orbitally isotropic. Remarkably, this effect can be seen only in two-particle quantities; single-particle observables remain anisotropic for any value of the Hund's coupling. Importantly, we find that the orbital isotropy can be induced both at half filling and for the case of four electrons per lattice site, where the magnetic instability is associated with different, antiferromagnetic and ferromagnetic, modes, respectively.

Manifestation of Strongly Correlated Electrons in a 2D Kagome Metal–Organic Framework

Abstract2D and layered electronic materials characterized by a kagome lattice, whose valence band structure includes two Dirac bands and one flat band, can host a wide range of tunable topological and strongly correlated electronic phases. While strong electron correlations have been observed in inorganic kagome crystals, they remain elusive in organic systems, which benefit from versatile synthesis protocols via molecular self‐assembly and metal‐ligand coordination. Here, direct experimental evidence of local magnetic moments resulting from strong electron–electron Coulomb interactions in a 2D metal–organic framework (MOF) is reported. The latter consists of di‐cyano‐anthracene (DCA) molecules arranged in a kagome structure via coordination with copper (Cu) atoms on a silver surface [Ag(111)]. Temperature‐dependent scanning tunneling spectroscopy reveals magnetic moments spatially confined to DCA and Cu sites of the MOF, and Kondo screened by the Ag(111) conduction electrons. By density functional theory and mean‐field Hubbard modeling, it is shown that these magnetic moments are the direct consequence of strong Coulomb interactions between electrons within the kagome MOF. The findings pave the way for nanoelectronics and spintronics technologies based on controllable correlated electron phases in 2D organic materials.

Topological approach to electron correlations at fractional quantum Hall effect

The classification of homotopy invariants in interacting multi-electron 2D systems at quantizing magnetic fields is presented, explaining the topologically protected correlations occurring at integer and fractional quantum Hall effects. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to the binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants, which are universal and robust against local disorder and single-particle crystal field, as illustrated by experimental observations in various materials with different microscopic structure, like GaAs 2DES, graphene monolayer and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to single-particle perturbations, temperature chaos and variation of the electron interaction strength. The nonzero repulsive interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

Strain effect on electronic structure and transport properties of zigzag α-T 3 nanoribbons: a mean-field theoretical study

The α-T 3 lattice, a minimal model that presents flat bands, has sparked much interest in research but the finite-size effect and interaction has been rarely involved. Here we theoretically study the electronic structure and transport properties of zigzag-edge α-T 3 nanoribbons (ZαT 3NRs) with and without uniaxial strain, where the exemplary widths N = 40 and 41 for two series are considered. By adopting the mean-field Hubbard model combined with the nonequilibrium Green’s function method, we show that the spin-degenerate dispersionless flat band at the Fermi energy for the pristine ribbons is split into spin-up and -down flat bands under electron–electron Coulomb interaction. Specifically, the two bands are shifted toward in an opposite direction and away from the Fermi energy, which leads to an energy gap opening in the case of α ≠ 1. All three series of ZαT 3NRs with width N = 3n, 3n + 1, 3n + 2 (where n is a positive integer) exhibit an energy gap. This differs from the simple tight-binding calculations without considering electron–electron Coulomb interaction, for which the gap is always zero in the case of N = 3n + 1. Here, the origin of the energy gap for N = 3n + 1 arises from Coulomb repulsion between electrons. Importantly, the energy gap can be effectively manipulated by an uniaxial strain and Coulomb interaction if α ≠ 1. The gap linearly increases (decreases) when a tensile (compressive) strain increases, and it also monotonously increases as enhancing Coulomb interaction. Interestingly, a ground state of antiferromagnetic to ferromagnetic transition occurs when α increases from 0.8 to 1, leading to a semiconductor to metallic transition. Besides, the α-, strain- and interaction-dependent conductance is also explored. The findings here may be of importance in the band gap engineering and electromechanical applications of α-T 3 nanoribbon-based devices.

Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields.

Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

100-Trillion-Frame-per-Second Single-Shot Compressed Ultrafast Photography via Molecular Alignment

Compressed ultrafast photography (CUP) has the highest imaging speed and sequence depth in capturing ultrafast nonrepeatable or unstable dynamic events with snapshots. However, due to the Coulomb interaction of electrons in a streak camera, it is difficult for the imaging speed of CUP to break the speed limit of ${10}^{12}$ frames/s. Here, we propose a molecular-alignment-assisted CUP (MACUP) scheme by introducing a gas-phase temporal-spatial converter with all-optical deflection imaging into conventional CUP. Based on our simulation of a carbon dioxide molecular deflector, combined with point-spread restrictions in imaging, MACUP is able to achieve an imaging speed beyond 180 \ifmmode\times\else\texttimes\fi{} ${10}^{12}$ frames/s and a sequence depth of about 300 frames in a single exposure. To demonstrate the feasibility of MACUP, we simulate the spatiotemporal intensity measurement of a chirped femtosecond laser pulse and study the image reconstruction accuracy in the intensity and wavelength evolutions. These results show that MACUP is a promising single-shot ultrafast optical imaging strategy to unravel unprecedented dynamics in ultrafast atomic and molecular optics.