Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userShape of the zeroth Landau level in graphene with non-diagonal disorder
82
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
We report on magneto-transport measurements on low-density, large-area monolayer epitaxial graphene devices grown on SiC. We show that the zero-energy Landau level (LL) in monolayer graphene, which is predicted to be magnetic field ($B$)-independent, can float up above the Fermi energy at low $B$. This is supported by the temperature ($T$)-driven flow diagram approximated by the semi-circle law as well as the $T$-independent point in the Hall conductivity $sigma_{xy}$ near $e^2/h$. Our experimental data are in sharp contrast to conventional understanding of the zeroth LL and metallic-like behavior in pristine graphene prepared by mechanical exfoliation at low $T$. This surprising result can be ascribed to substrate-induced sublattice symmetry breaking which splits the degeneracy of the zeroth Landau level. Our finding provides a unified picture regarding the metallic behavior in pristine graphene prepared by mechanical exfoliation, and the insulating behavior and the insulator-quantum Hall transition in monolayer epitaxial graphene.
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 results 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.
We develop a theory for a qualitatively new type of disorder in condensed matter systems arising from local twist-angle fluctuations in two strongly coupled van der Waals monolayers twisted with respect to each other to create a flat band moire superlattice. The new paradigm of twist angle disorder arises from the currently ongoing intense research activity in the physics of twisted bilayer graphene. In experimental samples of pristine twisted bilayer graphene, which are nominally free of impurities and defects, the main source of disorder is believed to arise from the unavoidable and uncontrollable non-uniformity of the twist angle across the sample. To address this new physics of twist-angle disorder, we develop a real-space, microscopic model of twisted bilayer graphene where the angle enters as a free parameter. In particular, we focus on the size of single-particle energy gaps separating the miniband from the rest of the spectrum, the Van Hove peaks, the renormalized Dirac cone velocity near charge neutrality, and the minibandwidth. We find that the energy gaps and minibandwidth are strongly affected by disorder while the renormalized velocity remains virtually unchanged. We discuss the implications of our results for the ongoing experiments on twisted bilayer graphene. Our theory is readily generalized to future studies of twist angle disorder effects on all electronic properties of moire superlattices created by twisting two coupled van der Waals materials with respect to each other.
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 bottom 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].
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
