States In Monolayer Graphene Research Articles

Collective excitations of fractional quantum Hall states in monolayer graphene

We study the collective excitations of fractional quantum Hall states in graphene. We focus on states which allow for chiral symmetry breaking orders, specifically antiferromagnetism and charge density wave order. We investigate numerically how the collective excitation spectra depend on filling and the flux attachment scheme for two classes of variational states, the T\"oke-Jain sequence and the Modak-Mandal-Sengupta sequence.

Spin and valley ordering of fractional quantum Hall states in monolayer graphene

We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors ${\ensuremath{\nu}}_{G}=\ensuremath{-}2+n/3\phantom{\rule{4pt}{0ex}}(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $\text{SU}(4)$ symmetric limit. For all the fractions we study, there are two-component states for which the competing phases are generalizations of those occurring at neutrality ${\ensuremath{\nu}}_{G}=0$. They are ferromagnetic, antiferromagnetic, charge-density wave, and K\'ekul\'e phases, depending on the values of Ising or $XY$ anisotropies in valley space. The varying spin-valley content of the states leads to ground-state quantum numbers that are different from the ${\ensuremath{\nu}}_{G}=0$ case. For filling factor ${\ensuremath{\nu}}_{G}=\ensuremath{-}2+5/3$, there is a parent state in the $\text{SU}(4)$ limit that has a flavor content $(1,1/3,1/3,0)$ where the two components that are one-third filled form a two-component singlet. The addition of anisotropies leads to the formation of new states that have no counterpart at ${\ensuremath{\nu}}_{G}=0$. While some of them are predicted by the variational approach, we find notably that negative Ising-like valley anisotropy leads to the formation of a state that is a singlet in both spin and valley space and lies beyond the reach of the variational method. Also fully spin polarized two-component states at $\ensuremath{\nu}=\ensuremath{-}2+4/3$ and $\ensuremath{-}2+5/3$ display an emergent $\text{SU}(2)$ valley symmetry because they do not feel point-contact anisotropies. We discuss implications for current experiments concerning possible spin transitions.

Zero energy states in graphene in Aharonov–Bohm magnetic dots via Wirtinger calculus

The properties of zero-energy states in monolayer graphene in the presence of circular step magnetic field profile in Aharonov–Bohm geometry are investigated via Wirtinger calculus. The clear physical arguments used in presented derivation and its simplicity show the advantage of proposed mathematical approach. The variant proof of Aharonov–Casher theorem is presented.

Nanoscale strain engineering of giant pseudo-magnetic fields, valley polarization, and topological channels in graphene.

The existence of nontrivial Berry phases associated with two inequivalent valleys in graphene provides interesting opportunities for investigating the valley-projected topological states. Examples of such studies include observation of anomalous quantum Hall effect in monolayer graphene, demonstration of topological zero modes in "molecular graphene" assembled by scanning tunneling microscopy, and detection of topological valley transport either in graphene superlattices or at bilayer graphene domain walls. However, all aforementioned experiments involved nonscalable approaches of either mechanically exfoliated flakes or atom-by-atom constructions. Here, we report an approach to manipulating the topological states in monolayer graphene via nanoscale strain engineering at room temperature. By placing strain-free monolayer graphene on architected nanostructures to induce global inversion symmetry breaking, we demonstrate the development of giant pseudo-magnetic fields (up to ~800 T), valley polarization, and periodic one-dimensional topological channels for protected propagation of chiral modes in strained graphene, thus paving a pathway toward scalable graphene-based valleytronics.

Explanation of an unexpected occurrence of fractional quantum Hall effect states in monolayer graphene

Recent experiment reveals the appearance of incompressible fractional quantum Hall effect states in monolayer graphene at and , substituting the compressible Hall metal states at these fillings in the lowest Landau level in a narrow magnetic field window depending on the sample parameters. Simultaneously, none such behavior has been observed either for or , . We propose an explanation of these observations in terms of homotopy of monolayer graphene in consistence with a general theory of correlated states in planar Hall systems.

Fast split operator method for computation of time dependent quantum states of bilayer graphene in a magnetic field

A fast split operator method for computing time-dependent quantum states in bilayer graphene in a magnetic field is developed. The method is about an order of magnitude faster than the existing split operator method. It can also be used to compute time-dependent states in monolayer graphene and other systems with a Hamiltonian that depends linearly on momentum. The new method is based on an operator splitting that reduces the cubic order local error that appears in any split operator approximation to the evolution operator. The reduced error allows a larger time step to be used and hence reduces computational cost. The computational cost and accuracy of the existing and new split operator methods are analysed for the test problem of computing the motion of a Landau wave packet in bilayer graphene in crossed electric and magnetic fields. A comparison with the Chebyshev polynomial method is also given.

SO(8) fermion dynamical symmetry and strongly correlated quantum Hall states in monolayer graphene

A formalism is presented for treating strongly-correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle--hole generators. The graphene SO(8) algebra is isomorphic to an SO(8) algebra that has found broad application in nuclear physics, albeit with physically very different generators, and exhibits a strong formal similarity to SU(4) symmetries that have been proposed to describe high-temperature superconductors. The well-known SU(4) symmetry of quantum Hall ferromagnetism for single-layer graphene is recovered as one subgroup of SO(8), but the dynamical symmetry structure associated with the full set of SO(8) subgroup chains extends quantum Hall ferromagnetism and allows analytical many-body solutions for a rich set of collective states exhibiting spontaneously-broken symmetry that may be important for the low-energy physics of graphene in strong magnetic fields. The SO(8) symmetry permits a natural definition of generalized coherent states that correspond to symmetry-constrained Hartree--Fock--Bogoliubov solutions, or equivalently a microscopically-derived Ginzburg--Landau formalism, exhibiting the interplay between competing spontaneously broken symmetries in determining the ground state.

Disorder effects on helical edge transport in graphene under a strong tilted magnetic field

In a recent experiment, Young et al. [Nature {\bf 505}, 528 (2014)] observed a metal to insulator transition as well as transport through helical edge states in monolayer graphene under a strong, tilted magnetic field. Under such conditions, the bulk is a magnetic insulator which can exhibit metallic conduction through helical edges. It was found that two-terminal conductance of the helical channels deviates from the expected quantized value at low-temperatures ($=e^2/h$ per edge, at zero temperature). Motivated by this observation, we study the effect of disorder on the conduction through the edge channels. We show that, unlike the situation in semiconducting quantum wells, a disorder Rashba spin-orbit coupling does not lead to backscattering, at least to leading order. Instead we find the lack of perfect anti-alignment of the electron spins in the helical channels to be the most likely source for backscattering arising from scalar (i.e. spin-independent) impurities. The intrinsic spin-orbit coupling and other time-reversal symmetry breaking and/or sublattice-parity breaking potentials also lead to (sub-leading) corrections to the channel conductance.

Fractional quantum Hall effect in Hofstadter butterflies of Dirac fermions

We report on the influence of a periodic potential on the fractional quantum Hall effect (FQHE) states in monolayer graphene. We have shown that for two values of the magnetic flux per unit cell (one-half and one-third flux quantum) an increase of the periodic potential strength results in a closure of the FQHE gap and appearance of gaps due to the periodic potential. In the case of one-half flux quantum this causes a change of the ground state and consequently the change of the momentum of the system in the ground state. While there is also crossing between low-lying energy levels for one-third flux quantum, the ground state does not change with the increase of the periodic potential strength and is always characterized by the same momentum. Finally, it is shown that for one-half flux quantum the emergent gaps are due entirely to the electron–electron interaction, whereas for the one-third flux quantum per unit cell these are due to both non-interacting electrons (Hofstadter butterfly pattern) and the electron–electron interaction.

Chiral symmetry breaking and the quantum Hall effect in monolayer graphene

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu = 0$ and $\nu = \pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $|\nu|=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $\nu = 0$ and $|\nu| = 1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted.

Localized States at Zigzag Edges of Bilayer Graphene

We report the existence of zero-energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wave functions of these peculiar surface states. It is shown that zero-energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene and (ii) states with a finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.