Bound states of charges on top of graphene in a magnetic field

Abstract

We show theoretically that in an external magnetic field, like charges on top of graphene monolayer may be mutually attracted to form macromolecules. For this to happen, graphene needs to be in a quantum Hall plateau state with the local chemical potential being between the Landau levels. One or several graphene electron(s) get localized in the middle between charges and provide overscreening of the Coulomb repulsion between the charges. The size of the resulting macromolecules is of the order of the magnetic length (∼10 nm for magnetic field 10 T). The possible stable macromolecules that unit charges can form on graphene in a magnetic field are classified. The binding survives significant temperatures, exceeding the mobility barriers for many ionically bond impurities. The influence of possible lattice-scale effects of valley mixing are discussed. Tuning the doping of graphene or the magnetic field, the binding of impurities can be turned on and off and the macromolecule size may be tuned. This opens the perspective to nanoscopic manipulation of ions on graphene by using magnetic field and gating.

Screening of a charged impurity in graphene in a magnetic field

“…In this regime, the first experimental observation of Landau-level splitting into discrete states due to lifting the orbital degeneracy was reported. This experiment provides a motivation for the present study where, in contrast to the earlier theoretical treatments [27][28][29][30][31][32], the main accent is made on the role of polarization effects.…”

Magnetic Minibands and Electron–Electron Bound States in Ac-Driven Graphene with Space-Modulated Gap

“…It leads to such many-body phenomena as superconductivity and charge-density waves. Study of interactions of Dirac electrons with elementary excitations and tunable impurities had led to the prediction and observation of new effects in the filed of graphenelike materials [18,19,[34][35][36][37][38]. In this context we can point such phenomena as renormalization of Dirac spectrum due to interactions of electrons with lattice vibrations [39,40], effect of the electron-phonon coupling on the magnetooptical conductivity [41], a new structure of magnetophonon resonances determined by the electron-phonon hybrid states formed in the spectrum between the discrete energy levels (Landau levels) appearing in graphene in the strong magnetic field [42,43], effect of the electron-electron interaction on the graphene resistance and magnetoresistance [44,45], etc.…”

“…In this context we can point such phenomena as renormalization of Dirac spectrum due to interactions of electrons with lattice vibrations [39,40], effect of the electron-phonon coupling on the magnetooptical conductivity [41], a new structure of magnetophonon resonances determined by the electron-phonon hybrid states formed in the spectrum between the discrete energy levels (Landau levels) appearing in graphene in the strong magnetic field [42,43], effect of the electron-electron interaction on the graphene resistance and magnetoresistance [44,45], etc. In [38] the emergence of macromolecules due to the screening of Coulomb repulsion between impurity charges in graphene had been investigated. This screening was provided by the strong magnetic field which localized electrons between impurities so theirs binding could be tuned on or tuned off by magnetic field intensity changing.…”

“…This screening was provided by the strong magnetic field which localized electrons between impurities so theirs binding could be tuned on or tuned off by magnetic field intensity changing. Such mechanism of charge bound states had been offered in [38] to manipulate the macro-molecules size.…”

The properties of strong couple bound polaron in monolayer graphene

“…The result that the binding survives the high temperatures has been argued. Which opens the perspective to nanoscopic manipulation of ions on graphene by using macroscopic tools [7]. The key properties of cloaked states in circularly symmetric potentials have been discussed, and cloaking should be observable in quantum corral geometries via scanning tunneling probe measurements [8].…”