Superfluid Stiffness Bounds in Time-Reversal Symmetric Superconductors

Area of Science:

• Condensed matter physics
• Quantum geometry
• Superconductivity

Background:

• Quantum geometry influences superfluid stiffness in flatband superconductors.
• Moiré materials are a key example of systems exhibiting this phenomenon.

Purpose of the Study:

• Derive an expression for superfluid stiffness in time-reversal symmetric superconductors at zero temperature.
• Clarify the physical origin of the quantum geometric contribution to superfluid stiffness.

Main Methods:

• Utilized mean-field theory to compute the ground state energy as a function of pairing momentum.
• Derived general lower and upper bounds for superfluid stiffness applicable to continuum and lattice models.

Main Results:

• Identified broken Galilean invariance in the interaction Hamiltonian as the source of the quantum geometric contribution.
• Showcased that effects of broken Galilean invariance extend beyond previous quantum metric parametrizations.
• Demonstrated that a derived lower bound is saturated by systems with Landau-level form factors.

Conclusions:

• The study clarifies the physical origin of geometric contributions to superfluid stiffness.
• Provides a novel perspective on quantum geometry effects in interacting electron systems.
• The derived bounds and insights are applicable to both continuum and lattice models.