Chiral separation effect catalyzed by heavy impurities

We investigate the influence of the Kondo effect, namely, the nonperturbative effect induced by heavy impurities, on the chiral separation effect (CSE) in quark matter. We employ a simple effective model incorporating the Kondo condensate made of a light quark and a heavy quark, and compute the response function of the axial current to the magnetic field in the static and dynamical limits. As a result, we find that the Kondo effect catalyzes the CSE in both of the limits, and in particular the CSE in the dynamical limit can be enhanced by a factor of approximately 3. Our findings clearly show that the presence of heavy impurities in quark matter can play an important role in the transport phenomena of light quarks induced by a magnetic field.

Figure 1

Schematic behavior of the dispersions in Eq. (8) ($p=|\mathit{p}|$). The solid red, dashed blue, and dotted purple curves correspond to $p_0=E_{\mathit{p}}^{+}$ (q.p.), $p_0=E_{\mathit{p}}^{-}$ (q.h.), and $p_0=E_{\mathit{p}}^{\mathrm{a}}$ (a.p.), respectively. The gray horizontal line indicates $p_0=0$, corresponding to the Fermi level.

Figure 2

Diagrammatic interpretation of each term in Eq. (32). The arrows are placed such that the corresponding modes carry their positive energies.

Figure 3

$\mu$ dependence of the response function in the static limit (${\tilde{\mathrm{\Pi }}}_5^{\mathrm{sta}}$) with $\mathrm{\Delta }=0.02\mathrm{GeV}$ (red dash-dotted), $\mathrm{\Delta }=0.05\mathrm{GeV}$ (purple dashed), and $\mathrm{\Delta }=0.1\mathrm{GeV}$ (blue solid). The black dashed curve indicates the response function in normal matter given in Eq. (37).

Figure 4

$\mu$ dependence of the response function in the dynamical limit (${\tilde{\mathrm{\Pi }}}_5^{\mathrm{dyn}}$) with $\mathrm{\Delta }=0.02\mathrm{GeV}$ (red dash-dotted), $\mathrm{\Delta }=0.05\mathrm{GeV}$ (purple dashed), and $\mathrm{\Delta }=0.1\mathrm{GeV}$ (blue solid). The black dashed curve indicates the response function in normal matter given in Eq. (38).

Figure 5

Gap dependence of the response function in the static limit (${\tilde{\mathrm{\Pi }}}_5^{\mathrm{sta}}$) (upper panel) and dynamical limit (${\tilde{\mathrm{\Pi }}}_5^{\mathrm{dyn}}$) (lower panel) at $\mu =0.5\mathrm{GeV}$ and at several temperatures. The black dashed line indicates the response function in normal matter given in Eq. (37). The blue filled and open circles in the dynamical limit show the discontinuous behavior at $T=0$ (see the main text).

Figure 6

$\mu$ dependence at $T=0$ and $\mathrm{\Delta }=0.1\mathrm{GeV}$ of each process contributing to the response function (upper panel), and their $\mathrm{\Delta }$ dependence at $T=0$ and $\mu =0.5\mathrm{GeV}$ (lower panel). We compare the total value of the response function (blue solid), the sum of pair-creation and pair-annihilation processes of $\mathrm{q}.\mathrm{p}.+\mathrm{q}.\mathrm{h}.$ (magenta dashed), and the sum of pair-creation and pair-annihilation processes of $\mathrm{q}.\mathrm{p}.+\mathrm{a}.\mathrm{p}.$ (brown dash-dotted).