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The NMR relaxation rate and the static spin susceptibility in graphene are studied within a tight-binding description. At half filling, the NMR relaxation rate follows a power law as $T^2$ on the particle-hole symmetric side, while with a finite chemical potential $mu$ and next-nearest neighbor $t$, the $(mu+3t)^2$ terms dominate at low excess charge $delta$. The static spin susceptibility is linearly dependent on temperature $T$ at half filling when $t=0$, while with a finite $mu$ and $t$, it should be dominated by $(mu+3t)$ terms in low energy regime. These unusual phenomena are direct results of the low energy excitations of graphene, which behave as massless Dirac fermions. Furthermore, when $delta$ is high enough, there is a pronounced crossover which divides the temperature dependence of the NMR relaxation rate and the static spin susceptibility into two temperature regimes: the NMR relaxation rate and the static spin susceptibility increase dramatically as temperature increases in the low temperature regime, and after the crossover, both decrease as temperature increases at high temperatures. This crossover is due to the well-known logarithmic Van Hove singularity in the density of states, and its position dependence of temperature is sensitive to $delta$.
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Recent NMR experiments by Singer et al. [Singer et al. Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magnetic field and temperature dependent NMR 13C spin-lattice relaxation is given in the framework of the Tomonaga-Luttinger liquid. The low temperature properties are governed by a gapped relaxation due to a spin gap (~ 30K), which crosses over smoothly to the Luttinger liquid behaviour with increasing temperature.
We investigate the impact of two types of disorder, bond randomness and site dilution, on the spin dynamics in the Kitaev model on a honeycomb lattice. The ground state of this model is a canonical quantum spin liquid with spin fractionalization into two types of quasiparticles, itinerant Majorana fermions and localized fluxes. Using unbiased quantum Monte Carlo simulations, we calculate the temperature evolution of the dynamical spin structure factor, the magnetic susceptibility, and the NMR relaxation rate. In the dynamical spin structure factor, we find that the two types of disorder affect seriously the low-energy peak dominantly originating from the flux excitations, rather than the high-energy continuum from the Majorana excitations, in a different way: The bond randomness softens the peak to the lower energy with broadening, whereas the site dilution smears the peak and in addition develops the other sharp peaks inside the spin gap including the zero energy. We show that the zero-energy spin excitations, which originate from the Majorana zero modes induced around the site vacancies, survive up to the temperature comparable to the energy scale of the Kitaev interaction. For the bond randomness, the low-temperature susceptibility does not show any qualitative change against the weak disorder, but it changes to divergent behavior while increasing the strength of disorder. Similar distinct behaviors for the weak and strong disorder are observed also in the NMR relaxation rate; an exponential decay changes into a power-law decay. In contrast, for the site dilution, we find no such crossover; divergent behavior in the susceptibility and a power-law decay in the NMR relaxation rate appear immediately with the introduction of the site dilution. We discuss the relevance of our results to experiments for the Kitaev candidate materials with disorders.
Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution $chi_{textrm{imp}}$ to susceptibility, defined originally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in $chi_{textrm{imp}}$, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local susceptibility $chi_{textrm{loc}}$ and to compare them with $chi_{textrm{imp}}$ obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in $chi_{textrm{imp}}$ are unphysical. Instead, the low-energy excitations of the impurity in arbitrary bands only without gap at the Fermi energy are still a Fermi liquid and paramagnetic. We also demonstrate that unlike the traditional NRG yielding $chi_{textrm{loc}}$ less accurate than $chi_{textrm{imp}}$, the FDM method allows a high-precision dynamical calculation of $chi_{textrm{loc}}$ at much reduced computational cost, with an accuracy at least one order higher than $chi_{textrm{imp}}$. Moreover, artifacts in the FDM algorithm to $chi_{textrm{imp}}$, and origins of the spurious non-Fermi-liquid and diamagnetic features are clarified. Our work provides an efficient high-precision algorithm to calculate the spin susceptibility of impurity for arbitrary structured bands, while negating the applicability of Wilsons definition to such cases.
We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.
Cyclotron spin-flip excitation in a nu=2 quantum Hall system, being separated from the ground state by a slightly smaller gap than the cyclotron energy and from upper magnetoplasma excitation by the Coulomb gap [S. Dickmann and I.V. Kukushkin, Phys. Rev. B 71, 241310(R) (2005) ; L.V. Kulik, I.V. Kukushkin, S. Dickmann, V.E. Kirpichev, A.B. Vankov, A.L. Parakhonsky, J.H. Smet, K. von Klitzing, and W. Wegscheider, Phys. Rev. B 72, 073304 (2005)] cannot relax in a purely electronic way except only with the emission of a shortwave acoustic phonon (k~3*10^7/cm). As a result, relaxation in a modern wide-thickness quantum well occurs very slowly. We calculate the characteristic relaxation time to be ~1s. Extremely slow relaxation should allow the production of a considerable density of zero-momenta cyclotron spin-flip excitations in a very small phase volume, thus forming a highly coherent ensemble - the Bose-Einstein condensate. The condensate state can be controlled by short optical pulses (<1 mcs), switching it on and off.
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