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Register a new userMultiorbital Ferroelectric Superconductivity in doped SrTiO3
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SrTiO$_3$ is a unique example of a system which exhibits both quantum paraelectricity and superconductivity. Thus, it is expected that the superconducting state is closely related to the intrinsic ferroelectric instability. Indeed, recent experiments suggest existence of a coexistent phase of superconductivity and ferroelectricity in Ca-substituted SrTiO$_3$. In this paper, we propose that SrTiO$_3$ can be a platform of the ferroelectric superconductivity, which is characterized by a ferroelectric transition in the superconducting state. By analyzing a multiorbital model for $t_{2g}$ electrons, we show that the ferroelectric superconductivity is stabilized through two different mechanisms which rely on the presence of the spin-orbit coupling. First, the ferroelectric superconducting state is stabilized in the dilute carrier density regime due to a ferroelectricity-induced Lifshitz transition. Second, it is stabilized under a magnetic field independent of the carrier density. The importance of the multiorbital or multiband nature for the ferroelectric superconductivity is clarified. Then, we predict a topological Weyl superconducting state in the ferroelectric superconducting phase of SrTiO$_3$.
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The soft ferro-electric phonon in SrTiO3 observed with optical spectroscopy has an extraordinary strong spectral weight which is much stronger than expected in the limit of a perfectly ionic compound. The charged phonon in SrTiO3 is caused by the close-to-covalent character of the Ti-O ionic bond and implies a strong coupling between the soft ferro-electric phonon and the inter band transitions across the 3 eV gap of SrTiO3. We demonstrate that this coupling leads, in addition to the charged phonon effect, to a pairing interaction involving the exchange of two transverse optical phonons. This process owes its relevance to the strong electron-phonon coupling and to the fact that the interaction mediated by a single transverse optical phonon vanishes at low electron density. We use the experimental soft phonon spectral weight to calculate the strength of the bi-phonon mediated pairing interaction in the electron doped material and show that it is of the correct magnitude when compared to the experimental value of the superconducting critical temperature.
SrTiO$_3$ exhibits a superconducting dome upon doping with Nb, with a maximum critical temperature mbox{$T_mathrm{c} approx 0.4$~K}. Using microwave stripline resonators at frequencies from 2 to 23~GHz and temperatures down to 0.02~K, we probe the low-energy optical response of superconducting SrTiO$_3$ with charge carrier concentration from 0.3 to $2.2times 10^{20}$~cm$^{-3}$, covering the majority of the superconducting dome. We find single-gap electrodynamics even though several electronic bands are superconducting. This is explained by a single energy gap $2Delta$ due to gap homogenization over the Fermi surface consistent with the low level of defect scattering in Nb-doped SrTiO$_3$. Furthermore, we determine $T_mathrm{c}$, $2Delta$, and the superfluid density as a function of charge carrier concentration, and all three quantities exhibit the characteristic dome shape.
We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our Ansatz is an optimized linear superposition of Affleck-Kennedy-Lieb-Tasaki valence bond states, rendering the combination a valence bond liquid dubbed Orbital Resonant Valence Bond. We show that the undoped (one electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Andersons resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths -- W the carriers bandwidth -- could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
Recent experiments in multiband Fe-based and heavy-fermion superconductors have challenged the long-held dichotomy between simple $s$- and $d$-wave spin-singlet pairing states. Here, we advance several time-reversal-invariant irreducible pairings that go beyond the standard singlet functions through a matrix structure in the band/orbital space, and elucidate their naturalness in multiband systems. We consider the $stau_{3}$ multiorbital superconducting state for Fe-chalcogenide superconductors. This state, corresponding to a $d+d$ intra- and inter-band pairing, is shown to contrast with the more familiar $d +text{i}d$ state in a way analogous to how the B- triplet pairing phase of enhe superfluid differs from its A- phase counterpart. In addition, we construct an analogue of the $stau_{3}$ pairing for the heavy-fermion superconductor CeCu$_{2}$Si$_{2}$, using degrees-of-freedom that incorporate spin-orbit coupling. Our results lead to the proposition that $d$-wave superconductors in correlated multiband systems will generically have a fully-gapped Fermi surface when they are examined at sufficiently low energies.
We demonstrate that SrTiO$_3$ can be a platform for observing the bulk odd-frequency superconducting state owing to the multiorbital/multiband nature. We consider a three-orbital tight-binding model for SrTiO$_3$ in the vicinity of a ferroelectric critical point. Assuming an intraorbital spin-singlet $s$-wave superconducting order parameter, it is shown that the odd-frequency pair correlations are generated due to the intrinsic LS coupling which leads to the local orbital mixing. Furthermore, we show the existence of additional odd-frequency pair correlations in the ferroelectric phase, which is induced by an odd-parity orbital hybridization term proportional to the ferroelectric order parameter. We also perform a group theoretical classification of the odd-frequency pair amplitudes based on the fermionic and space group symmetries of the system. The classification table enables us to predict dominant components of the odd-frequency pair correlations based on the symmetry of the normal state Hamiltonian that we take into account. Furthermore, we show that experimental signatures of the odd-parity orbital hybridization, which is an essential ingredient for the ferroelectricity-induced odd-frequency pair correlations, can be observed in the spectral functions and density of states.
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