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Register a new userPeculiar Nature of Snake States in Graphene
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We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to the two-dimensional electron gas (2DEG) snake states in graphene exibit peculiar properties related to the underlying dynamics of the Dirac fermions. The current carried by snake states is locally uncompensated even if the Fermi energy lies between the first non-zero energy Landau levels of the conduction and valence bands. The nature of these states is studied by calculating the current density distribution. It is shown that besides the snake states in finite samples surface states also exist.
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We study a model of a $p$-$n$ junction in single-layer graphene in the presence of a perpendicular magnetic field and spin-orbit interactions. By solving the relevant quantum-mechanical problem for a potential step, we determine the exact spectrum of spin-resolved dispersive Landau levels. Close to zero energy, we find a pair of linearly dispersing zero modes, which possess a wave-vector-dependent spin polarization and can be regarded as quantum analogous of spinful snake states. We show that the Rashba spin-orbit interaction, in particular, produces a wave vector shift between the dispersions of these modes with observable interference effects. These effects can in principle provide a way to detect the presence of Rashba spin-orbit interaction and measure its strength. Our results suggest that a graphene $p$-$n$ junction in the presence of strong spin-orbit interaction could be used as a building block in a spin field-effect transistor.
A pseudo-magnetic field kink can be realized along a graphene nanoribbon using strain engineering. Electron transport along this kink is governed by snake states that are characterized by a single propagation direction. Those pseudo-magnetic fields point towards opposite directions in the K and K valleys, leading to valley polarized snake states. In a graphene nanoribbon with armchair edges this effect results in a valley filter that is based only on strain engineering. We discuss how to maximize this valley filtering by adjusting the parameters that define the stress distribution along the graphene ribbon.
We analyze the nature of the single particle states, away from the Dirac point, in the presence of long-range charge impurities in a tight-binding model for electrons on a two-dimensional honeycomb lattice which is of direct relevance for graphene. For a disorder potential $V(vec{r})=V_0exp(-|vec{r}-vec{r}_{imp}|^2/xi^2)$, we demonstrate that not only the Dirac state but all the single particle states remain extended for weak enough disorder. Based on our numerical calculations of inverse participation ratio, dc conductivity, diffusion coefficient and the localization length from time evolution dynamics of the wave packet, we show that the threshold $V_{th}$ required to localize a single particle state of energy $E(vec{k})$ is minimum for the states near the band edge and is maximum for states near the band center, implying a mobility edge starting from the band edge for weak disorder and moving towards the band center as the disorder strength increases. This can be explained in terms of the low energy Hamiltonian at any point $vec{k}$ which has the same nature as that at the Dirac point. From the nature of the eigenfunctions it follows that a weak long range impurity will cause weak anti localization effects, which can be suppressed, giving localization if the strength of impurities is sufficiently large to cause inter-valley scattering. The inter valley spacing $2|vec{k}|$ increases as one moves in from the band edge towards the band center, which is reflected in the behavior of $V_{th}$ and the mobility edge.
Snake states and Aharonov-Bohm interferences are examples of magnetoconductance oscillations that can be observed in a graphene p-n junction. Even though they have already been reported in suspended and encapsulated devices including different geometries, a direct comparison remains challenging as they were observed in separate measurements. Due to the similar experimental signatures of these effects a consistent assignment is difficult, leaving us with an incomplete picture. Here we present measurements on p-n junctions in encapsulated graphene revealing several sets of magnetoconductance oscillations allowing for their direct comparison. We analysed them with respect to their charge carrier density, magnetic field, temperature and bias dependence in order to assign them to either snake states or Aharonov-Bohm oscillations. Furthermore we were able to consistently assign the various Aharonov-Bohm interferences to the corresponding area which the edge states enclose. Surprisingly, we find that snake states and Aharonov-Bohm interferences can co-exist within a limited parameter range.
Metal atomic chains have been reported to change their electronic or magnetic properties by slight mechanical stimulus. However, the mechanical response has been veiled because of lack of information on the bond nature. Here, we clarify the bond nature in platinum (Pt) monatomic chains by our developed in-situ transmission electron microscope method. The stiffness is measured with sub N/m precision by quartz length-extension resonator. The bond stiffnesses at the middle of the chain and at the connecting to the base are estimated to be 25 and 23 N/m, respectively, which are higher than the bulk counterpart. Interestingly, the bond length of 0.25 nm is found to be elastically stretched to 0.31 nm, corresponding to 24% in strain. Such peculiar bond nature could be explained by a novel concept of string tension. This study is a milestone that will significantly change the way we think about atomic bonds in one-dimensional substance.
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