Robustness of flat band superconductivity against disorder in a two-dimensional Lieb lattice model

Abstract

Recently, the possibility of high-temperature superconductivity (SC) in flat-band (FB) systems has been the focus of a great deal of activity. This study reveals that unlike conventional intra-band SC for which disorder has a dramatic impact, that associated with FBs is surprisingly robust to disorder-induced fluctuations and quasi-particle localization. In particular, for weak off-diagonal disorder, the critical temperature decreases linearly with disorder amplitude for conventional SC, whereas it is only quadratic in the case of SC in FBs. Our findings could have a major impact on the research and development of new compounds whose high purity will no longer be a critical barrier to their synthesis.

Figures (6)

• Figure 1: (a) Lieb lattice for a given configuration of disorder ($W/t=0.8$). Grey symbols are the orbital positions, colored bonds give the hopping values in the half-filled lattice. (b) Map of the square of the wave-function amplitude of a typical FB state. Only $\mathcal{B}$ sublattice is represented.
• Figure 2: (a-c) Quasi-particle density of states for $W/t=0.4, 0.8$ and $1.6$. The blue continuous lines correspond to $W/t=0$. (d-f) Spectral functions along the $\Gamma-M$ direction for the same values of the disorder strength as in panels (a-c). The system contains $40\times40$ unit cells. The dashed blue lines are the dispersions for $W/t=0$.
• Figure 3: Average pairing on sublattice $\mathcal{A}$ for three different system sizes, for $\nu=1.0$(a) and for $\nu=3.0$(b). The inset represents the average pairing on sublattice $\mathcal{B}$.
• Figure 4: (a) SFW at $T = 0$ as a function of $W/t$ at $\nu=1.0$ and $3.0$. The inset represents the ratio (R) of the SFW at $\nu=3.0$ divided by that obtained at $\nu=1.0$. (b)$D_s$ as a function of temperature for $\nu=3.0$, for $W/t=1.6$ and $N_c=16\times16$. Grey circles are the average values, the continuous lines correspond to $15$ different realizations of the disorder.
• Figure 5: BKT temperature (symbols) as a function of $W/t$ for $\nu=1.0$ and $3.0$. Dashed lines are linear and quadratic fits: $y=0.06 \times (1-0.40(W/t)^2 )$ and $y=0.029 \times (1-1.25(W/t) )$.