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Register a new userThe effect of a Chern-Simons term on dynamical gap generation in graphene
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Authors
M.E. Carrington
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We study the effect of a Chern-Simons term on dynamical gap generation in a low energy effective theory that describes some features of mono-layer suspended graphene. We use a non-perturbative Schwinger-Dyson approach. We solve a set of coupled integral equations for eight independent dressing functions that describe fermion and photon degrees of freedom. We find a strong suppression of the gap, and corresponding increase in the critical coupling, as a function of increasing Chern-Simons coefficient.
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We study dynamical symmetry breaking in three-dimensional QED with a Chern-Simons (CS) term, considering the screening effect of $N$ flavor fermions. We find a new phase of the vacuum, in which both the fermion mass and a magnetic field are dynamically generated, when the coefficient of the CS term $kappa$ equals $N e^2/4 pi$. The resultant vacuum becomes the finite-density state half-filled by fermions. For $kappa=N e^2/2 pi$, we find the fermion remains massless and only the magnetic field is induced. For $kappa=0$, spontaneous magnetization does not occur and should be regarded as an external field.
We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.
In the standard electroweak theory that describes nature, the Chern-Simons number associated with the vacua as well as the unstable sphaleron solutions play a crucial role in the baryon number violating processes. We recall why the Chern-Simons number should be generalized from a set of discrete values to a dynamical (quantum) variable. Via the construction of an appropriate Hopf invariant and the winding number, we discuss how the geometric information in the gauge fields is also captured in the Higgs field. We then discuss the choice of the Hopf variable in relation to the Chern-Simons variable.
We study the frequency dependencies of the fermion and photon dressing functions in dynamical gap generation in graphene. We use a low energy effective QED-like description, but within this approximation, we include all frequency dependent effects including retardation. We obtain the critical coupling by calculating the gap using a non-perturbative Dyson-Schwinger approach. Compared to the results of our previous calculation [1] which used a Lindhard screening approximation instead of including a self-consistently calculated dynamical screening function, the critical coupling is substantially reduced.
Introducing a chemical potential in the functional method, we construct the effective action of QED$_3$ with a Chern-Simons term. We examine a possibility that charge condensation $langlepsi^daggerpsi rangle$ remains nonzero at the limit of the zero chemical potential. If it happens, spontaneous magnetization occurs due to the Gauss law constraint which connects the charge condensation to the background magnetic field. It is found that the stable vacuum with nonzero charge condensation is realized only when fermion masses are sent to zero, keeping it lower than the chemical potential. This result suggests that the spontaneous magnetization is closely related to the fermion mass.
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