The properties of the ground state of relativistic matter in a magnetic field are examined within the framework of a Nambu-Jona-Lasinio model. The main emphasis of this study is the normal ground state, which is realized at sufficiently high temperatures and/or sufficiently large chemical potentials. In contrast to the vacuum state, which is characterized by the magnetic catalysis of chiral symmetry breaking, the normal state is accompanied by the dynamical generation of the chiral shift parameter $\Delta${}. In the chiral limit, the value of $\Delta${} determines a relative shift of the longitudinal momenta (along the direction of the magnetic field) in the dispersion relations of opposite chirality fermions. We argue that the chirality remains a good approximate quantum number even for massive fermions in the vicinity of the Fermi surface and, therefore, the chiral shift is expected to play an important role in many types of cold dense relativistic matter, relevant for applications in compact stars. The qualitative implications of the revealed structure of the normal ground state on the physics of protoneutron stars are discussed. A noticeable feature of the $\Delta${} parameter is that it is insensitive to temperature when T$\ll${}$\mu${}0, where $\mu${}0 is the chemical potential, and increases with temperature for T>$\mu${}0. The latter implies that the chiral shift parameter is also generated in the regime relevant for heavy ion collisions.

The dynamics responsible for lifting the degeneracy of the Landau levels in the quantum Hall (QH) effect in graphene is studied by utilizing a low-energy effective model with a contact interaction. A detailed analysis of the solutions of the gap equation for Dirac quasiparticles is performed at both zero and nonzero temperatures. The characteristic feature of the solutions is that the order parameters connected with the QH ferromagnetism and magnetic catalysis scenarios necessarily coexist. The solutions reproduce correctly the experimentally observed QH plateaus in graphene in strong magnetic fields. The phase diagram of this system in the plane of temperature and electron chemical potential is analyzed. The phase transitions corresponding to the transitions between different QH plateaus in graphene are described.

For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor $\nu =0$: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field $E_{\perp }$, and (ii) a layer-polarized solution, which is the ground state at large values of $E_{\perp }$. The critical value of $E_{\perp }$ that determines the transition point is a linear function of the magnetic field, i.e., $E_{\perp ,\mathrm{cr}}=E_{\perp }^{\mathrm{off}}+aB$, where $E_{\perp }^{\mathrm{off}}$ is the offset electric field and $a$ is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the $n=2$ Landau level sinks below the $n=0$ and $n=1$ ones). DOI: http://dx.doi.org/10.1103/PhysRevB.85.235460 ©2012 American Physical Society

In two-flavor dense quark matter, we describe the dynamics in the single plane wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state satisfying the color and electric neutrality conditions. We find that because the neutral LOFF state itself suffers from a chromomagnetic instability in the whole region where it coexists with the (gapped or gapless) two-flavor superconducting phases, it cannot cure this instability in those phases. This is unlike the recently revealed gluonic phase which seems to be able to resolve this problem.

Recently, a new class of models describing the quark mass hierarchy has been introduced. In this class, while the $t$ quark plays a minor role in electroweak symmetry breaking, it is crucial in providing the quark mass hierarchy. In this paper, we analyze the dynamics of a particular model in this class, in which the $b^{\prime }$ and $t^{\prime }$ quarks of the fourth family are mostly responsible for dynamical electroweak symmetry breaking. The low energy effective theory in this model is derived. It has a clear signature, a $2+1$ structure of composite Higgs doublets: two nearly degenerate ${\Phi }_{b^{\prime }}\sim {\overline{b}}_R^{\prime }(t^{\prime },b^{\prime }{)}_L$ and ${\Phi }_{t^{\prime }}\sim {\overline{t}}_R^{\prime }(t^{\prime },b^{\prime }{)}_L$, and a heavier top-Higgs resonance ${\Phi }_t\sim {\overline{t}}_R(t,b{)}_L$. The properties of these composites are described in detail, and it is shown that the model satisfies the electroweak precision data constraints. The signatures of these composites at the Large Hadron Collider are briefly discussed.