We study the Coulomb-to-dipole transition which occurs when the separation $d$ of an electron-hole bilayer system is varied with respect to the characteristic in-layer distances. An analysis of the classical ground state configurations for harmonically confined clusters with $N\leq30$ reveals that the energetically most favorable state can differ from that of two-dimensional pure dipole or Coulomb systems. Performing a normal mode analysis for the N=19 cluster it is found that the lowest mode frequencies exhibit drastic changes when $d$ is varied. Furthermore, we present quantum-mechanical ground states for N=6, 10 and 12 spin-polarized electrons and holes. We compute the single-particle energies and orbitals in self-consistent Hartree-Fock approximation over a broad range of layer separations and coupling strengths between the limits of the ideal Fermi gas and the Wigner crystal.
We study the Wigner crystal melting in a two dimensional quantum system of particles interacting via the 1/r Coulomb potential. We use quantum Monte Carlo methods to calculate its phase diagram, locate the Wigner crystal region, and analyze its instabilities towards the liquid phase. We discuss the role of quantum effects in the critical behavior of the system, and compare our numerical results with the classical theory of melting, and the microemulsion theory of frustrated Coulomb systems. We find a Pomeranchuk effect much larger then in solid helium. In addition, we find that the exponent fo…
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…
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 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…
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 argue that long-range Coulomb forces convert an isolated (N,N) armchair carbon nanotube into a strongly-renormalized *Luttinger liquid*. At high temperatures, we find anomalous temperature dependences for the interaction and impurity contributions to the resistivity, and similar power-law dependences for the local tunneling density of states. At low temperatures, the nanotube exhibits spin-charge separation, visible as an extra energy scale in the discrete tunneling density of states (for which we give an analytic form), signaling a departure from the orthodox theory of Coulomb blockade.
We have derived the interaction between Jahn-Teller centers due to optical and acoustic phonons. Without Coulomb repulsion the model leads to a global phase separation at low temperature. At long distances Coulomb repulsion always dominates the short range attraction leading to phase separation on a short scale. On the basis of Monte-Carlo simulation of microscopic lattice-gas model we have formulated an effective phenomenological model. In the limit of low density of polarons, phase separation takes place in the form of charged bubbles. In the limit of high density, charge segregation occurs …
Coulomb screening, together with degeneracy, is characteristic of the metallic electron gas. While there is little trace of its effects in transport and noise in the bulk, at mesoscopic scales the electronic fluctuations start to show appreciable Coulomb correlations. Within a strictly standard Boltzmann and Fermi-liquid framework, we analyze these phenomena and their relation to the mesoscopic fluctuation-dissipation theorem, which we prove. We identify two distinct screening mechanisms for mesoscopic fluctuations. One is the self-consistent response of the contact potential in a non-uniform …
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…
The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and 1/r^{12} repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the i…
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 study the inter-valley scattering induced by the Coulomb repulsion as a purely electronic mechanism for the origin of superconductivity in few layers of graphene. The pairing is strongly favored by the presence of van Hove singularities (VHS's) in the density of states (DOS). We consider three different hetherostructures: twisted bilayer graphene (TBG), rhombohedral trilayer graphene (RTG) and Bernal bilayer graphene (BBG). We obtain trends and estimates of the superconducting (SC) critical temperature in agreement with the experimental findings, which might identify the inter-valley Coulom…
Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb inte…
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）
On a lattice model, we study the possibility of existence of gapped broken inversion symmetry phase (GBISP) of electrons with long-range Coulomb interaction in bilayer graphene using both self-consistent Hartree-Fock approximation (SCHFA) and the renormalized-ring-diagram approximation (RRDA). RRDA takes into account the charge-density fluctuations beyond the mean field. While GBISP at low temperature and low carrier concentration is predicted by SCHFA, we show here the state can be destroyed by the charge-density fluctuations. We also present a numerical algorithm for calculating the self-ene…
We implement a self-consistent Hartree-Fock approximation based on a microscopic model in real space, which allows us to consider the interplay between the Hubbard and the extended Coulomb interaction in twisted bilayer graphene at the magic angle. These two interactions tend to favor different symmetry breaking patterns, having therefore complementary roles in the regimes where one or the other dominates. We show that, for sufficiently large values of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic ground state at the charge neutrality point, while at half-filling…
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…
We study the effect of a strong electron-electron (e-e) interaction in a system of two concentric one-dimensional rings with incommensurate areas A_1 and A_2, coupled by a tunnel amplitude. For noninteracting particles the magnetic moment (persistent current) m of the many-body ground state and first excited states is an irregular function of the external magnetic field. In contrast, we show that when strong e-e interactions are present the magnetic field dependence of m becomes periodic. In such a strongly correlated system disorder can only be caused by inter-ring charge fluctuations, contro…
We report a theoretical study of the many-body effects of electron-electron interaction on the ground-state and spectral properties of double-layer graphene. Using a projector-based renormalization method we show that if a finite voltage difference is applied between the graphene layers electron-hole pairs can be formed and---at very low temperatures---an excitonic instability might emerge in a double-layer graphene structure. The single-particle spectral function near the Fermi surface exhibits a prominent quasiparticle peak, different from neutral (undoped) graphene bilayers. Away from the F…
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…
We investigate interaction effects in transport phenomena in bilayer graphene (BLG). For the minimal conductivity in pristine BLG, we find that the conductivity assumes a constant value in the limit $T\to 0$, with the first correction being $\propto \sqrt{T}$. This has to be contrasted from the standard $1/T^2$ in Fermi liquids (neglecting additional logarithms and above all disorder). We furthermore study the Coulomb drag resistivity between two BLGs in the whole range from deep within the Fermi liquid regime all the way to the charge neutrality (CN) point. We find that in the Fermi liquid re…
We derive the renormalization group equations describing all the short-range interactions in bilayer graphene allowed by symmetry and the long range Coulomb interaction. For certain range of parameters, we predict the first order phase transition to the uniaxially deformed gapless state accompanied by the change of the topology of the electron spectrum.
One of the most dominant candidates for the paired quantum Hall (QH) state at filling factor $ν=5/2$ is the Moore-Read (MR) Pfaffian state. A salient problem, however, is that it does not occur exactly at the Coulomb interaction, but rather at a modified interaction, which favors particle-hole symmetry breaking. In an effort to find a better state, in this work, we investigate the possible connection between the paired QH state and the antisymmetrized bilayer ground state, which is inspired by the intriguing identity that the MR Pfaffian state is entirely equivalent to the antisymmetrized proj…
Exciton instability in graphene bilayer systems is studied in the case of a short-ranged Coulomb interaction and a finite voltage difference between the layers. Self-consistent exciton gap equations are derived and solved numerically and analytically under controlled approximation. We obtain that a critical strength of the Coulomb interaction exists for the formation of excitons. The critical strength depends on the amount of voltage difference between the layers and on the inter-layer hopping parameter.
We develop a two stage renormalization group which connects the continuum Hamiltonian for twisted bilayer graphene at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only which is valid at distances much longer than the moire period. In the first stage, the Coulomb interaction renormalizes the Fermi velocity and the interlayer tunnelings in such a way as to suppress the ratio of the same sublattice to opposite sublatice tunneling, hence approaching the so-called chiral limit. In the second stage, the interlayer tunneling is treated non-pe…
Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models taking into account screening from the moire bands left outside the model space. Based on an atomic-scale tight-binding model, we develop a numerically tractable approximation to the polarization function and study its behavior for different twist angles. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadrati…
We study the electronic properties of AA-stacked bilayer graphene in a transverse electric field. The strong on-site Coulomb repulsion stabilizes the antiferromagnetic order in such a system. The antiferromagnetic order is suppressed by the transverse bias voltage, at least partially. The inter-plane Coulomb repulsion and non-zero voltage stabilize an exciton order parameter. The exciton order parameter coexists with the antiferromagnetism and can be as large as several tens of meV for realistic values of the bias voltage and interaction constants. The application of a transverse bias voltage …
We consider a \textit{mass-asymmetric} electron and hole bilayer. Electron and hole Coulomb correlations and electron and hole quantum effects are treated on first princles by path integral Monte Carlo methods. For a fixed layer separation we vary the mass ratio $M$ of holes and electrons between 1 and 100 and analyze the structural changes in the system. While, for the chosen density, the electrons are in a nearly homogeneous state, the hole arrangement changes from homogeneous to localized, with increasing $M$ which is verified for both, mesoscopic bilayers in a parabolic trap and for a macr…
We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such 2D exponentially localized -- yet valley polarized -- Wannier states, centered on the sites of the honeycomb lattice, paying particular attention to maintaining all the unobstructed symmetries. This includes the unitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and the chiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remains topologically obstructed and is not represented in a simple site-to-si…
In the present work, we consider the excitonic effects in the twisted bilayer graphene (tBLG) within the rotated bilayer Hubbard model. Both, intralayer and interlayer Coulomb interactions have been considered and the half-filling condition is imposed for the electronic densities is both layers of the bilayer. We calculate the excitonic pairing gap parameter and the chemical potential for different twist angles and different values of the interlayer Coulomb interaction parameter. Furthermore, we show the appearance of the electronic flat bands in the electronic band structure, mediated by the …
We study how finite size effects may appear when a quantum dot in the Kondo Coulomb blockade regime is embedded into a mesoscopic device with finite wires. These finite size effects appear when the size of the mesoscopic device containing the quantum dot is of the order of the size of Kondo cloud and affect all thermodynamic and transport properties of the Kondo quantum dot. We also generalize our results to the experimentally relevant case where the wires contain several transverse modes/channels. Our results are based on perturbation theory, Fermi liquid theory and slave boson mean field the…
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $ν=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is li…
Using a combination of quantum Monte Carlo simulations, functional renormalization group calculations and mean-field theory, we study the Hubbard model on the Bernal-stacked honeycomb bilayer at half-filling as a model system for bilayer graphene. The free bands consisting of two Fermi points with quadratic dispersions lead to a finite density of states at the Fermi level, which triggers an antiferromagnetic instability that spontaneously breaks sublattice and spin rotational symmetry once local Coulomb repulsions are introduced. Our results reveal an inhomogeneous participation of the spin mo…
In the present paper, the Gutzwiller density functional theory (LDA+G) has been applied to study a bilayer system of LaCoO$_3$ grown along the $(111)$ direction on SrTiO$_3$. The LDA calculations show that there are two nearly flat bands located at the top and bottom of $e_{g}$ bands of Co atoms with the Fermi level crossing the lower one, which is almost half-filled. After including both the spin-orbit coupling and the Coulomb interaction in the LDA+G method, we find that the interplay between spin-orbit coupling and Coulomb interaction stabilizes a very robust ferromagnetic insulator phase w…
Using exact diagonalization in the disc geometry we predict a novel even-odd effect in the Coulomb blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors is analogous to the fluctuations in the relative number difference between the two layers in quantum Hall dro…
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb $U/r$ potential. The studies of models without disorder and spin and including disorder and spin show that the electron solid is formed in two stages, giving rise to an intriguing solid-liquid regime at intermediate couplings
We study excitonic condensation in an electron-hole bilayer system with unequal layer densities at zero temperature. Using mean-field theory we solve the BCS gap equations numerically and investigate the effects of intra-layer interactions. We analyze the stability of the Sarma phase with $\bk,-\bk$ pairing by calculating the superfluid mass density and also by checking the compressibility matrix. We find that with bare Coulomb interactions the superfluid density is always positive in the Sarma phase, due to a peculiar momentum structure of the gap function originating from the singular behavi…
We report the nanoscale imaging of Ti-doped bilayer calcium ruthenates during the Mott metal-insulator transition by microwave impedance microscopy. Different from a typical first-order phase transition where coexistence of the two terminal phases takes place, a new metallic stripe phase oriented along the in-plane crystalline axes emerges inside both the G-type antiferromagnetic insulating state and paramagnetic metallic state. The effect of this electronic state can be observed in macroscopic measurements, allowing us to construct a phase diagram that takes into account the energetically com…
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 study the ground-state structures of identical classical point charges with Coulomb interactions, confined between two symmetric parallel charged walls. For the well understood homogeneous dielectric case with no electrostatic images, the charges evenly condense on the opposite walls, thereby forming a bilayer Wigner crystal; five structures compete upon changing the inter-wall separation. Here, we consider a dielectric jump between the walls and a solvent in which charges are immersed, implying repulsive images. Using recently developed series representations of lattice sums for Coulomb la…
We study the ground state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for the exact Coulombic energies under scrutiny. The complete phase transition scenario --including critical phenomena-- can subsequently be worked out in detail, thereby unifying a rather scattered or contradictory body of literature, hitherto plagued by the inaccuracies inherent to long range interaction potentials.
