We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electron-electron interaction, split into two (levels) associated with a "bond ordering" formation having a "Kekule pattern", which respects the chiral symmetry. Since the Kekule pattern has a three-fold degeneracy, domain structures are implied, for which we show that in-gap states localized along the domain boundaries exist as topological states. Based on this a possibility of a quantum-liquid ground state of graphene in magnetic fields is discussed.
We have studied the interplay of an Anderson impurity in Landau quantized graphene, with special emphasis on the influence of the chemical potential. Within the slave-boson mean-field theory, we found reentrant Kondo behaviour by varying the chemical potential or gate voltage. Between Landau levels, the density of states is suppressed, and by changing the graphene's Fermi energy, we cross from metallic to semiconducting regions. Hence, the corresponding Kondo behaviour is also influenced. The f-level spectral function reveals both the presence of Landau levels in the conduction band and the Ko…
We consider the interplay between the antiferromagnetic and Kekulé valence bond solid orderings in the zero energy Landau levels of neutral monolayer and bilayer graphene. We establish the presence of Wess-Zumino-Witten terms between these orders: this implies that their quantum fluctuations are described by the deconfined critical theories of quantum spin systems. We present implications for experiments, including the possible presence of excitonic superfluidity in bilayer graphene.
The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding filling factors $ν=$0, 1, 2, & 3. Measurements of the activation energy gap in tilted magnetic fields suggest that the Landau level splitting at the newly formed $ν=$1, 2, & 3 filling factors are independent of spin, consistent with the formation of a quantum Hall ferromag…
The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is dominated by the non-relativistic second Landau level wave function, by tuning the magnetic field a topological quantum phase transition from an Abelian composite fermion to a non-Abelian parton fractional quantum Hall state can be induced at filling factors $1/2, ~2/5$ and $3/7$. The parton states host exotic anyons that can potentially be utilized to store an…
We present magneto-Raman scattering studies of electronic inter Landau level excitations in quasi-neutral graphene samples with different strengths of Coulomb interaction. The band velocity associated with these excitations is found to depend on the dielectric environment, on the index of Landau level involved, and to vary as a function of the magnetic field. This contradicts the single-particle picture of non-interacting massless Dirac electrons, but is accounted for by theory when the effect of electron-electron interaction is taken into account. Raman active, zero-momentum inter Landau leve…
Trilayer graphene in the fractional Quantum Hall Effect regime displays a set of unique interaction-induced transitions that can be tuned entirely by the applied bias voltage. These transitions occur near the anti-crossing points of two Landau levels. In a large magnetic field ($> 8$ T) the electron-electron interactions close the anti-crossing gap, resulting in some unusual transitions between different Landau levels. For the filling factor $ν=\frac23$, these transitions are accompanied by a change of spin polarization of the ground state. For a small Zeeman energy, this provides an unique op…
We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest Landau level. Employing a supersymmetric technique, we calculate the exact density of states for the Cauchy (Lorentzian) distribution for various types of disorders. We use a numerical technique to establish the localization-delocalization (LD) transition in the lowest Landau level. For some types of disorder the LD transition is shown to belong to a different universality class, as compared to the correspon…
We study many-body ground states for the partial integer fillings of the $N=1$ Landau level in graphene, by constructing a model that accounts for the lattice scale corrections to the Coulomb interactions. Interestingly, in contrast to the $N=0$ Landau level, this model contains not only pure delta function interactions but also some of its derivatives. Due to this we find several important differences with respect to the $N=0$ Landau level. For example at quarter filling when only a single component is filled, there is a degeneracy lifting of the quantum hall ferromagnets and ground states wi…
At the charge neutral point, graphene exhibits a very unusual high resistance metallic state and a transition to a complete insulating phase in a strong magnetic field. We propose that the current carriers in this state are the charged vortices of the XY valley pseudospin order-parameter, a situation which is dual to a conventional thin superconducting film. We study energetics and the stability of this phase in the presence of disorder.
We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.
We have investigated tunneling current through a suspended graphene Corbino disk in high magnetic fields at the Dirac point, i.e. at filling factor $ν$ = 0. At the onset of the dielectric breakdown the current through the disk grows exponentially before ohmic behaviour, but in a manner distinct from thermal activation. We find that Zener tunneling between Landau sublevels dominates, facilitated by tilting of the source-drain bias potential. According to our analytic modelling, the Zener tunneling is strongly affected by the gyrotropic force (Lorentz force) due to the high magnetic field
We describe a technique which allows a direct measurement of the relative Fermi energy in an electron system using a double layer structure, where graphene is one of the two layers. We illustrate this method by probing the Fermi energy as a function of density in a graphene monolayer, at zero and in high magnetic fields. This technique allows us to determine the Fermi velocity, Landau level spacing, and Landau level broadening in graphene. We find that the N=0 Landau level broadening is larger by comparison to the broadening of upper and lower Landau levels.
We study RKKY interactions for magnetic impurities on graphene in situations where the electronic spectrum is in the form of Landau levels. Two such situations are considered: non-uniformly strained graphene, and graphene in a real magnetic field. RKKY interactions are enhanced by the lowest Landau level, which is shown to form electron states binding with the spin impurities and add a strong non-perturbative contribution to pairwise impurity spin interactions when their separation $R$ no more than the magnetic length. Beyond this interactions are found to fall off as $1/R^3$ due to perturbati…
We perform a systematic {\it ab initio} study of the work function and its uniform strain dependence for graphene and silicene for both tensile and compressive strains. The Poisson ratios associated with armchair and zigzag strains are also computed. Based on these results, we obtain the deformation potential, crucial for straintronics, as a function of the applied strain. Further, we propose a particular experimental setup with a special strain configuration that generates only the electric field, while the pseudomagnetic field is absent. Then, applying a real magnetic field, one should be ab…
We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and the strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν=-1, -4/3, -5/3, -8/5, -1/2, and discuss the nature of their ground states, collective excitations, and relation to the more familiar states in GaAs using a tractable model. In particular, we present evidence that the ν=-1/2 state, which was recently reported experimentally, is non-Abelian, and described by either the Moore-…
The quantum Hall (QH) effect in two-dimensional (2D) electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors $ν=0,\pm 1,\pm 4$ are discovered at magnetic fields $B>$20 T, indicating the lifting of the four-fold degeneracy of the previously observed QH states at $ν=\pm(|n|+1/2)$, where $n$ is the Landau level index. In particular, the presence of the $ν=0, \pm 1$ QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effec…
We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat…
We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wavevectors $\pm {\bf q^{*}}$. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, which suggests an instability toward a charge density wave. A symmetry broken stripe phase is formed at large system size limit, which is robust against purturbation from disorder scattering. Such a quantum phase is experimentally observable throug…
We study the collective modes of the quantum Hall states in undoped bilayer graphene in a strong perpendicular magnetic and electric field. Both for the well-known ferromagnetic state that is relevant for small electric field $E_\perp$ and the analogous valley/layer polarized one suitable for large $E_\perp$, the low energy physics is dominated by magnetoexcitons with zero angular momentum that are even combinations of excitons that conserve Landau orbitals. We identify a long wave length instability in both states, and argue that there is an intermediate range of the electric field $E^{(1)}_\…
In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed.
In this proceedings paper we report on a calculation of graphene's Landau levels in a magnetic field. Our calculations are based on a self-consistent Hartree-Fock approximation for graphene's massless-Dirac continuum model. We find that because of graphene's chiral band structure interactions not only shift Landau-level energies, as in a non-relativistic electron gas, but also alter Landau level wavefunctions. We comment on the subtle continuum model regularization procedure necessary to correctly maintain the lattice-model's particle hole symmetry properties.
The degeneracy of Landau levels flanking charge neutrality in twisted bilayer graphene is known to change from eight-fold to four-fold when the twist angle is reduced to values near the magic angle of $\approx 1.05^\circ$. This degeneracy lifting has been reproduced in experiments by multiple groups, and is known to occur even in devices which do not harbor the correlated insulators and superconductors. We propose $C_3$ symmetry breaking as an explanation of such robust degeneracy lifting, and support our proposal by numerical results on the Landau level spectrum in near-magic-angle twisted bi…
Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the properties of magnetoexcitons and magnetoplasmons - elementary electron-hole excitations in graphene in quantizing magnetic field. We show that, at small enough background dielectric screening, the mixing lead…
Layer stacking and crystal lattice symmetry play important roles in the band structure and the Landau levels of multilayer graphene. ABA-stacked trilayer graphene possesses mirror-symmetry-protected monolayer-like and bilayer-like band structures. Broken mirror symmetry by a perpendicular electric field therefore induces hybridization between these bands and various quantum Hall phases emerge. We experimentally explore the evolution of Landau levels in ABA-stacked trilayer graphene under electric field. We observe a variety of valley and orbital dependent Landau level evolutions. These evoluti…
Graphene, with its massless linearly-dispersing carriers, in the quantum Hall regime provides an instructive comparison with conventional two-dimensional (2D) systems in which carriers have a nonzero band mass and quadratic dispersion. We investigate the influence of Landau level mixing in graphene on Wigner crystal states in the $n^\mathrm{th}$ Landau level obtained using single Landau level approximation. We show that the Landau level mixing does not qualitatively change the phase diagram as a function of partial filling factor $ν$ in the $n^\mathrm{th}$ level. We find that the inter-Landau …
In a magnetic field graphene trilayers support a characteristic multiplet of 12 zero(-energy)-mode Landau levels with a threefold degeneracy in Landau orbitals. It was earlier noted for bilayer graphene that Coulombic vacuum fluctuations, specific to graphene, lift the orbital degeneracy of such zero-energy modes and that these Lamb-shfted" orbital modes, with filling, get mixed via the Coulomb interaction. It is pointed out that analogous orbital Lamb shift and mixing of zero-mode levels can also take place, with an enriched symmetry content, in ABC-stacked trilayer graphene; and its conseque…
Density of states (DOS) of graphene under a high uniform magnetic field and white-noise random potential is numerically calculated. The disorder broadened zero-energy Landau band has a Gaussian shape whose width is proportional to the random potential variance and the square root of magnetic field. Wegner-type calculation is used to justify the results.
The electronic spectrum of three coupled graphene layers (graphene trilayers) is investigated in the presence of an external magnetic field. We obtain analytical expressions for the Landau level spectrum for both the ABA and ABC - type of stacking, which exhibit very different dependence on the magnetic field. The effect of layer asymmetry and of external gate voltages can strongly influence the properties of the system.
We study the relaxation dynamics of the electron system in graphene flakes under Landau quantization regime using a novel approach of time-resolved Raman scattering. The non-resonant character of the experiment allows us to analyze the field dependence of the relaxation rate. Our results clearly evidence sharp increase in the relaxation rate upon the resonance between the energy of the Landau transition and the G-band and shed new light on relaxation mechanism of the Landau-quantized electrons in graphene beyond the previously studied Auger scattering.
Recent studies show that the electronic structures of graphene can be modified by strain and it was predicted that strain in graphene can induce peaks in the local density of states (LDOS) mimicking Landau levels (LLs) generated in the presence of a large magnetic field. Here we report scanning tunnelling spectroscopy (STS) observation of nine strain-induced peaks in LDOS at 77 K along a graphene ridge created when the graphene layer was cleaved from a sample of highly oriented pyrolytic graphite (HOPG). The energies of these peaks follow the progression of LLs of massless 'Dirac fermions' (DF…
Magnetotransport measurements are performed in ultraclean (lithographically patterned) graphene nanoribbons down to 70 nm. At high magnetic fields, a fragmentation of the electronic spectrum into a Landau levels pattern with unusual features is unveiled. The singular Landau spectrum reveals large magneto-oscillations of the Fermi energy and valley degeneracy lifting. Quantum simulations suggest some disorder threshold at the origin of mixing between opposite chiral magnetic edge states and disappearance of quantum Hall effect.
Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate $k^{3/2}$ dispersion. We speculate on the possibility of unususal localization physics associated with these modes.
We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different ave…
A single graphene layer exhibits an anomalous Landau level spectrum. A massless Dirac like low energy electronic spectrum underlies this anomaly. We study, analytically and numerically, the effect of a uniform electric field $(E)$ on the anomalous Landau levels. We solve the problem exactly within the Dirac cone approximation and find an interesting scaling of the spectrum, leading to the collapse of the Landau levels at a critical $E_c(B)$, for a given magnetic field $B$. We offer a physical interpretation of our result, which uses `graphene relativity' and the boost operation. Electric field…
We study nonlinear optical response of Landau quantized graphene to an intense electromagnetic wave. In particular, we consider high harmonic generation process. It is shown that one can achieve efficient generation of high harmonics with strong radiation fields -- when the work of the wave electric field on the magnetic length is larger than pump photon energy. At that high harmonics generation process takes place for a wide range of the pump wave frequencies and intensities even for significant broadening of Landau levels because of impurities in graphene.
The zero-energy Landau level of bilayer graphene is shown to be anomalously sharp (delta-function like) against bond disorder as long as the disorder is correlated over a few lattice constants.The robustness of the zero-mode anomaly can be attributed to the preserved chiral symmetry. Unexpectedly, even when we apply a finite potential difference (i.e., an electric field) between the top and the bottom layers, the valley-split $n=0$ Landau levels remain anomalously sharp although they are now shifted away from the zero energy, while the $n=1$ Landau levels exhibit the usual behavior.
We observed broken-symmetry quantum Hall effects and level crossings between spin- and valley- resolved Landau levels (LLs) in Bernal stacked trilayer graphene. When the magnetic field was tilted with respect to sample normal from $0^{\circ}$ to $66^\circ$, the LL crossings formed at intersections of zeroth and second LLs from monolayer-graphene-like and bilayer-graphene-like subbands, respectively, exhibited a sequence of transitions. The results indicate the LLs from different subbands are coupled by in-plane magnetic fields ($B_{\parallel}$), which was explained by developing the tight-bind…
In [Phys. Rev. Lett. vol. 119, p. 133901 (2017)] it was argued that two parallel graphene layers in the presence of electron drift support unstable plasmon modes. Here we show that the predicted plasmon instability is an artifact of errors upon evaluation of graphene polarizability in the presence if electron drift. Crucial role of broken Galilean invariance and spatial dispersion of conductivity for suppression of plasmon instabilities is highlighted.
We demonstrate the use of a quantum transport model to study heavily graded graphene p-n junctions in the quantum Hall regime. A combination of p-n interface roughness and delta function disorder potential allows us to compare experimental results on different devices from the literature. We find that wide p-n junctions suppress mixing of $n \neq 0$ Landau levels. Our simulations spatially resolve carrier transport in the device, for the first time, revealing separation of higher order Landau levels in strongly graded junctions, which suppresses mixing.
Precise infrared magnetotransmission experiments have been performed in magnetic fields up to 32 T on a series of multilayer epitaxial graphene samples. We observe changes in the spectral features and broadening of the main cyclotron transition when the incoming photon energy is in resonance with the lowest Landau level separation and the energy of a K point optical phonon. We have developed a theory that explains and quantitatively reproduces the frequency and magnetic field dependence of the phenomenon as the absorption of a photon together with the simultaneous creation of an intervalley, i…
We report on polarization selection rules of inter-Landau level transitions using reflection-type optical Hall effect measurements from 600 to 4000 cm-1 on epitaxial graphene grown by thermal decomposition of silicon carbide. We observe symmetric and anti-symmetric signatures in our data due to polarization preserving and polarization mixing inter-Landau level transitions, respectively. From field-dependent measurements we identify that transitions in decoupled graphene mono-layers are governed by polarization mixing selection rules, whereas transitions in coupled graphene mono-layers are gove…
Heterostructures formed between two different van der Waals materials enable interactions and functionalities absent in each component. In this work we show that vicinity to an atomically thin WSe$_2$ sheet dramatically impacts the energies of the symmetry-broken low Landau levels of bilayer graphene, possibly due to screening. We present a systematic study of the magnetic field and electrical displacement field dependences of the Landau level gaps at filling factor $ν$ = 1, 2, 3, and compare to BN encapsulated pristine bilayer graphene. The exchange-dominated energy splitting between the N = …
In inhomogeneously strained graphene, low-energy electrons experience a valley-antisymmetric pseudo-magnetic field which leads to the formation of localized states at the edge between the valence and conduction bands, understood in terms of peculiar n=0 pseudo-magnetic Landau levels. Here we show that such states can manifest themselves as an isolated quadruplet of low-energy conductance resonances in a suspended stretched graphene ribbon, where clamping by the metallic contacts results in a strong inhomogeneity of strain near the ribbon ends.
We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.
We show that valley degeneracy in rotationally faulted multilayer graphene may be broken in the presence of a magnetic field and interlayer commensurations. This happens due to a simultaneous breaking of both time-reversal and inversion symmetries leading to a splitting of Landau levels linear in the field. Our theoretical work is motivated by an experiment [Y. J. Song et al., Nature 467, 185 (2010)] on epitaxially grown multilayer graphene where such linear splitting of Landau levels was observed at moderate fields. We consider both bilayer and trilayer configurations and, although a linear s…
We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moiré superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magneti…
It is quite easy to control spin polarization and spin direction of a system via magnetic fields. However, there is no such a direct and efficient way to manipulate valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. The pseudomagnetic fields, which are quite different from real magnetic fields, pointing in opposite directions at the two distinct valleys of graphene. Therefore, coexistence of the pseudomagnetic fie…
In the presence of strong magnetic fields the electronic bandstructure of graphene drastically changes. The Dirac cone collapses into discrete non-equidistant Landau levels, which can be externally tuned by changing the magnetic field. In contrast to conventional materials, specific Landau levels are selectively addressable using circularly polarized light. Exploiting these unique properties, we propose the design of a tunable laser operating in the technologically promising terahertz spectral range. To uncover the many-particle physics behind the emission of light, we perform a fully quantum …
We present the results of an experimental study of the interaction of quantized Landau level (LL) edge-states at the physical edge of graphene by using a graphene pn junction device with a ring-shaped geometry for the channel. The unique device geometry allows the interactions between edge-states to be probed at both electrostatic edges defined by pn junctions and at the graphene physical edge. Measurements show that while the lowest LL edge-state is decoupled from the other LLs along the electrostatic junction, all the edge-states strongly equilibrate at the graphene physical edge despite the…
If bilayer graphene is placed in a high perpendicular magnetic field, several quantum Hall plateaus are observed at low enough temperatures. Of these, the $σ_{xy}=4ne^2/h$ sequence ($n\neq0$) is explained by standard Landau quantization, while the other integer plateaus arise due to interactions. The low-energy excitations in both cases are magnetoexcitons, whose dispersion relation depends on single- and many-body effects in a complicated manner. Analyzing the magnetoexciton modes in bilayer graphene, we find that the mixing of different Landau level transitions not only renormalizes them, bu…
Here we address the concerns of Svintsov and Ryzhii [arXiv:1812.03764] on our article on negative Landau damping in graphene [Phys. Rev. Lett. 119, 133901 (2017)]. We prove that due to the differences between the kinetic and canonical momenta, the conductivity of drift-current biased graphene is ruled by a Galilean transformation when the electron-electron interactions predominate and force the electron gas to move with constant velocity, similar to a moving medium. Furthermore, it is shown that the nonlocal effects in graphene neither preclude a negative Landau damping nor the emergence of in…
Broadening of the Landau levels in graphene and the associated quantum Hall plateau-to-plateau transition are investigated numerically. For correlated bond disorder, the graphene-specific n=0 Landau level of the Dirac fermions becomes anomalously sharp accompanied by the Hall transition exhibiting a fixed-point-like criticality. Similarly anomalous behavior for the n=0 Landau level is also shown to occur in correlated random magnetic fields, which suggests that the anomaly is generic to disorders that preserve the chiral symmetry.
We investigate the charge carrier dynamics in bilayer graphene subject to monochromatic laser irradiation within the Landau level quantization regime. Even though the radiation field does not lift the energy degeneracy of the lowest Landau levels (LLs), it nevertheless has a strong effect on the photoinduced pseudospin polarization response for higher LLs ($n\ge2$). Our results show that the photoinduced bandgaps lead to a finite response of the averaged pseudospin polarization with nontrivial oscillating behavior. It is shown that the contribution from these higher LL transitions turns out to…
The quantum Hall states of graphene have a filled Dirac sea of Landau levels. The short ranged SU(4) symmetry breaking interactions can induce a staggered polarization of the sea of Dirac-Landau levels. We study this effect in the extended Hubbard model on a honeycomb lattice using mean field variational wavefunctions. We find a valley symmetry broken, anti-ferromagnetic spin ordered phase at $ν=\pm 1$ when the on-site interaction is dominant. Our mean field solution is consistent with the recently reported experimental results of Z. Jiang et. al.\cite{jiang}
Electronic structure of graphene monolayer-bilayer junction in a magnetic field is studied within an effective-mass approximation. The energy spectrum is characterized by interface Landau levels, i.e., the locally flat bands appearing near the boundary region, resulting in a series of characteristic peaks in the local density of states. Their energies are independent of boundary types such as zigzag or armchair. In the atomic scale, the local density of states shows a Kekulé pattern due to the valley mixing in the armchair boundary, while does not in the zigzag boundary.
We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the $N=0$ and 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest-order in the parameter $κ= \frac{e^2/ε\ell}{\hbar v_F/\ell}=\frac{e^2}{εv_F\hbar}$ which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the $N=0$ Landau level for $κ\lesssim 2$. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to t…
We predict the general feasibility and demonstrate the specific design of the THz laser operating between Landau levels in graphene placed on a polar substrate in a magnetic field of order 1 T. Steady state operation under a continuous wave optical pumping is possible due to an interplay between Auger and surface-phonon mediated relaxation of carriers. The scheme is scalable to other materials with massless Dirac fermions, for example surface states in 3D topological insulators such as Bi$_2$Se$_3$ or Bi$_2$Te$_3$.
In a magnetic field bilayer graphene supports an octet of zero-energy Landau levels with an extra twofold degeneracy in Landau orbitals n=0 and n=1. It is shown that this orbital degeneracy is lifted due to Coulombic quantum fluctuations of the valence band (the Dirac sea); this is a quantum effect analogous to the Lamb shift in the hydrogen atom. A detailed study is made of how these zero-energy levels evolve, with filling, into a variety of pseudo-zero-mode Landau levels in the presence of possible spin and valley breaking and Coulomb interactions, and a comparison is made with experimental …
