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Register a new userSelection rules for Cooper pairing in two-dimensional interfaces and sheets
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Added by
Mathias S. Scheurer
Publication date
2015
fields
Physics
and research's language is
English
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Thin sheets deposited on a substrate and interfaces of correlated materials offer a plethora of routes towards the realization of exotic phases of matter. In these systems, inversion symmetry is broken which strongly affects the properties of possible instabilities -- in particular in the superconducting channel. By combining symmetry and energetic arguments, we derive general and experimentally accessible selection rules for Cooper instabilities in noncentrosymmetric systems which yield necessary and sufficient conditions for spontaneous time-reversal-symmetry breaking at the superconducting transition and constrain the orientation of the triplet vector. We discuss in detail the implications for various different materials. For instance, we conclude that the pairing state in thin layers of Sr$_2$RuO$_4$ must, as opposed to its bulk superconducting state, preserve time-reversal symmetry with its triplet vector being parallel to the plane of the system. All pairing states of this system allowed by the selection rules are predicted to display topological Majorana modes at dislocations or at the edge of the system. Applying our results to the LaAlO$_3$/SrTiO$_3$ heterostructures, we find that while the condensates of the (001) and (110) oriented interfaces must be time-reversal symmetric, spontaneous time-reversal-symmetry breaking can only occur for the less studied (111) interface. We also discuss the consequences for thin layers of URu$_2$Si$_2$ and UPt$_3$ as well as for single-layer FeSe. On a more general level, our considerations might serve as a design principle in the search for time-reversal-symmetry-breaking superconductivity in the absence of external magnetic fields.
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When both two-electron textit{and} two-hole Cooper-pairing are treated on an equal footing in the ladder approximation to the Bethe-Salpeter (BS) equation, the zero-total-momentum Cooper-pair energy is found to have two textit{real} solutions $mathcal{E}_{0}^{BS}=pm 2hbar omega_{{D}%}/sqrt{{e}^{2/lambda }+{1}}$ which coincide with the zero-temperature BCS energy gap $Delta =hbar omega_{D}/sinh (1/lambda) $ in the weak coupling limit. Here, $hbar omega_{D}$ is the Debye energy and $lambda geq 0$ the BCS model interaction coupling parameter. The interpretation of the BCS energy gap as the binding energy of a Cooper-pair is often claimed in the literature but, to our knowledge, never substantiated even in weak-coupling as we find here. In addition, we confirm the two purely-textit{imaginary} solutions assumed since at least the late 1950s as the textit{only} solutions, namely, $mathcal{E}_{0}^{BS}=pm i2hbar omega_{{D}}/sqrt{{e}^{2/lambda}{-1}}.$
The Cooper pairing mechanism of heavy-fermion superconductors, while long hypothesized as due to spin fluctuations, has not been determined. It is the momentum space (k-space) structure of the superconducting energy gap delta(k) that encodes specifics of this pairing mechanism. However, because the energy scales are so low, it has not been possible to directly measure delta(k) for any heavy-fermion superconductor. Bogoliubov quasiparticle interference (QPI) imaging, a proven technique for measuring the energy gaps of high-Tc superconductors, has recently been proposed as a new method to measure delta(k) in heavy-fermion superconductors, specifically CeCoIn5. By implementing this method, we immediately detect a superconducting energy gap whose nodes are oriented along k||(+-1, +-1)pi/a0 directions. Moreover, we determine the complete k-space structure of the delta(k) of a heavy-fermion superconductor. For CeCoIn5, this novel information includes: the complex band structure and Fermi surface of the hybridized heavy bands, the fact that highest magnitude delta(k) opens on a high-k band so that gap nodes occur at quite unanticipated k-space locations, and that the Bogoliubov quasiparticle interference patterns are most consistent with dx2-y2 gap symmetry. The availability of such quantitative heavy band- and gap-structure data will be critical in identifying the microscopic mechanism of heavy fermion superconductivity in this material, and perhaps in general.
In multiorbital materials, superconductivity can exhibit new exotic forms that include several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control 3d-orbitals occupancy by electrostatic doping. However, the presence of multiple superconducting condensates in these systems has not yet been demonstrated. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO3/SrTiO3 interface in the entire phase diagram. We evidence a transition from single-band to two-band superconductivity driven by electrostatic doping, which we relate to the filling of the different 3d-orbitals based on numerical simulations of the quantum well. Interestingly, the superconducting transition temperature decreases while the second band is populated, which challenges the Bardeen-Cooper-Schrieffer theory. To explain this behaviour, we propose that the superconducting order parameters associated with the two bands have opposite signs with respect to each other.
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