Edge quantum criticality and emergent supersymmetry in topological phases.

Zixiang Li, Yi‐Fan Jiang, Hong Yao

Proposed as a fundamental symmetry describing our Universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, it has been predicted that SUSY may emerge in low-energy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing state-of-the-art sign-problem-free quantum Monte Carlo simulations of an interacting two-dimensional topological superconductor, we show convincing evidence that the N=1 SUSY emerges at its edge quantum critical point (EQCP) while its bulk remains gapped and topologically nontrivial. Remarkably, near the EQCP, we find that the edge Majorana fermion acquires a mass that is identical with that of its bosonic superpartner. To the best of our knowledge, this is the first observation that fermions and bosons have equal dynamically generated masses, a hallmark of emergent SUSY. We further discuss experimental signatures of such EQCP and associated SUSY.

Ruben Verresen, Ryan Thorngren, Nick G. Jones +2 more

Tarun Grover, D. N. Sheng, Ashvin Vishwanath

In contrast to ordinary symmetries, supersymmetry interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here we theoretically show that supersymmetry emerges naturally in topological superconductors, which are well-known condensed matter systems. Specifically, we argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display supersymmetry when probed at long distances and times. Supersymmetry entails several experimental consequences for these systems, such as, exact relations between quantities measured in disparate experiments, and in some cases, exact knowledge of the universal critical exponents. The topological surface states themselves may be interpreted as arising from spontaneously broken supersymmetry, indicating a deep relation between topological phases and SUSY. We discuss prospects for experimental realization in films of superfluid He$_3$-B.

Bohm‐Jung Yang, Eun-Gook Moon, Hiroki Isobe +1 more

Longwen Zhou, Jiangbin Gong, Xue-Jia Yu

Topologically protected edge states exactly at topological phase boundaries challenge the conventional belief that topological states must be associated with a bulk energy gap. Because periodically driven (Floquet) systems host unusually intricate topological phase boundaries, topological edge states can be prolific at such Floquet quantum criticality. Working on a class of chiral-symmetric, Floquet-driven Majorana fermion chains, we analytically and computationally show that the precise boundaries between different Floquet topological gapped phases can accommodate topological edge modes, including the so-called critical Majorana π modes. We also identify a general bulk-edge correspondence formula to predict and understand the emergence of topological edge modes at Floquet quantum criticality. Of direct interest to quantum simulation experiments, our work opens an avenue for exploring topological physics intrinsic to nonequilibrium phase boundaries. The authors develop a theoretical framework to characterize the topology and edge states at the nonequilibrium critical points of periodically driven (Floquet) quantum systems. The rule of bulk-edge correspondence applicable to both gapped and gapless Floquet topological phases in 1D chiral symmetric driven systems is proposed.

Ruben Verresen, Nick G. Jones, Roderich Moessner +1 more