We study effects of a repulsive Coulomb interaction on the spectral gap in monolayer and bilayer graphene in the vicinity of the charge neutrality point by employing the functional renormalization-group technique. In both cases Coulomb interaction supports the gap once it is open. For monolayer graphene we correctly reproduce results obtained previously by several authors, e.g., an apparent logarithmic divergence of the Fermi velocity and the gap as well as a fixed point corresponding to a quantum phase transition at infinitely large Coulomb interaction. On the other hand, we show that the gap introduces an additional length scale at which renormalization flow of diverging quantities saturates. An analogous analysis is also performed for bilayer graphene with similar results. We find an additional fixed point in the gapless regime with linear spectrum corresponding to the vanishing electronic band mass. This fixed point is unstable with respect to gap fluctuations and can not be reached as soon as the gap is opened. This preserves the quadratic scaling of the spectrum and finite electronic band mass.
In single-layer graphene sheets non-local interband exchange leads to a renormalized Fermi-surface effective mass which vanishes in the low carrier-density limit. We report on a comparative study of Fermi surface effective mass renormalization in single-layer and AB-stacked bilayer graphene. We explain why the mass does not approach zero in the bilayer case, although its value is still strongly suppressed.
High-harmonic generation (HHG) in solids is an emerging method to probe ultrafast electron dynamics in solids at attosecond timescale. In this work, we study HHG from monolayer and bilayer graphene. Bilayer graphenes with AA and AB stacking are considered in this work. It is found that the monolayer and bilayer graphenes exhibit significantly different harmonic spectra. The difference in the spectra is attributed to the interlayer coupling between the two layers. Also, the intraband and interband contributions to the total harmonic spectrum play a significant role. Moreover, interesting polari…
We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe$_2$ reveal the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of…
We investigate the many-body instabilities of electrons interacting near Van Hove singularities arising in monolayer and twisted bilayer graphene. We show that a pairing instability must be dominant over the tendency to magnetic order as the Fermi level is tuned to the Van Hove singularity in the conduction band of graphene. As a result of the extended character of the saddle points in the dispersion, we find that the pairing of the electrons takes place preferentially in a channel of f-wave symmetry, with an order parameter vanishing at the position of the saddle points along the Fermi line. …
Performing a leading-order renormalization group analysis, here we compute the effects of generic local or short-range electronic interactions in monolayer and Bernal bilayer graphene. Respectively in these two systems chiral quasiparticles display linear and biquadratic band touching, leading to linearly vanishing and constant DOS. Consequently, the former system remains stable for weak enough local interactions, and supports a variety of ordered phases only beyond a critical strength of interactions. By contrast, ordered phases can nucleate for sufficiently weak interactions in bilayer graph…
We investigate the electron properties of the monolayer and bilayer silicene which is the honeycomb lattice consist of silicon atoms, including the optical conductivity and charged impurity scattering, due to the quasipatricle Dirac-like behaviors near the K-point of silicene. The spin, valley, sublattice degrees of freedom are taken into consider in the multi-band tight-binding model. In momentum space, the scattering matrix which connects the two bare (without interaction) Green's functions in the quasiparticle momentum transport process, could be momentum-independent for the single impuirit…
We have investigated the Coulomb screening properties and collective excitations in a graphene bilayer. The static screening effect is anisotropic and is much stronger in the undoped graphene bilayer than in a monolayer graphene [1]. The dynamic screening shows the properties of a Dirac gas in the low frequency and that of a Fermi gas in the high frequency. The transition from the Dirac to the Fermi gas is also observed in the plasmon spectrum. Finally, we find that an electron gas in a doped graphene bilayer has quite similar properties as those of a Fermi gas in materials containing two ener…
Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular electric field, which induces topological transitions accompanied by changes of the Chern numbers. In the regime where the applied electric field induces gaps between the flat bands, we find a relatively uniform distribution of the Berry curvature. Consequently, interaction-induced valley- and/or spin-polarized states at integer filling factors are energetic…
Twisted van der Waals heterostructures with flat electronic bands have recently emerged as a platform for realizing correlated and topological states with an extraordinary degree of control and tunability. In graphene-based moiré heterostructures, the correlated phase diagram and band topology depend strongly on the number of graphene layers, their relative stacking arrangement, and details of the external environment from the encapsulating crystals. Here, we report that the system of twisted monolayer-bilayer graphene (tMBG) hosts a variety of correlated metallic and insulating states, as wel…
We report a study of the quantum Hall states (QHSs) sequence of holes in mono- and bilayer WSe$_2$. The QHSs sequence transitions between predominantly even and predominantly odd filling factors as the hole density is tuned in the range $1.6 - 12\times10^{12}$ cm$^{-2}$. The QHSs sequence is insensitive to the transverse electric field, and tilted magnetic field measurements reveal an insensitivity of the QHSs sequence to the in-plane magnetic field, evincing that the hole spin is locked perpendicular to the WSe$_2$ plane. These observations imply that the QHSs sequence is controlled by the Ze…
We build a microscopic model to study the intra- and inter-layer superexchange due to electrons hopping in chromium trihalides ($\mathrm{CrX}_3$, X= Cl, Br, and I). In evaluating the superexchange, we identify the relevant intermediate excitations in the hopping. In our study, we find that the intermediate hole-pairs excitations in the $p$-orbitals on X ion play a crucial role in mediating various types of exchange interactions. In particular, the inter-layer antiferromagnetic exchange may be realized by the hole-pair-mediated superexchange. Interestingly, we also find that these virtual hoppi…
We present a scanning tunneling spectroscopy (STS) study of the local electronic structure of single and bilayer graphene grown epitaxially on a SiC(0001) surface. Low voltage topographic images reveal fine, atomic-scale carbon networks, whereas higher bias images are dominated by emergent spatially inhomogeneous large-scale structure similar to a carbon-rich reconstruction of SiC(0001). STS spectroscopy shows a ~100meV gap-like feature around zero bias for both monolayer and bilayer graphene/SiC, as well as significant spatial inhomogeneity in electronic structure above the gap edge. Nanoscal…
The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. Using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb …
Coulomb drag experiments in which the inter-layer resistivity is measured are important as they provide information on the Coulomb interactions in bilayer systems. When the layer densities are low correlation effects become significant to account for the quantitative description of experimental results. We investigate systematically various models of effective inter-layer interactions in a bilayer system and compare our results with recent experiments. In the low density regime, the correlation effects are included via the intra- and inter-layer local-field corrections. We employ several theor…
We discuss t-J-U model on a honeycomb monolayer that has the same low-energy description of the kinetic term as graphene bilayer, and in particular study coexistence of antiferromagnetism and superconducting correlations that originate from Cooper pairs without phase coherence. We show that the model is relevant for the description of graphene bilayer and that the presence of the d + i d superconducting correlations with antiferromagnetism can lead to quadratic dependence in small magnetic fields of the gap of the effective monolayer consistent with the transport measurements of Velasco et al.…
The number of atomic layers confined in a two-dimensional structure is crucial for the electronic and magnetic properties. Single-layer and bilayer $J_{\rm eff} = 1/2$ square lattices are well-known examples where the presence of the extra layer turns the XY-anisotropy to the $c$-axis anisotropy. We report on experimental realization of a hybrid SrIrO$_3$/SrTiO$_3$ superlattice that integrates monolayer and bilayer square lattices in one layered structure. By synchrotron x-ray diffraction, resonant x-ray magnetic scattering, magnetization, and resistivity measurements, we found that the hybrid…
We perform a general group-theoretical study of the Kondo problem in monolayer and bilayer graphene around the charge neutrality point. Utilizing the group representation theory, we derive from symmetry considerations a family of the Kondo models for all symmetric placements with either 3- or 6-fold rotational axis of an impurity atom in an arbitrary orbital state. We find six possible classes of the partially anisotropic four-channel Kondo model. As the key result, we argue several possibilities to realize the regime of the dominant channel-symmetric two-channel Kondo effect, protected by the…
Nonreciprocal perfect Coulomb drag in electron-hole bilayers: coherent exciton superflow as a diode
Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大李政道研究所与物理与天文学院）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）
By tilting the samples in the magnetic field, we measured and compared the Skyrmion excitations in the bilayer quantum Hall (QH) state at the Landau-level filling factor $ν=2$ and in the monolayer QH state at $ν=1$. The observed number of flipped spins is $N_s=14$ in the bilayer system with a large tunneling gap, and $N_s=7$ in the bilayer system with a small tunneling gap, while it is $N_s=7$ in the monolayer system. The difference is interpreted due to the interlayer exchange interaction. Moreover, we have observed seemingly preferred numbers $N_s=14,7,1$ for the flipped spins by tilting bil…
We find exact analytic expressions for the energies and wavefunctions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of $AA$ and $AB/BA$ tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of…
Flat band moiré superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin 'flavor' symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect (AHE) in correlated metallic states nearby most odd integer fillin…
We investigate the effect of on-site Coulomb repulsion $U$ on the band gap of the electrically gated bilayer graphene by employing coherent potential approximation in the paramagnetic state, based on an ionic two-layer Hubbard model. We find that, while either the on-site Coulomb repulsion $U$ or the external perpendicular electric field $E$ alone will favor a gapped state in the bilayer graphene, competition between them will surprisingly lead to a suppression of the gap amplitude. Our results can be applied to understand the discrepancies of gap size reported from optical and transport measu…
The polarizability of twisted bilayer graphene, due to the combined effect of electron-hole pairs, plasmons, and acoustic phonons is analyzed. The screened Coulomb interaction allows for the for- mation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron-hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among t…
The X-ray edge singularity of bilayer graphene is studied by generalizing the path integral approach based on local action which was employed for monolayer graphene. In sharp contrast to the case of monolayer graphene, the bilayer graphene is found to exhibit the edge singularity even at half-filling and its characteristics are determined by interlayer coupling. At finite bias the singular behaviors sensitively depend on the relative magnitude of fermi energy and applied bias, which is due to the peculiar shape of energy band at finite bias.
In the low-energy two-band as well as four-band continuum models, we study the supercritical instability in gapped bilayer graphene in the field of a charged impurity. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge as the lowest-energy bound state dives into the lower continuum tends to zero as the gap $Δ$ vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for $Δ\to 0$. The different scalings of the kinetic energy of quasiparticl…
We consider the low energy effective field model of graphene monolayer. Coulomb interactions are taken into account. The model is simulated numerically using the lattice discretization with staggered fermions. The two point fermionic Green functions are calculated. We find that in the insulator phase these Green functions almost do not depend on energy. This indicates that the effective field model (in its insulator phase) does not correspond to the real graphene.
We analyze the phase diagram of twisted graphene bilayers near a magic angle. We consider the effect of the long range Coulomb interaction, treated within the self consistent Hartree-Fock approximation, and we study arbitrary band fillings. We find a rich phase diagram, with different broken symmetry phases, although tehy do not show necessarily a gap at the Fermi energy. There are non trivial effects of the electrostatic potential on the shape and the gaps of the bands in the broken symmetry phases. The results suggest that the non superconducting broken symmetry phases observed experimentall…
Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize…
We investigate the interband and intraband transition of the monolayer and AB-stacked bilayer silicene in low-energy tight-binding model under the electric field, where we focus on the dynamical polarization function, screening due to the charged impurity, and the plasmon dispersion. We obtain the logarithmically divergen polarization function within the random-phase-approximation (RPA) whose logarithmic singularities corresponds to the discontinuities of the first derivative which is at the momentum ${\bf q}=2{\bf k}_{F}$ in static case and indicate the topological phase transition point from…
Low-energy electronic structure of (unbiased) bilayer graphene is made of two Fermi points with quadratic dispersions, if trigonal-warping and other high order contributions are ignored. We show that as a result of this qualitative difference from single-layer graphene, short-range (or screened Coulomb) interactions are marginally relevant. We use renormalization group to study their effects on low-energy properties of the system, and show that the two quadratic Fermi points spontaneously split into four Dirac points, at zero temperature. This results in a nematic state that spontaneously brea…
We report neutron inelastic scattering measurements and analysis of the spectrum of magnons propagating within the Fe2O4 bilayers of LuFe2O4. The observed spectrum is consistent with six magnetic modes and a single prominent gap, which is compatible with a single bilayer magnetic unit cell containing six spins. We model the magnon dispersion by linear spin-wave theory and find very good agreement with the domain-averaged spectrum of a spin-charge bilayer superstructure comprising one Fe3+ -rich monolayer and one Fe2+ -rich monolayer. These findings indicate the existence of polar bilayers in L…
