Impact of ordering competition on the global phase diagram of iron pnictides

We consider the impact of the competition among superconductivity, spin density wave, and nematic order in iron pnictides and show that the ordering competition substantially reshapes the global phase diagram. We perform a detailed renormalization group analysis of an effective field theory of iron pnictides and derive the flow equations of all the physical parameters. Using these results, we find that superconductivity can be strongly suppressed by the ordering competition, and we also extract the $T$ dependence of the superfluid density. Moreover, the phase transitions may become first order. Interestingly, our renormalization group (RG) analysis reveals that the nematic order exists only in an intermediate temperature region, $T_m<T<T_n$, but is destroyed at $T>T_n$ by thermal fluctuation and at $T<T_m$ by the ordering competition. This anomalous existence of nematic order leads to a backbending of the nematic transition line on the phase diagram, consistent with the observed reentrance of tetragonal structure at low temperatures. A modified phase diagram is obtained based on the RG results.

Figure 1

Schematic phase diagram of iron pnictides on the $x-T$ plane [16, 17, 18], where $x$ denotes the doping concentration. The two points $x_1$ and $x_2$ are the SC and SDW QCPs, respectively. The nematic transition line bends back towards lower $x$ in the SC dome, showing reentrant behavior [19].

Figure 2

Flows of $a_s, u_m, u_s, g_m$, and $\zeta$ and $T$ dependence of $g_m$ (inset) at SDW QCP. The parameter $g_m$ is positive at small $l$ and high $T$, but becomes negative suddenly once $l$ exceeds some critical value of $l_m$ and $T$ is lower than $T_m$.

Figure 3

$T$ dependence of $g_m$ for different values of bare parameter $a_m^0$, which measures the distance to the SDW QCP $x_2$. As $a_m^0$ grows, $g_m$ varies with $T$ similarly, but its peak disappears and the temperature for $g_m$ to change sign increases.

Figure 4

Strong $T$ dependence of the superfluid density ${\rho }_s\left(T\right)$ at the SDW QCP. The inset shows that ${\rho }_s\left(T\right)$ is similar to ${(T/T_0)}^{1.5}$ only in a very restricted temperature range.

Figure 5

${\rho }_s\left(T\right)$ at different values of $a_m^0$. The suppression of the superfluid density takes place for any $a_m^0$, but is most significant at the SDW QCP where $a_m^0=0$.