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.
Non-diagonal (bond) disorder in graphene broadens Landau levels (LLs) in the same way as random potential. The exception is the zeroth LL, $n=0$, which is robust to the bond disorder, since it does not mix different $n=0$ states within a given valley
. The mechanism of broadening of the $n=0$ LL is the inter-valley scattering. Several numerical simulations of graphene with bond disorder had established that $n=0$ LL is not only anomalously narrow but also that its shape is very peculiar with three maxima, one at zero energy, $E=0$, and two others at finite energies $pm E$. We study theoretically the structure of the states in $n=0$ LL in the presence of bond disorder. Adopting the assumption that the bond disorder is strongly anisotropic, namely, that one type of bonds is perturbed much stronger than other two, allowed us to get an analytic expression for the density of states which agrees with numerical simulations remarkably well. On the qualitative level, our key finding is that delocalization of $E=0$ state has a dramatic back effect on the density of states near $E=0$. The origin of this unusual behavior is the strong correlation of eigenstates in different valleys.
In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the top and bott
om of the broadened LL, while states in the center of the LL (the critical region) remain delocalized. This well-known phenomenology is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE) [1]. One unnoticed issue is where the new states appear as the magnetic field is increased. Here we demonstrate that they appear predominantly inside the critical region. This leads to a certain ``spectral ordering of the localized states that explains the stripes observed in measurements of the local inverse compressibility [2-3], of two-terminal conductance [4], and of Hall and longitudinal resistances [5] without invoking interactions as done in previous work [6-8].
We present both the experimental and theoretical investigation of a non-trivial electron Landau levels shift in magnetic field in wide ~20 nm HgTe quantum wells: Landau levels split under magnetic fields but become degenerate again when magnetic fiel
d increases. We reproduced this behavior qualitatively within an isotropic 6-band Kane model, then using semiclassical calculations we showed this behavior is due to the mixing of the conduction band with total spin 3/2 with the next well subband with spin 1/2 which reduces the average vertical spin from 3/2 to around 1. This change of the average spin changes the Berry phase explaining the evolution of Landau levels under magnetic field.
Graphene has been proposed as a promising material for future nanoelectronics because of its unique electronic properties. Understanding the scaling behavior of this new nanomaterial under common experimental conditions is of critical importance for
developing graphene-based nanoscale devices. We present a comprehensive experimental and theoretical study on the influence of edge disorder and bulk disorder on the minimum conductivity of graphene ribbons. For the first time, we discovered a strong non-monotonic size scaling behavior featuring a peak and saturation minimum conductivity. Through extensive numerical simulations and analysis, we are able to attribute these features to the amount of edge and bulk disorder in graphene devices. This study elucidates the quantum transport mechanisms in realistic experimental graphene systems, which can be used as a guideline for designing graphene-based nanoscale devices with improved performance.
We have measured a strong increase of the low-temperature resistivity $rho_{xx}$ and a zero-value plateau in the Hall conductivity $sigma_{xy}$ at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our re
sults by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in $rho_{xx}$ and the anomalous $ u=0$ plateau in $sigma_{xy}$ in terms of coexisting electrons and holes in the same spin-split zero-energy Landau level.