The concept of a vestigial nematic order emerging from a "mother" spin or charge-density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range density-wave order. Interestingly, rare droplets with moderately large sizes undergo a second-order nematic transition even before the first-order quantum transition of the clean system. This gives rise to an extended regime of inhomogeneous nematic order, which is followed by a density-wave quantum Griffiths phase. As a result, a smeared quantum nematic transition, separated from the density-wave quantum transition, emerges in moderately disordered systems.
Bibliographical noteFunding Information:
We thank A. Chubukov, P. Orth, and J. Schmalian for fruitful discussions. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0012336.
© 2018 American Physical Society.