In this work, we study even-parity spin-singlet orbital-triplet pairing states for a two-band superconductor. An orbital $mathbf{d}_o(mathbf{k})$-vector is introduced to characterize orbital-dependent pairings, in analogy to the spin $mathbf{d}_s(mat
hbf{k})$-vector that describes spin-triplet pairings in $^3$He superfluid. Naively, one might think the double degeneracy of orbitals would be lifted by inter-orbital hybridizations due to crystal fields or electron-electron repulsive interactions, then spin-singlet orbital-dependent pairings may be severely suppressed. However, we demonstrate that orbital-triplet pairing, represented by the orbital $mathbf{d}_o(mathbf{k})$-vector, could exist under some circumstances. Remarkably, it could even coexist with nematic orders or charge-density-wave orders induced by interactions. The generalization to a single-band superconductor with two valleys (e.g.~honeycomb lattice with two sublattices) is also discussed. Moreover, the complex orbital $mathbf{d}_o$-vector spontaneously breaks time-reversal symmetry (TRS), which might give rise to the TRS-breaking orbital-polarization, analogous to the spin magnetism.
We have grown thulium tellurides (TmTe2, TmTe3) thin layers (less than four layers) on graphene/SiC (0001) by molecular beam epitaxy. The charge density waves (CDWs) and lattice superstructures (LSs) are investigated by scanning tunneling microscopy.
Clear CDW patterns in real space are observed on surface of metallic TmTe3. Two CDWs are with wave vectors 0.29c* and 0.31a* respectively. LSs with various periods are unveiled on the surface of TmTe2 and TmTe3. The electronic structures of these films are semiconducting. These results show that superstructures in rare earth tellurides can have two origins, CDWs or LSs.
Spontaneous time-reversal symmetry (TRS) breaking plays an important role in studying strongly correlated unconventional superconductors. When the superconducting gap functions with different pairing symmetries compete, an Ising ($Z_2$) type symmetry
breaking occurs due to the locking of the relative phase $Deltatheta_{12}$ via a second order Josephson coupling. The phase locking can take place even in the normal state in the phase fluctuation regime before the onset of superconductivity. If $Deltatheta_{12}=pmfrac{pi}{2}$, then TRS is broken, otherwise, if $Deltatheta_{12}=0$, or, $pi$, rotational symmetry is broken leading to a nematic state. In both cases, the order parameters possess a 4-fermion structure beyond the scope of mean-field theory. We employ an effective two-component $XY$-model assisted by a renormalization group analysis to address this problem. In addition, a quartetting, or, charge-``4e, superconductivity can also occur above $T_c$. Monte-Carlo simulations are performed and the results are in a good agreement with the renormalization group analysis. Our results provide useful guidance for studying novel symmetry breakings in strongly correlated superconductors.
The magnetic structures of MnBi2Te4(Bi2Te3)n can be manipulated by tuning the interlayer coupling via the number of Bi2Te3 spacer layers n, while the intralayer ferromagnetic (FM) exchange coupling is considered too robust to control. By applying hyd
rostatic pressure up to 3.5 GPa, we discover opposite responses of magnetic properties for n = 1 and 2. MnBi4Te7 stays at A-type antiferromagnetic (AFM) phase with a decreasing Neel temperature and an increasing saturation field. In sharp contrast, MnBi6Te10 experiences a phase transition from A-type AFM to a quasi-two-dimensional FM state with a suppressed saturation field under pressure. First-principles calculations reveal the essential role of intralayer exchange coupling from lattice compression in determining these magnetic properties. Such magnetic phase transition is also observed in 20% Sb-doped MnBi6Te10 due to the in-plane lattice compression.
