The strong long-range Coulomb interaction between massless Dirac fermions in graphene can drive a semimetal-insulator transition. We show that this transition is strongly suppressed when the Coulomb interaction is screened by such effects as disorder, thermal fluctuation, doping, and finite volume. It is completely suppressed once the screening factor $μ$ is beyond a threshold $μ_{c}$ even for infinitely strong coupling. However, such transition is still possible if there is an additional strong contact four-fermion interaction. The differences between screened and contact interactions are also discussed.
A sufficiently strong Coulomb interaction may open an excitonic fermion gap and thus drive a semimetal-insulator transition in graphene. In this paper, we study the Eliashberg theory of excitonic transition by coupling the fermion gap equation self-consistently to the equation of vacuum polarization function. Including the fermion gap into polarization function increases the effective strength of Coulomb interaction because it reduces the screening effects due to the collective particle-hole excitations. Although this procedure does not change the critical point, it leads to a significant enha…
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link …
The competing ground states of bilayer graphene are studied by applying renormalization group techniques to a bilayer honeycomb lattice with nearest neighbor hopping. In the absence of interactions, the Fermi surface of this model at half-filling consists of two nodal points with momenta $\mathbf{K}$, $\mathbf{K}'$, where the conduction band and valence band touch each other, yielding a semi-metal. Since near these two points the energy dispersion is quadratic with perfect particle-hole symmetry, excitonic instabilities are inevitable if inter-band interactions are present. Using a perturbativ…
We suggest that physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field describes a phase transition connected with the generation of excitonic and spin gaps. The strong-coupling regime is described using a phenomenological model with enhanced Zeeman splitting (spin gap) and excitonic gaps. The experimental form of the Hall conductivity $σ_{xy}$ with the additional $ν= 0, \pm 1$ plateaus is reproduced. The form of $σ_{xy}$ in the case of a strong-coupling regime with no enhanced Zeeman splitting is also discussed.
We predict the formation and superfluidity of polaritons in an optical microcavity formed by excitons in gapped graphene embedded there and microcavity photons. The Rabi splitting related to the creation of an exciton in a graphene layer in the presence of the band gap is obtained. The analysis of collective excitations as well as the sound velocity is presented. We show that the superfluid density and temperature of the Kosterlitz-Thouless phase transition are decreasing functions of the energy gap.
The possibility of excitonic condensation in a recently proposed electrically biased double-layer graphene system is studied theoretically. The main emphasis is put on obtaining a reliable analytical estimate for the transition temperature into the excitonic state. As in a double-layer graphene system the total number of fermionic "flavors" is equal to N=8 due to two projections of spin, two valleys, and two layers, the large-$N$ approximation appears to be especially suitable for theoretical investigation of the system. On the other hand, the large number of flavors makes screening of the bar…
Graphene, a single sheet of graphite with honeycomb lattice structure, has massless carriers with tunable density and polarity. We investigate the ground state phase diagram of two graphene sheets (embedded in a dielectric) separated by distance $d$ where the top layer has electrons and the bottom layer has holes, using mean-field theory. We find that a uniform excitonic condensate occurs over a large range of carrier densities and is weakly dependent on the relative orientation of the two sheets. We obtain the excitonic gap, quasiparticle energy and the density of states. We show that both, t…
We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap $m$ and disorder scattering rate $Γ$, we found a critical line on the plane of interaction strength $λ$ and disorder strength $g$. The phase diagram is divided into two regions: in the region with large $λ$ and small $g$, $m \neq 0$ and $Γ= 0$; in the other region, $m = 0$ and $Γ\neq 0$ for nonzero $g$. In particular, there is no coexistence of finite fermion gap and finite scattering rate. These results imply…
We have considered the AB-stacked bilayer graphene Josephson junction. The bilayers are supposed to be in the charge equilibrium states and at the half-filling in each of the electronic layers of the construction and at each value of the external gate. By considering the interacting bilayers in both sides of the junction and by taking into account both intralayer and interlayer Coulomb interaction effects, we have calculated the normal and excitonic tunnel currents through the junction. The electronic band renormalizations have been taken into account, due to the excitonic pairing effects and …
We investigate the excitonic instability in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for exciton condensation in the ladder approximation, showing that it blows up at a critical value of the interaction strength α= e^2/4πv_F sensitive to further many-body corrections. Under static screening of the interaction, we find that taking into account electron self-energy corrections increases the critical coupling to α_c \approx 2.09, for a number N = 4 of two-component Dirac fermions. We show that the dynamical screenin…
Optical responses in an excitonic insulating (EI) system with strong electron correlation are studied. We adopt the two-orbital Hubbard model with a finite energy difference between the two orbitals where the spin state degree of freedom exists. This model is analyzed by the variational cluster approach. In order to include the local electron correlation effect, the vertex correction is taken into account in the formulation of the optical conductivity spectra. We calculate a finite-temperature phase diagram, in which an EI phase appears between a low-spin band insulating state and a high-spin …
A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta an…
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 …
By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N \leq 15 interacting particles, where the fine structure constant α parametrizes the Coulomb interaction. We explore three different theoretical concepts: (i) Sucher's positive projection ("no-pair") approach, (ii) a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and (i…
We theoretically investigate the possibility of excitonic condensation in a system of two graphene monolayers separated by an insulator, in which electrons and holes in the layers are induced by external gates. In contrast to the recent studies of this system, we take into account the screening of the interlayer Coulomb interaction by the carriers in the layers, and this drastically changes the result. Due to a large number of electron species in the system (two projections of spin, two valleys, and two layers) and to the suppression of backscattering in graphene, the maximum possible strength…
In this paper, we consider the spectral properties of the bilayer graphene with the local excitonic pairing interaction between the electrons and holes. We consider the generalized Hubbard model, which includes both intralayer and interlayer Coulomb interaction parameters. The solution of the excitonic gap parameter is used to calculate the electronic band structure, single-particle spectral functions, the hybridization gap, and the excitonic coherence length in the bilayer graphene. We show that the local interlayer Coulomb interaction is responsible for the semimetal-semiconductor transition…
We analyze the Coulomb interacting problem in undoped graphene layers by using an excitonic variational ansatz. By minimizing the energy, we derive a gap equation which reproduces and extends known results. We show that a full treatment of the exchange term, which includes the renormalization of the Fermi velocity, tends to suppress the phase transition by increasing the critical coupling at which the excitonic instability takes place.
We suggest that physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field describes a phase transition connected with the generation of an excitonic gap. The experimental form of the Hall conductivity is reproduced and the main characteristics of the dynamics are described. Predictions of the behavior of the gap as a function of temperature and a gate voltage are made.
Trilayer graphene is receiving an increasing level of attention due to its stacking--dependent magnetoelectric and optoelectric properties, and its more robust ferromagnetism relative to monolayer and bilayer variants. Additionally, rhombohedral stacked trilayer graphene presents the possibility of easily opening a gap via either an external electric field perpendicular to the layers, or via the application of external strain. In this paper, we consider an external electric field to open a bandgap in rhombohedral trilayer graphene and study the excitonic optical response of the system. This is…
Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy difference corresponding to the crystalline field splitting. The effective model is represented by the spin operators and the pseudo-spin operators for the spin-state degrees of freedom. The ground state phase diagram is analyzed by the mean-field approximation. In addition to the low-spin state and high-spin state phases, two kinds of the exci…
We present the results of the Monte-Carlo simulation of graphene-like statistical model in terms of occupation numbers. We study the problem of the phase transition in graphene to an insulating phase. Only antiferromagnetic order parameter was studied at the moment by means of Hybrid Monte-Carlo process on the hexagonal lattice because of the sign problem for excitonic order parameter in fermionic determinant. Therefore we have studied the possibility of the phase transition to an excitonic phase by means of simplified Monte-Carlo process on the hexagonal lattice. We show that this phase, whic…
We present an $\textit{ab initio}$ study of the excitonic states of a prototypical high-temperature superconductor La$_2$CuO$_4$ and compare them to the isostructural single-layer nickelate La$_2$NiO$_4$. Key difference in the low-energy electronic structure leads to very different excitonic behavior. Excitons in La$_2$CuO$_4$ are delocalized and can freely move in the CuO$_2$ plane without disturbing the antiferromagnetic order. In contrast, in La$_2$NiO$_4$ we find the low-lying excitonic states to be extremely localized, producing a nearly flat dispersion. The theoretically obtained exciton…
Pezzini et al. reported an unconventional mass enhancement in topological nodal line semimetal ZrSiS (Nat. Phys. 14, 178 (2018), whose origin remains puzzling. In this material, strong short-range interactions might induce excitonic particle-hole pairs. Here we study the renormalization of fermion velocities and find that the mass enhancement in ZrSiS can be well understood if we suppose that ZrSiS is close to the quantum critical point between semimetal and excitonic insulator. Near this quantum critical point, the fermion velocities are considerably reduced by excitonic quantum fluctuation, …
In the present paper, we consider the excitonic effects on the single particle normal density of states (DOS) in the bilayer graphene (BLG). The local interlayer Coulomb interaction is considered between the particles on the non-equivalent sublattice sites in different layers of the BLG. We show the presence of the excitonic shift of the neutrality point, even for the noninteracting layers. Furthermore, for the interacting layers, a very large asymmetry in the DOS structure is shown between the particle and hole channels. At the large values of the interlayer hopping amplitude, a large number …
In this work the effects of impurity in various insulating phases of the twisted bilayer graphene (TBG) are studied. The well-accepted continuum model\cite{b} is employed and the local density of states (DOS) is calculated. It is found that insulating phases breaking different symmetries proposed in previous theories\cite{pa,op1,Lee_2019} are distinguishable via the number and properties of in-gap bound state peaks induced by impurities in local DOS. Insulating phases breaking the same previously proposed symmetries can be further classified by the remaining anti-unitary symmetries and disting…
We show that double-layer graphene (DLG), where an external potential induces an charge-imbalance between $n$- and $p$-type layers, is a promising candidate to realize an exciton condensate in equilibrium. To prove this phenomenon experimentally, we suggest to couple two DLG systems, separated by a thin insulating barrier, and measure the excitonic Josephson effect. For this purpose we calculate the ac and dc Josephson currents induced by tunneling excitons and show that the former only occurs when the gate potentials of the DLG systems differ, irrespective of the phase relationship of their e…
In this work, we calculate the optical response and the nonlinear Hall response of twisted bilayer graphene (TBG) in the insulating states. Different insulating states, including spin-valley polarized (SPVP) state, spin-polarized quantum Hall(SPQH) state, spin-polarized valley Hall (SPVH) state, and spin polarized Kramers-intervalley coherence (SPKIVC) state, are considered. We calculate the optical conductivity ($σ_{xx}$) of these four states and we find that the spin-valley polarized state shows a two-peak feature which is different from the other three states. In order to distinguish the ot…
We consider magic-angle twisted bilayer graphene (TBG) at filling $ν=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry, and is stabilized by a hexagonal boron nitride (hBN) substrate. We identify three different types of domain wall, and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moiré systems. We comment on th…
We study the conditions for spontaneously generating an excitonic mass gap due to Coulomb interactions between anisotropic Dirac fermions in uniaxially strained graphene. The mass gap equation is realized as a self-consistent solution for the self-energy within the Hartree-Fock mean-field and static random phase approximations. It depends not only on momentum, due to the long-range nature of the interaction, but also on the velocity anisotropy caused by the presence of uniaxial strain. We solve the nonlinear integral equation self-consistently by performing large scale numerical calculations o…
We perform transport measurements in high quality bilayer graphene pnp junctions with suspended top gates. At a magnetic field B=0, we demonstrate band gap opening by an applied perpendicular electric field, with an On/Off ratio up to 20,000 at 260mK. Within the band gap, the conductance decreases exponentially by 3 orders of magnitude with increasing electric field, and can be accounted for by variable range hopping with a gate-tunable density of states, effective mass, and localization length. At large B, we observe quantum Hall conductance with fractional values, which arise from equilibrat…
Close to charge neutrality, the low-energy properties of high-quality suspended devices based on atomically thin graphene layers are determined by electron-electron interactions. Bernal-stacked layers, in particular, have shown a remarkable even-odd effect with mono- and tri-layers remaining gapless conductors, and bi- and tetra-layers becoming gapped insulators. These observations $-$at odds with the established notion that (Bernal) trilayers and thicker multilayers are semi-metals$-$ have resulted in the proposal of a physical scenario leading to a surprising prediction, namely that even-lay…
Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton condensation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the …
In the present paper, we describe the antiferromagnetic and excitonic correlations in the AA-stacked bilayer graphene. We consider the applied external electric field potential to the structure which leads to the electronic charge imbalance between the layers in the system. By using the generalized two-layer Hubbard Hamiltonian, we consider different particle filling regimes in the layers. We calculate the important energy scales in the system and we establish the conditions for the appearance of the antiferromagnetic order in the system. We consider both large and small Coulomb interaction li…
Motivated by recent experiments, which give strong evidence for an excitonic insulating phase in $\rm TmSe_{0.45}Te_{0.55}$, we developed a scheme to quantitatively construct, for generic two-band models, the phase diagram of an excitonic insulator. As a first application of our approach, we calculated the phase diagram for an effective mass two-band model with long-range Coulomb interaction. The shielded potential approximation is used to derive a generalized gap equation controlling for positive (negative) energy gaps the transition from a semi-conducting (semi-metallic) phase to an insulati…
We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state withou…
Dirac electrons in graphene in the presence of Coulomb interactions of strength $β$ have been shown to display power law behavior with $β$ dependent exponents in certain correlation functions, which we call the mass susceptibilities of the system. In this work, we first discuss how this phenomenon is intimately related to the excitonic insulator transition, showing the explicit relation between the gap equation and response function approaches to this problem. We then provide a general computation of these mass susceptibilities in the ladder approximation, and present an analytical computation…
We present a combined experimental and theoretical study of twisted double bilayer graphene with twist angles between 1° and 1.35°. Consistent with moiré band structure calculations, we observe insulators at integer moiré band fillings one and three, but not two. An applied transverse electric field separates the first moiré conduction band from neighbouring bands, and favors the appearance of correlated insulators at 1/4, 1/2, and 3/4 band filling. Insulating states at 1/4 and 3/4 band filling emerge only in a parallel magnetic field (B_{||}), whereas the resistance at half band filling is we…
We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is $SU(4)$ symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are negle…
We present evidence of a drastic renormalization of the optical conductivity of graphene on SrTiO$_3$ resulting in almost full transparency in the ultraviolet region. These findings are attributed to resonant excitonic effects further supported by \emph{ab initio} Bethe-Salpeter equation and density functional theory calculations. The ($π$,$π$*)-orbitals of graphene and Ti-3\textit{d} $t_{2g}$ orbitals of SrTiO$_3$ are strongly hybridized and the interactions of electron-hole states residing in those orbitals play dominant role in the graphene optical conductivity. These interactions are prese…
We study the quantum criticality of the phase transition between the Dirac semimetal and the excitonic insulator in two dimensions. Even though the system has a semimetallic ground state, there are observable effects of excitonic pairing at finite temperatures and/or finite energies, provided that the system is in proximity to the excitonic insulating transition. To determine the quantum critical behavior, we consider three potentially important interactions, including the Yukawa coupling between Dirac fermions and the excitonic order parameter fluctuation, the long-range Coulomb interaction, …
We studied the unusual Quantum Hall Effect (QHE) near the charge neutrality point (CNP) in high-mobility graphene sample for magnetic fields up to 18 T. We observe breakdown of the delocalized QHE transport and strong increase in resistivities $ρ_{xx},|ρ_{xy}|$ with decreasing Landau level filling for $ν< 2$, where we identify two insulating regimes. For $1 \gtrsim |ν| \gtrsim 1/2$ we find an exponential increase of $ρ_{xx,xy} \sim e^{a(H-H_c)}$ within the range up to several resistance quanta $R_K$, while the Hall effect gradually disappears, consistent with the Hall insulator (HI) with local…
We analyze the dissipative conductance of the zero-plateau quantum Hall state appearing in undoped graphene in strong magnetic fields. Charge transport in this state is assumed to be carried by a magnetic domain wall, which forms by hybridization of two counter--propagating edge states of opposing spin due to interactions. The resulting non--chiral edge mode is a Luttinger liquid of parameter K, which enters a gapped, perfectly conducting state below a critical value K_c\approx 1/2. Backscattering in this system involves spin flip, so that interaction with localized magnetic moments generates …
We investigate electronic transport in dual-gated twisted bilayer graphene. Despite the sub-nanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite inter-layer screening and extract the capacitance between the atomically-spaced layers. …
The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under $\mathcal{PT}$, where $\mathcal{P}$ and $\mathcal{T}$ denote particle-hole conjugation and time reversal, respectively. In contrast, $\mathcal{PT}$-even perturbati…
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is…
Using a combination of ultraviolet-vacuum ultraviolet reflectivity and spectroscopic ellipsometry, we observe a resonant exciton at an unusually high energy of 6.3eV in epitaxial graphene. Surprisingly, the resonant exciton occurs at room temperature and for a very large number of graphene layers $N$$\approx$75, thus suggesting a poor screening in graphene. The optical conductivity ($σ_1$) of resonant exciton scales linearly with number of graphene layer (up to \emph{at least} 8 layers) implying quantum character of electrons in graphene. Furthermore, a prominent excitation at 5.4eV, which is …
This paper (concerning the infinite-mass boundary condition) has been withdrawn by the author. Another, independent study regarding the zigzag boundary condition has appeared in Phys. Rev. B 82, 125419 (2010).
In this paper, the effects of the external transverse magnetic field $B$ (perpendicular to the surface of the layers) on the electronic and excitonic properties are studied in the AA-stacked bilayer graphene (BLG). The effects of the Coulomb interactions and excitonic pairing have been taken into account and analyzed in detail within the bilayer Hubbard model. Both half-filling and partial filling regimes have been taken into account and the magnetic field dependence of a series of physical parameters was found. It is shown that the difference between the average electron concentrations in the…
The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. While there have been many proposals to explain the insulating behaviour, the commensurability at which these states appear suggests that they are Mott insulators. Here we focus on the insulating states with $\pm 2$ electrons or holes with respect to the charge neutrality point. We show that the theoretical expectations for the Mott insulating states are not compatible with the experimentally observed dependence on temperature and magnetic field if,…
Excitonic bound states are characterised by a binding energy $ε_b$ and a single-particle band gap $Δ_b$. This work provides a theoretical description for both strong ($ε_b\simΔ_b$) and weak ($ε_b\llΔ_b$) excitonic bound states, with particular application to biased bilayer graphene. Standard description of excitons is based on a wave function that is determined by a Schrödinger-like equation with screened attractive potential. The wave function approach is valid only in the weak binding regime $ε_b\llΔ_b$. The screening depends on frequency (dynamical screening) and this implies retardation. I…
A recent paper on the insulating state of monolayer WTe2 reported the observation of large oscillations in the conductivity that are periodic in 1/B, resembling quantum oscillations in metals. This remarkable observation has inspired suggestions of exotic physics such as spin-charge separation. We show that a rather more conventional but still nontrivial explanation in terms of gap modulation may be possible in a model of excitonic insulator subject to a magnetic field.
Motivated by the recently experimental reported signatures of the tunable Mott insulating state and superconductivity in an ABC graphene trilayer superlattice, we investigate the charge compressibility, the spin correlation, and the superconducting instability within the Hubbard model on a three-layer honeycomb lattice. It is found that an antiferromagnetically ordered Mott insulator emerges beyond a critical $U_c$ at half-filling, and the electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns in a wide doped region. The effective pairing inte…
