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We study the effect of electron interaction on the spin-splitting and the $g$-factor in graphene in perpendicular magnetic field using the Hartree and Hubbard approximations within the Thomas-Fermi model. We found that the $g$-factor is enhanced in comparison to its free electron value $g=2$ and oscillates as a function of the filling factor $ u $ in the range $2leq g^{ast}lesssim 4$ reaching maxima at even $ u $ and minima at odd $ u $. We outline the role of charged impurities in the substrate, which are shown to suppress the oscillations of the $g^{ast}$-factor. This effect becomes especially pronounced with the increase of the impurity concentration, when the effective $g$-factor becomes independent of the filling factor reaching a value of $g^{ast}approx 2.3$. A relation to the recent experiment is discussed.
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Dirac electrons in graphene are to lowest order spin 1/2 particles, owing to the orbital symmetries at the Fermi level. However, anisotropic corrections in the $g$-factor appear due to the intricate spin-valley-orbit coupling of chiral electrons. We resolve experimentally the $g$-factor along the three orthogonal directions in a large-scale graphene sample. We employ a Hall bar structure with an external magnetic field of arbitrary direction, and extract the effective $g$-tensor via resistively-detected electron spin resonance. We employ a theoretical perturbative approach to identify the intrinsic and extrinsic spin orbit coupling and obtain a fundamental parameter inherent to the atomic structure of $^{12}$C, commonly used in ab-initio models.
We investigate the electron transport through a graphene p-n junction under a perpendicular magnetic field. By using Landauar-Buttiker formalism combining with the non-equilibrium Green function method, the conductance is studied for the clean and disordered samples. For the clean p-n junction, the conductance is quite small. In the presence of disorders, it is strongly enhanced and exhibits plateau structure at suitable range of disorders. Our numerical results show that the lowest plateau can survive for a very broad range of disorder strength, but the existence of high plateaus depends on system parameters and sometimes can not be formed at all. When the disorder is slightly outside of this disorder range, some conductance plateaus can still emerge with its value lower than the ideal value. These results are in excellent agreement with the recent experiment.
Impurities are unavoidable during the preparation of graphene samples and play an important role in graphenes electronic properties when they are adsorbed on graphene surface. In this work, we study the electronic structures and transport properties of a two-terminal zigzag graphene nanoribbon (ZGNR) device whose scattering region is covered by various adsorbates within the framework of the tight-binding approximation, by taking into account the coupling strength $gamma$ between adsorbates and carbon atoms, the adsorbate concentration $n_i$, and the on-site energy disorder of adsorbates. Our results indicate that when the scattering region is fully covered by homogeneous adsorbates, i.e., $n_i=1$, a transmission gap opens around the Dirac point and its width is almost proportional to $gamma^2$. In particular, two conductance plateaus of $G=2e^2/h$ appear in the vicinity of the electron energy $E=pm gamma$. When the scattering region is partially covered by homogeneous adsorbates ($0<n_i<1$), the transmission gap still survives around the Dirac point even at low $n_i$, and its width is firstly increased by $n_i$ and then declined by further increasing $n_i$; whereas the conductance decreases with $n_i$ in the regime of low $n_i$ and increases with $n_i$ in the regime of high $n_i$. While in the presence of disordered adsorbates whose on-site energies are random variables characterized by the disorder degree, the transmission gap disappears at low $n_i$ and reappears at relatively high $n_i$. Furthermore, the transmission ability of the ZGNR device can be enhanced by the adsorbate disorder when the disorder degree surpasses a critical value, contrary to the localization picture that the conduction of a nanowire becomes poorer with increasing the disorder degree. The physics underlying these transport characteristics is discussed. Our results are in good agreement with experiments.
We report a systematic study on strong enhancement of spin-orbit interaction (SOI) in graphene driven by transition-metal dichalcogenides (TMDs). Low temperature magnetotoransport measurements of graphene proximitized to different TMDs (monolayer and bulk WSe$_2$, WS$_2$ and monolayer MoS$_2$) all exhibit weak antilocalization peaks, a signature of strong SOI induced in graphene. The amplitudes of the induced SOI are different for different materials and thickness, and we find that monolayer WSe$_2$ and WS$_2$ can induce much stronger SOI than bulk ones and also monolayer MoS$_2$. The estimated spin-orbit (SO) scattering strength for the former reaches $sim$ 10 meV whereas for the latter it is around 1 meV or less. We also discuss the symmetry and type of the induced SOI in detail, especially focusing on the identification of intrinsic and valley-Zeeman (VZ) SOI via the dominant spin relaxation mechanism. Our findings offer insight on the possible realization of the quantum spin Hall (QSH) state in graphene.
The search of new means of generating and controlling topological states of matter is at the front of many joint efforts, including bandgap engineering by doping and light-induced topological states. Most of our understading, however, is based on a single particle picture. Topological states in systems including interaction effects, such as electron-electron and electron-phonon, remain less explored. By exploiting a non-perturbative and non-adiabatic picture, here we show how the interaction between electrons and a coherent phonon mode can lead to a bandgap hosting edge states of topological origin. Further numerical simulations witness the robustness of these states against different types of disorder. Our results contribute to the search of topological states, in this case in a minimal Fock space.
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