اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEvolution with Magnetic Field of Discrete Scale Invariant Supercritical States in Graphene
95
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate the quasi-bound states of a Coulomb impurity in graphene in the presence of a magnetic field. These states exhibit the dramatic and rather rare property of discrete scale invariance when the Coulomb potential is supercritical. We show using both Wentzel-Kramers-Brillouin (WKB) approximation and numerical studies that the supercritical states are converted to subcritical states as the field is increased. The local density of states is calculated and it shows direct signatures of discrete scale invariance. In a magnetic field, these signatures are gradually destroyed in a systematic way. Hence the effect that we propose can be detected via scanning tunneling microscope experiments. The range of magnetic field and energy resolution required are compatible with existing experimental setups. These experiments can be performed in a single sample by changing the field; they do not involve changing the nuclear charge.
قيم البحث
اقرأ أيضاً
We derive semiclassical quantization equations for graphene mono- and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a consequence of the spinor nature of the e
xcitations, is pointed out. The semiclassical eigenenergies show good agreement with the results of quantum mechanical calculations based on the Dirac equation of graphene and with numerical tight binding calculations.
We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a she
ll of degenerate states at the Fermi level. We derive a semi-analytical form for zero-energy states in a magnetic field and show that the shell remains degenerate in a magnetic field, in analogy to the 0th Landau level of bulk graphene. The magnetic field closes the energy gap and leads to the crossing of valence and conduction states with the zero-energy states, modulating the degeneracy of the shell. The closing of the gap with increasing magnetic field is present in all graphene quantum dot structures investigated irrespective of shape and edge termination.
We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 hat{z}$ in one domain and $B = B_1 hat{z}$ in the other domain, in the quantum Hall regime and in the low-energy limit. We
find that the magnetic edge states of the Dirac fermions, formed along the boundary between the two domains, have features strongly dependent on whether $B_0$ is parallel or antiparallel to $B_1$. In the parallel case, when the Zeeman spin splitting can be ignored, the magnetic edge states originating from the $n=0$ Landau levels of the two domains have dispersionless energy levels, contrary to those from the $n e 0$ levels. Here, $n$ is the graphene Landau-level index. They become dispersive as the Zeeman splitting becomes finite or as an electrostatic step potential is additionally applied. In the antiparallel case, the $n=0$ magnetic edge states split into electron-like and hole-like current-carrying states. The energy gap between the electron-like and hole-like states can be created by the Zeeman splitting or by the step potential. These features are attributed to the fact that the pseudo-spin of the magnetic edge states couples to the direction of the magnetic field. We propose an Aharonov-Bohm interferometry setup in a graphene ribbon for experimental study of the magnetic edge states.
Strain-inducing deformations in graphene alter charge distributions and provide a new method to design specific features in the band structure and transport properties. Novel approaches implement engineered substrates to induce specifically targeted
strain profiles. Motivated by this technique, we study the evolution of charge distributions with an increasing number of out-of-plane deformations as an example of a finite size periodic substrate. We first analyze a system of two overlapping deformations and determine the quantitative relation between geometrical parameters and features in the local density of states. We extend the study to sets of 3 and 4 deformations in linear and two-dimensional arrays and observe the emergence of moire patterns that are more pronounced for a hexagonal cell composed of 7 deformations. A comparison between the induced strain profile and spatial maps of the local density of states at different energies provides evidence for the existence of states confined by the pseudo-magnetic field in bounded regions, reminiscent of quantum dots structures. Due to the presence of these states, the energy level scaling to be observed by local probes should exhibit a linear dependence with the pseudo-field, in contrast to the expected scaling of pseudo-Landau levels.
We study the Fourier transform of the local density of states (LDOS) in graphene in the presence of a single impurity at high magnetic field. We find that the most pronounced features occur for energies of the STM tip matching the Landau level energi
es. The Fourier transform of the LDOS shows regions of high intensity centered around the center and the corners of the Brillouin zone (BZ). The radial intensity dependence of these features is determined by the form of the wavefunctions of the electrons in the quantum Hall regime. Moreover, some of these regions break rotational symmetry, and their angular dependence is determined by the chirality of the graphene electrons. For the zeroth Landau level, the ratio between the features at the corners and center of the BZ depends on the nature of the disorder: it goes to zero for potential disorder, and is finite for hopping disorder. We believe that a comparison between our analysis and experiments will help understand the form of the quasiparticle wavefunction, as well as the nature of disorder in graphene.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
