## Explorations in Dirac Fermions and Spin Liquids A dissertation presented by (2011)

### BibTeX

@MISC{Biswas11explorationsin,

author = {Rudro Rana Biswas and Subir Sachdev and Rudro Rana Biswas},

title = {Explorations in Dirac Fermions and Spin Liquids A dissertation presented by},

year = {2011}

}

### OpenURL

### Abstract

A significant portion of this dissertation is devoted to the study of the effects of impurities in substances whose low energy modes can be described by fermions obeying the gapless Dirac equation in 2+1 dimensions. First, we examine the case of a spin vacancy in the staggered flux spin liquid whose excitations are Dirac fermions coupled to a U(1) gauge field. This vacancy leads to an anomalous Curie susceptibility and does not induce any local orders. Next, a Coulomb charge impurity placed on clean graphene is considered. We find that the Dirac quasiparticles in graphene do not screen the impurity charge, to all orders in perturbation theory. However, electronic correlations are found to induce a cloud of charge having the same sign as the impurity charge. We also analyze the case of a local impurity in graphene in the presence of a magnetic field and derive the spatial fourier transform of tunneling spectroscopy data obtained on an almost-clean