Shijun Mao

Inverse magnetic catalysis in Nambu–Jona-Lasinio model beyond mean field

We study inverse magnetic catalysis in the Nambu–Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli–Villars regularization scheme.

BCS–BEC CROSSOVER IN RELATIVISTIC FERMI SYSTEMS

We review the BCS–BEC crossover in relativistic Fermi systems, including the QCD matter at finite density. In the first part, we study the BCS–BEC crossover in a relativistic four-fermion interaction model and show how the relativistic effect affects the BCS–BEC crossover. In the second part, we investigate both two-color QCD at finite baryon density and pion superfluid at finite isospin density, by using an effective Nambu–Jona–Lasinio model. We will show how the model describes the weakly interacting diquark and pion condensates at low density and the BEC–BCS crossover at high density.

From inverse to delayed magnetic catalysis in a strong magnetic field

We study the magnetic field effect on chiral phase transition in a Nambu–Jona-Lasinio model. In comparison with a mean-field approximation containing only quarks, including mesons as quantum fluctuations in the model leads to a transition from inverse to delayed magnetic catalysis at finite temperature and delays the transition at finite baryon chemical potential. The location of the critical end point depends nonmonotonically on the magnetic field.

Effect of discrete quark momenta on the Goldstone mode in a magnetic field

It is well known that, the quark dimension reduction in magnetic field leads to an increasing critical temperature of chiral restoration, namely the magnetic catalysis effect [1–7]. From the Goldstone theorem, the spontaneous breaking of a global symmetry implies the existence of Goldstone bosons. In two-flavor case, the neutral pion is identified as the Goldstone mode in the presence of a magnetic field. The pion properties such as its mass and decay constant play an important role in chiral dynamics [8, 9]. For instance, the neutral mesons are potential for explaining the inverse magnetic catalysis [10, 11] and delayed magnetic catalysis [12]. The Nambu–Jona-Lasinio (NJL) model at quark level describes well the chiral symmetry breaking in vacuum and its restoration at finite temperature and baryon density [13–17]. In the model, mesons are treated as quantum fluctuations, and neutral mesons can be affected by the external magnetic field through their constituent quarks. The neutral mesons in magnetized NJL model are investigated in vacuum and at finite temperature by taking different methods like the assumption of four-momentum independent meson polarizations [14], magnetic field independent regularization scheme [18, 19], and derivative expansion [20, 21] and Φ-derivable approach [22]. In this paper, we focus on how the quark dimension reduction in magnetic field affects the neutral meson properties at finite temperature and density in the Pauli-Villars regularization scheme. The SU(2) NJL model is defined through the Lagrangian density [13–17]

BCS-BEC crossover and thermodynamics in asymmetric nuclear matter with pairings in isospin I=0 and I=1 channels

The Bardeen/Cooper/Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover and phase diagram for asymmetric nuclear superfluid with pairings in isospin I = 0 and I = 1 channels are investigated at the mean-field level by using a density-dependent nucleon-nucleon potential. Induced by the in-medium nucleon mass and density-dependent coupling constants, neutron-proton Cooper pairs could be in BEC state at sufficiently low density, but there is no chance for the BEC formation of neutron-neutron and proton-proton pairs at any density and asymmetry. We calculate the phase diagram in asymmetry-temperature plane for weakly interacting nuclear superfluid and find that including the I = 1 channel changes significantly the phase structure at low temperature. There appears a new phase with both I = 0 and I = 1 pairings at low temperature and low asymmetry, and the gapless state in any phase with I = 1 pairing is washed out and all excited nucleons are fully gapped.

Flat edge modes of graphene and of Z2 topological insulator.

A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.

Deconfinement Phase Transition with External Magnetic Field in the Friedberg–Lee Model

The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. In the frame of functional renormalization group, we extend the often used potential expansion method for continuous phase transitions to the first-order phase transition in the model. By solving the flow equations we find that, the magnetic field displays a catalysis effect and it becomes more difficult to break through the confinement in hot and dense medium.

Helical edge modes preserved across transitions from topological insulators with indirect gaps to insulators or semimetals

Helical edge modes are characteristic of topological insulators in two dimensions. This paper demonstrates that helical edge modes remain across transitions to ordinary insulators or to semimetals under certain condition. Straight and zigzag edges are considered in a tight-binding model on square lattice. We focus on the case of indirect gap in bulk topological insulators, and obtain the spectrum of edge modes on both sides of transitions. For straight edge, the helical edge mode in topological insulators with strong particle-hole asymmetry has a reentrant region in momentum space. Edge modes show up even in ordinary insulators, but are absent in semimetals. In zigzag edge, the helical edge mode survives in both semimetals and ordinary insulators. However, the edge modes are absent inside the energy gap of ordinary insulators. All results are obtained analytically.