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Register a new userPersistent Friedel oscillations in Graphene due to a weak magnetic field
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Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/r^3$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is {em dominant} in a parametrically large spatial interval $p_0^{-1}lesssim rlesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and $p_0^{-1}=(k_Fl)^{4/3}/k_F$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.
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A weak perpendicular magnetic field, $B$, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. We explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that the electron-electron interaction lifetime acquires an anomalous $B$-dependence. Also, the ballistic zero-bias anomaly, $delta u(omega)$, where $omega$ is the energy measured from the Fermi level, emerges at a weak $B$ and has the form $delta u(B)sim B^2/omega^2$. Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous. We discuss experimental manifestations of the effects predicted. The microscopic origin of the $B$-field sensitivity is an extra phase acquired by the electron wave-function resulting from the chirality-induced pseudospin precession.
The Lindhard function represents the basic building block of many-body physics and accounts for charge response, plasmons, screening, Friedel oscillation, RKKY interaction etc. Here we study its non-Hermitian version in one dimension, where quantum effects are traditionally enhanced due to spatial confinement, and analyze its behavior in various limits of interest. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wavenumber and vanishes identically for all other wavenumbers at zero temperature. Consequently, no Friedel oscillations are induced by a non-Hermitian, imaginary impurity to lowest order in the impurity potential at zero temperature. Our findings are corroborated numerically on a tight-binding ring by switching on a weak real or imaginary potential. We identify conventional Friedel oscillations or heavily suppressed density response, respectively.
Effects associated with the interference of electron waves around a magnetic point defect in two-dimensional electron gas with combined Rashba-Dresselhaus spin-orbit interaction in the presence of a parallel magnetic field are theoretically investigated. The effect of a magnetic field on the anisotropic spatial distribution of the local density of states and the local density of magnetization is analyzed. The existence of oscillations of the density of magnetization with scattering by a non-magnetic defect and the contribution of magnetic scattering (accompanied by spin-flip) in the local density of electron states are predicted.
Friedel oscillation is a well-known wave phenomenon, which represents the oscillatory response of electron waves to imperfection. By utilizing the pseudospin-momentum locking in gapless graphene, two recent experiments demonstrate the measurement of the topological Berry phase by corresponding to the unique number of wavefront dislocations in Friedel oscillations. Here, we study the Friedel oscillations in gapped graphene, in which the pseudospin-momentum locking is broken. Unusually, the wavefront dislocations do occur as that in gapless graphene, which expects the immediate verification in the current experimental condition. The number of wavefront dislocations is ascribed to the invariant pseudospin winding number in gaped and gapless graphene. This study deepens the understanding of correspondence between topological quantity and wavefront dislocations in Friedel oscillations, and implies the possibility to observe the wavefront dislocations of Friedel oscillations in intrinsic gapped two-dimensional materials, e.g., transition metal dichalcogenides.
Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.
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