动力学集团近似下玻色子的奇异超导性
Exotic Superconductivity Through Bosons in a Dynamical Cluster Approximation
摘要：
本文采用动态集团近似（DCA）方法，利用数值精确的连续时间Monte-Carlo方法，研究了二维正方晶格上自旋- $1/2$费米子与标量玻色子耦合的混合体的超导不稳定性. Bogoliubov玻色子为费米子提供了一个有效的声子浴，并在费米子之间引起非局域的阻滞相互作用，这可以导致（奇异的）超导性。由于符号问题，我们能研究的最大的团簇在大小上被限制在$2 \times 2$，但这仍然允许我们研究配对不稳定性，以及它们在$s$和$d$波通道中可能的发散，以及与反铁磁波动的竞争。在费米子半填充时，我们发现当玻色子介导的相互作用与裸费米子排斥具有相同的量级时，$d$波是稳定的。它的临界温度可以达到$s$波的最高温度，这为在冷原子实验中探测它开辟了前景。
英文摘要：
We study the instabilities towards (exotic) superconductivity of mixtures of spin-$1/2$ fermions coupled to scalar bosons on a two-dimensional square lattice with the Dynamical-Cluster-Approximation (DCA) using a numerically exact continuous-time Monte-Carlo solver. The Bogoliubov bosons provide an effective phononic bath for the fermions and induce a non-local retarded interaction between the fermions, which can lead to (exotic) superconductivity. Because of the sign problem the biggest clusters we can study are limited to $2 \times 2$ in size, but this nevertheless allows us to study the pairing instablilities, and their possible divergence, in the $s$- and $d$ -wave channels as well as the competition with antiferromagnetic fluctuations. At fermionic half-filling we find that $d$-wave is stable when the mediated interaction by the bosons is of the same order as the bare fermionic repulsion. Its critical temperature can be made as high as the maximum one for $s$-wave, which opens perspectives for its detection in a cold atom experiment.
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