Due to Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g. quantum dots or quantum point contacts.
We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.PACS numbers: 75.70.Ak
We found out that the numerical code used to solve Eq. ͑33͒ in our paper unfortunately gives unreliable results close to E = 0, which led us to wrong conclusions in Sec. V. The gap around E = 0 and the superluminal velocity are both numerical artifacts. The correct solution of Eq. ͑33͒ shows that there is no gap around zero energy and that the dispersion close to E = 0 is an isotropic cone with a renormalized value of the group velocity, in agreement with other recent results. 1,2 This is also confirmed by the analytical solution of Eq. ͑33͒ for small E, K x , and k y which gives ͑in the units used in the paper͒with D p ͑1͒ ͑x͒ = ץD p ץp ͑x͒, D p ͑x͒ the parabolic cylinder function and erf͑x͒ the error function. Figures 17 and 18 should then be dismissed and replaced by the figures below. -2 -1 0 1 2 -3 -2 -1 0 1 2 3 E K x FIG. 17. The spectrum for the periodic superlattice in Fig. 16 with d B = d −B =1 at k y =0 ͑solid line͒ and k y =1 ͑dashed line͒. K x is the quasi-momentum. 2 1 0 1 2 2 1 0 1 2 k y E FIG. 18. ͑Color online͒ The allowed spectrum, ͉Tr ⍀͉ ഛ 2, varying E and k y , at d B = d −B = 1. The contour lines correspond to the values of Tr ⍀ in the interval ͓−2,2͔ at steps of 0.5, increasing from blue ͑inner dark gray͒ to red ͑outer dark gray͒.
A theoretical description of electron spin resonance (ESR) in 1D interacting metals is given, with primary emphasis on carbon nanotubes. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed using a low-energy field theory. Drastic differences in the ESR spectra of single-wall and multi-wall nanotubes are found. For single-wall tubes, the predicted double peak spectrum is linked to spin-charge separation. For multi-wall tubes, a single narrow asymmetric peak is expected.PACS numbers: 73.63.Fg, Electron spin resonance (ESR) serves as a valuable tool to experimentally probe the intrinsic spin dynamics of many systems. In ESR experiments one applies a static magnetic field and measures the absorption of radiation polarized perpendicular to the field direction. In the absence of SU (2) spin symmetry breaking terms in the system Hamiltonian, the absorption intensity is then simply a δ-peak at the Zeeman energy [1]. Since spin-orbit (SO) interactions are generally the leading terms breaking the SU (2) invariance, deviations in the ESR intensity from the δ-peak, e.g. shifts or broadenings, are directly connected to these couplings. In this Letter we theoretically address the spin-orbit interaction and the resulting ESR spectrum for interacting 1D metallic conductors, in particular for carbon nanotubes. Nanotubes constitute a new class of mesoscopic quantum wires characterized by the interplay of strong electron-electron interactions, reduced dimensionality, disorder, and unconventional spin dynamics [2][3][4][5][6]. ESR is an important technique to elucidate aspects of this interplay inaccessible to (charge) transport experiments. For interacting many-body systems, surprisingly little is known about ESR although it represents an interesting theoretical problem.Two main classes of nanotubes may be distinguished, namely single-wall nanotubes (SWNTs) which consist of just one wrapped-up graphite sheet, and multi-wall nanotubes (MWNTs). MWNTs contain additional inner shells, but transport is generally limited to the outermost shell [4]. Evidence for the Luttinger liquid (LL) behavior of interacting 1D electrons has been reported for charge transport in SWNTs [3], where one also expects to find spin-charge separation [5,6]. Conventional wisdom holds that the SO coupling in 1D conductors destroys spincharge separation [7]. Below we show that this statement is incorrect. Indeed, the SO interaction considered in Ref. [7] was intended for the limited class of semiconductor quantum wires in strong Rashba and confinement electric fields, but in fact does not represent the generic SO Hamiltonian for 1D conductors. The latter is derived below and determines the ESR intensity in SWNTs and MWNTs. A totally different ESR spectrum compared to expectations based on Ref. [7] emerges. In particular, the single δ-peak is split into two narrow peaks in SWNTs, while for the SO coupling of Ref.[7] the spectrum forms a broad band with thresholds at the lower and upper edge [8]. This qualitative difference can be trace...
We derive the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes taking into account acoustic phonon exchange within a continuum elastic description. In many cases, the nanotube can be described as a standard Luttinger liquid with possibly attractive interactions. We predict surprisingly strong attractive interactions for thin nanotubes. Once the tube radius reaches a critical value R0 ≈ 3.6 ± 1.4Å, the Wentzel-Bardeen singularity is approached, accompanied by strong superconducting fluctuations. The surprisingly large R0 indicates that this singularity could be reached experimentally. We also discuss the conditions for a Peierls transition due to acoustic phonons. PACS number(s): 73.63. Fg, 74.25.Kc
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