Origin of nematic order in FeSe

The origin of the 90-K nematic transition in the chalcogenide FeSe, which displays no magnetic order down to $T=0$, remains a major puzzle for a unifying theory for the iron-based superconductors. We analyze this problem in light of recent experimental data which reveal very small Fermi pockets in this material. We show that the smallness of the Fermi energy leads to a near degeneracy between magnetic fluctuations and fluctuations in the charge-current density-wave channel. Although the two fluctuation modes cooperate to promote the same preemptive Ising-nematic order, they compete for primary order. We argue that this explains why in FeSe the nematic order emerges when the magnetic correlation length is smaller than in other Fe-based materials. We argue that pressure lifts this near degeneracy and causes nonmonotonic behavior of the nematic transition.

Figure 1

Schematic of the SDW and iCDW ordered states with ordering vector $\left(\pi ,0\right)$. Although fluctuations in both channels support nematicity, they compete for long-range magnetic and charge orders. For iCDW, one has to distinguish between the pattern of the bond-current order parameter in real space [the real-space version of $i{\mathrm{\Phi }}_i$ from Eq. (2)] and the pattern of the actual current. To obtain the latter, one needs to transform ${\mathrm{\Phi }}_i$ to the orbital basis and combine with hoppings. We show the particular current pattern using the same conversion as in Ref. [34]. For $i{\mathrm{\Phi }}_i$ itself, diagonal components are of opposite signs. Other current patterns are also possible as long as they display $\left(\pi ,0\right)$ order.

Figure 2

(a) RG flow of the SDW and iCDW interactions ${\mathrm{\Gamma }}_{\mathrm{sdw}}$ (blue curve) and ${\mathrm{\Gamma }}_{\mathrm{icdw}}$ (red curve) as a function of decreasing energy $E.W$ is the bandwidth, $u_0=u_1\left(0\right)=u_2\left(0\right)=10u_3\left(0\right)$ is the bare interaction parameter, and the dashed line is the energy in which the two degenerate instabilities occur. The RG flow stops at the Fermi energy $E_F$: If $E_F$ is large (case I, Fe pnictides), only SDW fluctuations are relevant, whereas if $E_F$ is small (cases II/III, FeSe), both SDW and iCDW fluctuations are important. The insets show schematically the Fermi pockets in each case. (b) Ratio ${\mathrm{\Gamma }}_{\mathrm{icdw}}/{\mathrm{\Gamma }}_{\mathrm{sdw}}$ along the RG flow. (c) Electronic manifestation of the Ising-nematic order on the hole pockets. There is a $cos2\theta$ distortion with opposite signs for the two pockets and an overall shift in the chemical potential.

Figure 3

Density plot of the nematic transition $T_{\mathrm{nem}}$ as a function of the bare iCDW and SDW transitions $T_{\mathrm{iCDW}}$ and $T_{\mathrm{SDW}}$. To mimic the effect of pressure, they start at the same negative value $-\theta$ at zero pressure for which the nematic transition temperature is $T_{\mathrm{nem},0}$ and then vary in opposite ways upon increasing pressure, $T_{\mathrm{iCDW}}<-\theta$ and $T_{\mathrm{SDW}}>-\theta$.