Electron-electron Coulomb Interaction Research Articles

Low-temperature electrical transport properties of La doped BaSnO<sub>3</sub> films

A series of Ba<sub>0.94</sub>La<sub>0.06</sub>SnO<sub>3</sub> thin films are deposited on MgO(001) single crystal substrates by RF magnetron sputtering method, and their structure and electrical transport properties are systematically investigated. All films reveal degenerate semiconductor (metal) characteristics in electrical transport properties. In the high-temperature region (<inline-formula><tex-math id="M8">\begin{document}$T > {T_{\min }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M8.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M9">\begin{document}${T_{\min }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M9.png"/></alternatives></inline-formula> is the temperature at which the resistivity reaches a minimum value), the resistivity of each film increases with temperature, and exhibits a linear relationship with the square of the temperature. In the low-temperature region (<inline-formula><tex-math id="M10">\begin{document}$T < {T_{\min }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M10.png"/></alternatives></inline-formula>), the resistivity increases with decreasing temperature and varies linearly with <inline-formula><tex-math id="M11">\begin{document}$ \ln T $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M11.png"/></alternatives></inline-formula>. This temperature dependent behavior of resistivity cannot be explained by the general electron-electron interaction or weak localization effects in homogeneous disordered conductors and nor by Kondo effect. After quantitative analysis, it is found that the <inline-formula><tex-math id="M12">\begin{document}$ \ln T $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M12.png"/></alternatives></inline-formula> behavior of resistivity at low temperatures can be explained by the electron-electron Coulomb interaction effect in the presence of granularity. In addition, it is found that the Hall coefficient <inline-formula><tex-math id="M13">\begin{document}$ {R_{\text{H}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M13.png"/></alternatives></inline-formula> also varies linearly with <inline-formula><tex-math id="M14">\begin{document}$ \ln T $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231082_M14.png"/></alternatives></inline-formula> for the Ba<sub>0.94</sub>La<sub>0.06</sub>SnO<sub>3</sub> film, which also quantitatively accords with the theoretical prediction of the electron-electron Coulomb interaction effects in the granular metals. The results of cross-section high-resolution transmission electron microscope indicate that although the films have epitaxial structures as a whole, there are many strip-shaped amorphous regions in films, which makes the films have electrical transport properties similar to those of metal granular films. Our results provide strong support for the validity of the theory concerning the effects of Coulomb interaction on the conductivity and Hall coefficient in granular metals.

Regulating Singlet-Triplet Energy Gaps through Substituent-Driven Modulation of the Exchange and Coulomb Interactions.

Control of the singlet-triplet energy gap (ΔEST) is central to realizing productive energy conversion reactions, photochemical reaction trajectories, and emergent applications that exploit molecular spin physics. Despite this, no systematic methods have been defined to tune ΔEST in simple molecular frameworks, let alone by an approach that also holds chromophore size and electronic structural parameters (such as the HOMO-LUMO gap) constant. Using a combination of molecular design, photophysical and potentiometric experiments, and quantum chemical analyses, we show that the degree of electron-electron repulsion in excited singlet and triplet states may be finely controlled through the substitution pattern of a simple porphyrin absorber, enabling regulation of relative electronically excited singlet and triplet state energies by the designed restriction of the electron-electron Coulomb (J) and exchange (K) interaction magnitudes. This approach modulates the ΔEST magnitude by controlling the densities of state in the occupied and virtual molecular orbital manifolds, natural transition orbital polarization, and the relative contributions of one electron transitions involving select natural transition orbital pairs. This road map, which regulates electron density overlaps in the occupied and virtual states that define the singlet and triplet wave functions of these chromophores, enables new approaches to preserve excitation energy despite intersystem crossing.

Revisiting homogeneous electron gas in pursuit of properly normed ab initio Eliashberg theory

We address an issue of how to accurately include the self energy effect of the screened electron-electron Coulomb interaction in the phonon-mediated superconductors from first principles. In the Eliashberg theory for superconductors, self energy is usually decomposed using the $2\times 2$ Pauli matrices in the electron-hole space. We examine how the diagonal ($\sigma_{0}$ and $\sigma_{3}$) components resulting in the quasiparticle correction to the normal state, $Z$ and $\chi$ terms, behave in the homogeneous electron gas in order to establish a norm of treating those components in real metallic systems. Within the $G_{0}W_{0}$ approximation, we point out that these components are non-analytic near the Fermi surface but their directional derivatives and resulting corrections to the quasiparticle velocity are nevertheless well defined. Combined calculations using the $G_{0}W_{0}$ approximation and Eliashberg equations show us that the effective mass and pairing strength strikingly depend on both $Z$ and $\chi$, in a different manner. The calculations without the numerically demanding $\chi$ term is thus shown to be incapable of describing the homogeneous electron gas limit. This result poses a challenge to accurate first-principles Eliashberg theory.

Variable range hopping conduction mechanisms in reduced rutile TiO2

In this study, obtained samples via reducing Rutile TiO2 by Mg are analyzed to determine the titanium suboxide phases and the dominant structural phase in each sample. By increasing the heat treatment temperature or the amount of reducing agent (Mg), the amount of suboxide phases Ti n O2n−1 (1 ≤ n < 10) with the lower n values increases, and TiO is the main phase in the samples with a low electrical resistivity. The hopping conduction mechanism is also investigated in the temperature range of 11.5–300 K, and the characteristic parameters describing the conduction mechanism are determined and discussed. For samples with a low electrical resistivity, the nearest neighbor hopping (NNH) conduction mechanism governs the charge transport properties below 220 K, and a transition from the NNH to the Mott-variable range hopping (VRH) conduction regimes is observed at ∼65 K. In addition, the Efros-Shklovskii (ES)-VRH conduction process governs at low temperatures below 18 K, and the last crossover from the Mott-VRH to the ES-VRH models illustrates the strong electron-electron Coulomb interaction, which leads to the Coulomb gap (∼1 meV) at low temperatures. According to the obtained hopping parameters, the low resistivity samples are close to the metal-insulator transition. For samples with a high electrical resistivity, the hopping conduction relations are not fitted to the resistivity-temperature curves, and probably it is related to the resistive switching behavior of the material, which changes the nature and conductivity properties, and is depicted in the current-voltage (I-V) curve.

Electronic and magnetic properties of many-electron complexes in charged InAsxP1−x quantum dots in InP nanowires

We present here a microscopic theory of electronic complexes in charged $\mathrm{In}{\mathrm{As}}_{x}{\mathrm{P}}_{1\ensuremath{-}x}$ quantum dots in InP nanowires with a hexagonal cross section and determine the potential use of an array of such quantum dots as a synthetic spin chain for the possible construction of a topological qubit. The single-particle energies and wave functions are obtained by diagonalizing a microscopic atomistic tight-binding Hamiltonian of multiple quantum dots in the basis of $s{p}^{3}{d}^{5}{s}^{*}$ local atomic orbitals for a given random distribution of arsenic (As) vs phosphorus (P) atoms. The conduction band electronic states are found grouped into $s, p$, and $d$ quantum dot shells. For a double dot, the electronic shells can be understood in terms of interdot tunneling despite the random distribution of As atoms in each quantum dot. The single- and double-dot structures were charged with a finite number of electrons. The many-body Hamiltonian including Coulomb electron-electron interactions was constructed using single atomistic particle states and then diagonalized in the space of many-electron configurations. For a single dot filled with ${N}_{e}=1--7$ electrons, the ground state of a half-filled $p$-shell configuration with ${N}_{e}=4$ was found with total electronic spin $S=1$. The low-energy spectrum obtained using exact diagonalization of a Hamiltonian of a charged double dot filled with ${N}_{e}=8$ electrons, i.e., half-filled $p$ shells in each dot, was successfully fitted to the Hubbard-Kanamori and antiferromagnetic Heisenberg spin-1 Hamiltonians. The atomistic simulation confirmed the potential of InAsP/InP quantum dots in a nanowire for the design of synthetic spin chains.

Role of the rare-earth doping on the multiferroic properties of BaTiO3: First-principles calculation

Ab-initio spin-polarized Density Functional Theory plusU is used to study the electronic and magnetic properties of tetragonal doped barium titanate (Ba1-xEuxO3) system for different Europium concentrations. The Projector Augmented Wave (PAW) method and a Perdew-Zunger (LSDA) approximation, which has been used for the exchange correlation energy, have been considered taking into account a supercell model. The spin polarization as well as the Hubbard's potential have been used for the correction of the electron-electron Coulomb interactions in the rare-earth ions partially filled f-orbitals. The electronic bands-structure reveals that the band-gap energy as well as the dielectric properties decreases with the increase of the doping concentration. The modern theory of polarization also shows that the spontaneous electric polarization increases with the increase of the Europium content, whereas the states-density reveals ferromagnetic characteristics (with non-zero total magnetization), without an applied magnetic field, for the Ba1-xEuxO3 system.

Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition

We aim to understand how the spectrum of semi-Dirac fermions is renormalized due to long-range Coulomb electron-electron interactions at a topological Lifshitz transition, where two Dirac cones merge. At the transition, the electronic spectrum is characterized by massive quadratic dispersion in one direction, while it remains linear in the other. We have found that, to lowest order, the unconventional log squared (double logarithmic) correction to the quasiparticle mass in bare perturbation theory leads to resummation into strong mass renormalization in the exact full solution of the perturbative renormalization group equations. This behavior effectively wipes out the curvature of the dispersion and leads to Dirac cone restoration at low energy: the system flows towards Dirac dispersion which is anisotropic but linear in momentum, with interaction-depended logarithmic modulation. The Berry phase associated with the restored critical Dirac spectrum is zero - a property guaranteed by time-reversal symmetry and unchanged by renormalization. Our results are in contrast with the behavior that has been found within the large-$N$ approach.

Charge localization crossover from Mott to Efros-Shklovskii type variable range hopping mechanism in In1−xPbxTe compounds

We have investigated the electrical transport properties of the In1−xPbxTe compounds. Small Pb-doping is not incorporated in the In-site but randomly distributed in the matrix, found from the X-ray diffraction and elemental mapping by energy-dispersive X-ray spectroscopy measurements. The random distribution of Pb elements induces robust charge localization at low temperatures causing the variable range hopping (VRH) transport. The electrical resistivity ρ(T) of pristine InTe exhibits semiconducting to metal transition near 175 K. From the analysis of temperature exponent, we found that the VRH transport is changed from Mott to Efros-Shklovskii (ES) type with decreasing temperature, where the crossover temperatures are found as 14.4 K (x=0.01) and 13.36 (x=0.02), respectively. The magnetoresistance (MR) of the InTe shows that the weak antilocalization at low temperature (T≤3 K) and low magnetic field (H≤1 T) competes with weak localization with increasing temperature (T≥5 K). It is noteworthy that small Pb-doping exhibits unconventional negative MR (NMR) behavior because it is not a magnetic or topological material. The unconventional NMR behavior of Pb-doped compounds is attributed to the quantum mechanical interference under the magnetic field in ES type VRH transport. The charge localization crossover from Mott to ES type VRH transport mechanism suggests the strong electron-electron Coulomb interaction in the compounds, leading to the significant change of density of states and inducing the Coulomb gap at low temperatures.

Chiral excitonic instability of two-dimensional tilted Dirac cones

The electron-electron Coulomb interaction in Dirac-Weyl semimetals harbours a novel paradigm of correlation effects that hybridizes diverse realms of solid-state physics with their relativistic counterpart. Driving spontaneous mass acquisition, the excitonic condensate of strongly-interacting massless Dirac fermions is one such example whose exact nature remains debated. Here, by focussing on the two-dimensional tilted Dirac cones in the organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$, we show that the excitonic instability is controlled by a small chemicalpotential shift and an in-plane magnetic field. In combined analyses based on renormalization-group approaches and ladder approximation, we demonstrate that the nuclear relaxation rate is an excellent probe of excitonic-spin fluctuations in an extended parameter region. Comparative nuclear magnetic resonance (NMR) experiments show good agreements with this result, jointly revealing the importance of intervalley nesting between field-induced, spin-split Fermi pockets of opposite charge polarities. Our work provides an accurate framework to search for excitonic instability of strongly-interacting massless fermions.

A basis-set error correction based on density-functional theory for strongly correlated molecular systems

We extend to strongly correlated molecular systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner et al., J. Chem. Phys. 149, 194301 (2018)]. This basis-set correction relies on a mapping between wave-function calculations in a finite basis set and range-separated DFT (RSDFT) through the definition of an effective non-divergent interaction corresponding to the electron-electron Coulomb interaction projected in the finite basis set. This enables the use of RSDFT-type complementary density functionals to recover the dominant part of the short-range correlation effects missing in this finite basis set. To study both weak and strong correlation regimes, we consider the potential energy curves of the H10, N2, O2, and F2 molecules up to the dissociation limit, and we explore various approximations of complementary functionals fulfilling two key properties: spin-multiplet degeneracy (i.e., independence of the energy with respect to the spin projection Sz) and size consistency. Specifically, we investigate the dependence of the functional on different types of on-top pair densities and spin polarizations. The key result of this study is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin polarization without any significant loss of accuracy. Quantitatively, we show that the basis-set correction reaches chemical accuracy on atomization energies with triple-ζ quality basis sets for most of the systems studied here. In addition, the present basis-set incompleteness correction provides smooth potential energy curves along the whole range of internuclear distances.

Quantum simulation of electron Coulomb interactions

We review a strategy to use an ion-based analog quantum simulator to study the many-body electron-electron Coulomb interaction of an electron gas. This is made possible by an exact unitary dilatation mapping, which allows an experimentally challenging system to be replaced by an alternative one that may be experimentally more accessible. We show the feasibility of this simulation strategy mathematically. As a bonus, the dilatation transformation does not even need to be physically implemented when only the system spectrum is needed, in which case the simulation induces no experimental complexity overhead. This proposal is dimension-agnostic, and could be generalized as a simulation strategy between systems involving terms with different position or momentum dependence.

Low-temperature MnBi alloys: Electronic and magnetic properties, constitution, morphology and fabrication (Review article)

The article reviews the rich phenomena of physical properties of MnBi. The diverse phenomena include strong spin-orbit interaction, anomalous temperature dependence of the coercivity and the magneto-crystalline anisotropy field, unique magneto-optical properties. Issues addressed include the nature of the electronic ground states of MnBi, the electronic and magnetic structures, Fermi surface, magneto-crystalline anisotropy, x-ray magnetic dichroism. The discussion includes key experiments, such as optical and magneto-optical spectroscopic measurements, de Haas-van Alphen (dHvA) measurements, x-ray photoemission and x-ray absorption spectroscopy measurements as well as x-ray magnetic circular dichroism. The effect of the spin-orbit (SO) interaction and Coulomb repulsion U were found to be crucial for the Fermi surface, cyclotron masses, magneto-optical properties, and x-ray magnetic circular dichroism. The microscopic origin of unique magneto-crystalline anisotropy and giant Kerr effect in MnBi is analyzed in detail. The huge Kerr effect in MnBi is caused by the combination of a sizable magnetic moment on manganese, the large spin-orbit coupling of bismuth, and a strong hybridization between the manganese 3d and the bismuth 6p states. The magneto-optically active states are mainly the 6p states of Bi. We show that the observed temperature dependence of the magneto-crystalline anisotropy can be explained taking into account the spin-orbit interaction together with strong Coulomb electron-electron interaction. The SO coupling of Bi is equally responsible for the large magneto-crystalline anisotropy energy as is the exchange splitting of Mn. The fabrication, morphology, and constitution of low-temperature MnBi alloys in bulk, thin films, and nanoparticles are discussed. The nanocomposite permanent magnetic materials based on MnBi, (Co, Fe) and Nd2Fe14B are also discussed.

Magnetotransport in under and optimally hole-doped bulk nanocrystalline [formula omitted] manganites

Electrical-transport and magneto-transport in bulk nanocrystalline (BNC) La1-xCaxMnO3+δ (x = 1/8 with either δ = 0.00 or δ = 0.06, x = 3/8 with δ = 0.00) (LCMO) manganite system have been studied treating the bulk crystalline (BC) counterparts as the reference systems. Irrespective of the value of δ in under hole-doped (x = 1/8) LCMO, the metal-insulator (M-I) transition (not observed in the BC counterpart) appears at a temperature TMI≪TC, where TC is the temperature at which the ferromagnetic (FM)–paramagnetic (PM) second-order phase transition occurs. Oxygen off-stoichiometry makes the M-I transition more pronounced and reduces the overall magnitude of resistivity. Reducing the average crystallite size d below 150 nm, lowers both TMI and TC in the BNC samples with x = 1/8 and δ = 0.00 or 0.06 but decreases TMI while increasing TC in the optimally hole-doped x = 3/8 LCMO. The single-orbital double-exchange model, which predicts the coincidence, or otherwise, of the M-I and FM-PM transitions with some success in the BC LCMO, fails to correctly describe the above-mentioned results in BNC LCMO. The resistivity minima at low temperatures (Tmin), completely absent in BC, occur in BNC LCMO, regardless of the value of x,δ,d and the strength of the magnetic field (H). The mechanism for resistivity, ρ(T), changes from the adiabatic small polaron nearest-neighbor hopping (for x = 3/8) or from the Shklovskii-Efros variable range hopping, SE-VRH, (for x = 1/8), prevalent in BC, to the Mott-VRH in the PM insulating state in the BNC counterparts when d falls below 150 nm. At T < Tmin, the contributions due to the Mott-VRH (present only in the samples with x = 1/8 and δ = 0.00 or δ = 0.06) and the enhanced electron-electron Coulomb interaction (in all the BNC LCMO samples) are responsible for the negative temperature coefficient of resistivity (TCR). By contrast, the coherent electron-magnon scattering accounts for the positive TCR observed at T > Tmin. H suppresses the mean hopping energy difference between the hopping sites but increases the electron localization length. The field-induced enhancement in the localization length far outweighs the field-induced drop in the mean hopping energy difference to produce an increase in the mean hopping distance with H.

Many-body effect of mesoscopic localized states in MoS2 monolayer

Transition metal dichalcogenide monolayers provide an emerging material system to implement quantum photonics with intrinsic two-dimensional excitons or embedded zero-dimensional localized states. Here we demonstrate the mesoscopic localized states between two- and zero- dimensions, which is a many-body system with electron-electron Coulomb interactions. A fine structure splitting is observed, which is similar to quantum dots. Meanwhile the polarization is changed by the magnetic field, due to the nature of two-dimensional monolayers. Furthermore, a large quadratic diamagnetism with a coefficient of around $100\ \mathrm{\mu eV/T^2}$ is observed, as a unique consequence of the mesoscopic scale. The many-body effect also results in the emission energy variation and linewidth narrowing in the spectrum, which corresponds well to the theoretical analysis. These unique properties indicate the great potential of mesoscopic localized states in many-body physics and quantum photonics.

Multicomponent density functional theory with density fitting.

Multicomponent Density Functional Theory (MDFT) is a promising methodology to incorporate nuclear quantum effects, such as zero-point energy or tunneling, or to simulate other types of particles such as muons or positrons using particle densities as basic quantities. As for standard electronic DFT, a still ongoing challenge is to achieve the most efficient implementations. We introduce a multicomponent DFT implementation within the framework of auxiliary DFT, focusing on molecular systems comprising electrons and quantum protons. We introduce a dual variational procedure to determine auxiliary electron and proton densities which leads to a succession of approximate energy expressions. Electronic and protonic fitted densities are employed in (i) electron-electron, proton-proton, and electron-proton classical Coulomb interactions and (ii) electron exchange-correlation, proton-proton exchange, and electron-proton correlation (EPC) potentials. If needed, exact exchange among electrons or among protons is computed by the variational fitting of the corresponding Fock potential. The implementation is carried out in deMon2k. We test various electron proton correlation functionals on proton affinities. We find that auxiliary densities can be safely used in electron-electron, proton-proton, and electron-proton classical Coulomb interactions, as well as in EPC, albeit with some precautions related to the choice of the electronic auxiliary basis set that must be flexible enough. Computational tests reported indicate that introduction of density fitting in MDFT is clearly advantageous in terms of computational effort with good scaling properties with respect to the number of electrons and protons treated at the DFT level.

Diffuson contribution to anomalous Hall effect in disordered Co2FeSi thin films

A wide variation in the disorder strength, as inferred from an order of magnitude variation in the longitudinal resistivity of Co2FeSi (CFS) Huesler alloy thin films of fixed (50 nm) thickness, has been achieved by growing these films on Si(111) substrates at substrate temperatures ranging from room temperature (RT) to 600 C. An in-depth study of the influence of disorder on anomalous Hall resistivity,longitudinal resistivity(LR) and magnetoresistance, enabled by this approach, reveals the following. The side-jump mechanism gives a dominant contribution to anomalous Hall resistivity (AHR) in the CFS thin films, regardless of the degree of disorder present. A new and novel contribution to both LR and AHR characterized by the logarithmic temperature dependence at temperatures below the minimum, exclusive to the amorphous CFS films, originates from the scattering of conduction electrons from the diffusive hydrodynamic modes associated with the longitudinal component of magnetization, called diffusons. In these amorphous CFS films, the electron-diffuson, e d, scattering and weak localization (WL) mechanisms compete with that arising from the inelastic electron magnon, e m, scattering to produce the minimum in longitudinal resistivity, whereas the minimum in AHR is caused by the competing contributions from the e d and e m scattering, as WL does not make any contribution to AHR. In sharp contrast, in crystalline films, enhanced electron electron Coulomb interaction (EEI), which is basically responsible for the resistivity minimum, makes no contribution to AHR with the result that AHR does not exhibit a minimum.

Strain and screening: Optical properties of a small-diameter carbon nanotube from first principles

Carbon nanotubes (CNTs) are a one-dimensional material system with intriguing physical properties that lead to emerging applications. While CNTs are unusually strain resistant compared to bulk materials, their optical-absorption spectrum is highly strain dependent. It is an open question, as to what extent this is attributed to strain-dependent (i) electronic single-particle transitions, (ii) dielectric screening, or (iii) atomic geometries including CNT radii. We use cutting-edge theoretical spectroscopy to explain strain-dependent electronic structure and optical properties of an (8,0) CNT. Quasiparticle effects are taken into account using Hedin's GW approximation and excitonic effects are described by solving a Bethe-Salpeter-equation for the optical polarization function. This accurate first-principles approach allows us to identify an inuence of strain on screening of the Coulomb electron-electron interaction and to quantify the impact on electronic structure and optical absorption of one-dimensional systems. We interpret our thoroughly converged results using an existing scaling relation and extend the use of this relation to strained CNTs: We show that it captures optical absorption with satisfactory accuracy, as long as screening, quasiparticle gap, and effective electron and hole masses of the strained CNT are known.

Elastic response of the electron fluid in intrinsic graphene: The collisionless regime

The elastic response of an electron fluid at finite frequencies is defined by the electron viscosity $\eta(\omega)$. We determine $\eta(\omega)$ for graphene at the charge neutrality point in the collisionless regime, including the leading corrections due to the electron-electron Coulomb interaction. We find interaction corrections to $\eta(\omega)$ that are significantly larger if compared to the corresponding corrections to the optical conductivity. In addition, we find comparable contributions to the dynamic momentum flux due to single-particle and many-particle effects. We also demonstrate that $\eta(\omega)$ is directly related to the nonlocal energy-flow response of graphene at the Dirac point. The viscosity in the collisionless regime is determined with the help of the strain generators in the Kubo formalism. Here, the pseudo-spin of graphene describing its two sublattices plays an important role in obtaining a viscosity tensor that fulfills the symmetry properties of a rotationally symmetric system.

Hierarchy of information scrambling, thermalization, and hydrodynamic flow in graphene

We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, $\lambda_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.

Phase Transitions of the Polariton Condensate in 2D Dirac Materials.

For the quantum well in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon (e-ph) coupling can lead to the hybridizations of the exciton and the cavity photon known as polaritons, which can form the Bose-Einstein condensate above a threshold density. Additional physics due to the nontrivial Berry phase comes into play when the quantum well consists of the gapped two-dimensional Dirac material such as the transition metal dichalcogenide MoS_{2} or WSe_{2}. Specifically, in forming the polariton, the e-ph coupling from the optical selection rule due to the Berry phase can compete against the Coulomb electron-electron (e-e) interaction. We find that this competition gives rise to a rich phase diagram for the polariton condensate involving both topological and symmetry breaking phase transitions, with the former giving rise to the quantum anomalous Hall and the quantum spin Hall phases.