Pauli limited d-wave superconductors: quantum breached pair phase and thermal transitions

Abstract

We report a quantum phase transition in Pauli limited d-wave superconductors and give the mean field estimates of the associated quantum critical point. For a population imbalanced d-wave superconductor a stable ground state phase viz quantum breached pair phase has been identified which comprises of spatial coexistence of gapless superconductivity and nonzero magnetization. Based on the thermodynamic and quasiparticle indicators we for the first time analyze this phase, discuss the thermal behavior of Pauli limited d-wave superconductor, give accurate estimates of the thermal scales associated with such systems and map out the pseudogap regime. Our work shows that while the Pauli limited superconductors are known to exhibit exotic modulated superconducting phase at large imbalance of fermion populations; in the regime of weak imbalance an intriguing phase of competing orders is realized. We have established that rather than the superconducting pairing field, it is the average magnetization of the system that quantifies this quantum phase transition. Given that the existing Pauli limited superconductors possess unconventional pairing state symmetry of the superconducting order, our work promises to open up new avenues in the experimental research of these materials. We have also demonstrated an alternate scenario wherein the quantum breached pair phase is a natural outcome for a d-wave superconductor with unequal effective masses of the fermion species.

Imbalanced Fermi systems and exotic superconducting phases

“…Evidently, all the numerical approaches have different set of merits and caveats, and consequently different regimes of applicability. We now discuss the numerical implementation of the SPA technique in some detail [122,123,124,125,126]. The merits of this technique rests on its applicability, in principle to systems of arbitrary dimensions and lattice sizes, with moderate computation cost and its access to real frequency properties of the system.…”

“…This imposes constraint on the lattice size that can be accessed within reasonable computation time. In order to access larger system sizes a cluster based update scheme could be utilized wherein instead of diagonalizing for the entire lattice at each attempted update, a smaller cluster of size N c = L c ×L c surrounding the update site is diagonalized [123,124,126]. This reduces the cost per update to ∼ O(N 3 c ) and to ∼ N × O(N 3 c ) per lattice sweep, which scales linearly with the system size.…”

“…The static path approximation (SPA) technique was used at a fixed chemical potential and intermediate interactions to address the behavior of two-dimensional population imbalanced d-wave superconductor, in detail [126]. The corresponding phase diagram as shown in Figure 10 was mapped out in the magnetization-temperature (m-T) as well as in the field-temperature (h-T) plane.…”

“…Based on the real space signatures shown in Figure 11 and Figure 12 it, was inferred that both field and temperature leads to spatial inhomogeneity in the superconducting state, which shows up in the quasiparticle signatures as the "pseudogap" behavior. The phase diagram thus comprises of an additional thermal scale T pg as shown in Figure 10, where short range superconducting pair correlations die out, long after the loss of long range superconducting phase coherence at T c [126].…”

Mutual information, quantum phase transition, and phase coherence in Kondo systems

“…This ignores the temporal fluctuations of the auxiliary fields but takes full account of their spatial fluctuations and probabilistic distribution beyond the mean-field approximation [59][60][61][62][63][64]. To see how it works, we first integrate out all fermionic degrees of freedom and obtain an effective action only of the auxiliary fields,…”