In the magic angle twisted bilayer graphene (TBG), one of the most remarkable observations is the $C_3$-symmetry-breaking nematic state. We identify that the nematicity in TBG is the $E$-symmetry ferro bond order, which is the symmetry breaking in th
e effective hopping integrals. Thanks to the strong correlation and valley degree of freedom characteristics of the TBG, the nematicity in the TBG originates from prominent quantum interference among valley fluctuations and spin fluctuations. This novel valley + spin fluctuation interference mechanism also causes novel time-reversal-symmetry-broken valley polarization accompanied by a charge loop current. We discuss interesting similarities and differences between the TBG and Fe-based superconductors.
Spontaneous current orders due to odd-parity order parameters attract increasing attention in various strongly correlated metals. Here, we discover a novel spin-fluctuation-driven charge loop current (cLC) mechanism based on the functional renormaliz
ation group (fRG) theory. The present mechanism leads to the ferro-cLC order in a simple frustrated chain Hubbard model. The cLC appears between the antiferromagnetic and $d$-wave superconducting ($d$SC) phases. While the microscopic origin of the cLC has a close similarity to that of the $d$SC, the cLC transition temperature $T_{rm cLC}$ can be higher than the $d$SC one for wide parameter range. Furthermore, we reveal that the ferro cLC order is driven by the strong enhancement of the forward scatterings $g_2$ and $g_4$ owing to the two dimensionality based on the $g$-ology language. The present study indicates that the cLC can emerge in metals near the magnetic criticality with geometrical frustration
Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin-current, called the spin l
oop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensation that are mediated by transverse spin fluctuations around the pseudogap temperature $T^*$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC order is hidden in that neither internal magnetic field nor charge density modulation is induced, whereas the predicted sLC with finite wavenumber naturally gives the Fermi arc structure. In addition, the fluctuations of sLC order work as attractive pairing interaction between adjacent hot spots, which enlarges the d-wave superconducting transition temperature $T_c$. The sLC state will be a key ingredient in understanding the pseudogap, electronic nematicity as well as superconductivity in cuprates and other strongly correlated metals.
We propose a mechanism of spin-triplet superconductivity at the edge of $d$-wave superconductors. Recent theoretical research in $d$-wave superconductors predicted that strong ferromagnetic (FM) fluctuations are induced by large density of states due
to edge Andreev bound states (ABS). Here, we construct the linearized gap equation for the edge-induced superconductivity, and perform a numerical study based on a large cluster Hubbard model with bulk $d$-wave superconducting (SC) gap. We find that ABS-induced strong FM fluctuations mediate the $d pm ip$-wave SC state, in which the time-reversal symmetry is broken. The edge-induced $p$-wave transition temperature $T_{cp}$ is slightly lower than the bulk $d$-wave one $T_{cd}$, and the Majorana bound state may be created at the endpoint of the edge.
In several Fe-based superconductors, slight $C_4$ symmetry breaking occurs at $T^*$, which is tens of Kelvin higher than the structural transition temperature $T_S$. In this hidden nematic state at $T_S<T<T^*$, the orthorhombicity is tiny [$phi=(a-b)
/(a+b) ll 0.1$%], but clear evidences of bulk phase transition have been accumulated. To explain this long-standing mystery, we propose the emergence of antiferro-bond (AFB) order with the antiferro wavevector ${bf q}=(0,pi)$ at $T=T^*$, by which the characteristic phenomena below $T^*$ are satisfactorily explained. This AFB order originates from the inter-orbital nesting between the $d_{xy}$-orbital hole-pocket and the electron-pocket, and this inter-orbital bond order naturally explains the pseudogap, band-folding, and tiny nematicity that is linear in $T^*-T$. The hidden AFB order explains key experiments in both BaFe$_2$As$_2$ and NaFeAs, but it is not expected to occur in FeSe because of the absence of the $d_{xy}$-orbital hole-pocket.
The origin of diverse nematicity and their order parameters in Fe-based superconductors have been attracting increasing attention. Recently, a new type of nematic order has been discovered in heavily hole-doped ($n_d=5.5$) compound AFe$_2$As$_2$ (A=C
s, Rb). The discovered nematicity has $B_{2g}$ (=$d_{xy}$) symmetry, rotated by $45^circ$ from the $B_{1g}$ (=$d_{x^2-y^2}$) nematicity in usual compounds with $n_dapprox6$. We predict that the nematic bond order, which is the symmetry-breaking of the correlated hopping, is responsible for the $B_{2g}$ nematic order in AFe$_2$As$_2$. The Dirac pockets in AFe$_2$As$_2$ is essential to stabilize the $B_{2g}$ bond order. Both $B_{1g}$ and $B_{2g}$ nematicity in A$_{1-x}$Ba$_x$Fe$_2$As$_2$ are naturally induced by the Aslamazov-Larkin many-body process, which describes the spin-fluctuation-driven charge instability. The present study gives a great hint to control the nature of charge nematicity by modifying the orbital character and the topology of the Fermi surface.
We have theoretically explored the intrinsic spin Hall effect (SHE) in the iron-based superconductor family with a variety of materials. The study is motivated by an observation that, in addition to an appreciable spin-orbit coupling in the Fe 3d sta
tes, a character of the band structure in which Dirac cones appear below the Fermi energy may play a crucial role in producing a large SHE. Our investigation does indeed predict a substantially large spin Hall conductivity in the heavily hole-doped regime such as KFe$_2$As$_2$. The magnitude of the SHE has turned out to be comparable with that for Pt despite a relatively small spin-orbit coupling, which we identify to come from a huge contribution from the gap opening induced by the spin-orbit coupling at the Dirac point, which can become close to the Fermi energy for the heavy hole doping.
