Qumiao Si and Emilian Nica may not have come up with a new theory had the 2017 model of orbital-selective superconductivity been named differently. (Image Credit: Jeff Fitlow/Rice University)


Physicists Qumiao Si and Emilian Nica may not have come up with a new theory had their 2017 model of orbital-selective superconductivity been named differently. The new theory could explain how unconventional superconductivity arises in a diverse set of compounds. They argue that superconductivity in some iron-based and heavy-fermion materials arises from a phenomenon named "multiorbital singlet pairing."


Electrons can form pairs and pass through with no resistance in superconductors. Physicians aren't able to explain how pairs form in non-traditional superconductors, where quantum forces give rise to odd behavior. Heavy fermions contain electrons that are thousands of times larger than ordinary electrons.


In 2017, Si and Nica came up with the idea of selective pairing within atomic orbitals. This helped to explain unconventional superconductivity in alkaline iron selenides. One year later, they used the orbital-selective model on the heavy-fermion material. They thought about naming the model after a mathematical expression made famous by Wolfgang Pauli. Instead, they chose to name it d+d, which refers to mathematical wave functions describing quantum states.


"It's like you have a pair of electrons that dance with each other," said Si, Rice's Harry C. and Olga K. Wiess Professor of Physics and Astronomy. "You can characterize that dance by s- wave, p-wave and d-wave channels, and d+d refers to two different kinds of d-waves that fuse together into one."

After publishing the d+d model, Si provided lectures about the work and discovered that the audience confused the name with "d+id."


"People would approach me after a lecture and say, 'Your theory of d+id is really interesting,' and they meant it as a compliment, but it happened so often it got annoying," said Si.


Later in 2019, Si and Nica met-up during a visit to Los Alamos National Laboratory and shared stories about the d+d and d+id confusion.


"That led to a discussion of whether d+d might be connected with d+id in a meaningful way, and we realized it was not a joke," Nica said. "There are two types of superfluid pairing states of liquid helium-3, one called the B phase and the other the A phase," Nica said. "Empirically, the B phase is similar to our d+d, while the A phase is almost like a d+id."

The analogy got even more interesting when mathematics came into play. Matrix calculations are used to define quantum pairing states in helium-3, which is also the case for the d+d model.


"You have a number of different ways of organizing that matrix, and we realized our d+d matrix for the orbital space was like a different form of the d+id matrix that describes helium-3 pairing in spin space," Nica said. The associations with superfluid helium-3 pairing states have helped Si and Nica with their description of pairing states in iron-based and heavy-fermion superconductors.


"We use symmetries—like lattice or spin arrangements, or whether time moving forward versus backward is equivalent, which is time-reversal symmetry—to organize possible pairing states," he said. "Our revelation was that d+id can be found in the existing list. You can use the periodic table to construct it. But d+d, you cannot. It's beyond the periodic table because the table doesn't include orbitals."


Orbitals are needed to describe the behaviors of iron-based superconductors and heavy fermions, where "very strong electron-electron correlations play a crucial role."


"Based on our work, the table needs to be expanded to include orbital indices," Si said.


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