Universal dynamical scaling of long-range topological superconductors
Year: 2019
Authors: Defenu N., Morigi G., Dell’Anna L., Enss T.
Autors Affiliation: Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Univ Saarland, Theoret Phys, D-66123 Saarbrucken, Germany; Univ Padua, Dipartimento Fis & Astron G Galilei, Via Marzolo 8, I-35131 Padua, Italy.
Abstract: We study the out-of-equilibrium dynamics of p-wave superconducting quantum wires with long-range interactions when the chemical potential is linearly ramped across the topological phase transition. We show that the heat produced after the quench scales with the quench rate delta according to the scaling law delta(theta) where the exponent theta depends on the power-law exponent of the long-range interactions. The presence of the long-range pairing term increases the exponent theta and thus improves the adiabatic preparation of topological states. Moreover, we identify the parameter regimes where the heat scaling can be cast in terms of the universal equilibrium critical exponents and can thus be understood within the Kibble-Zurek framework. When the electron hopping decays more slowly in space than pairing, it dominates the equilibrium scaling. Surprisingly, in this regime the dynamical critical behavior arises only from pairing and thus exhibits a dynamical universality unrelated to equilibrium scaling. The discrepancy from the expected Kibble-Zurek scenario can be traced back to the presence of multiple universal terms in the equilibrium scaling functions of long-range interacting systems close to a second order critical point.
Journal/Review: PHYSICAL REVIEW B
Volume: 100 (18) Pages from: 184306-1 to: 184306-9
More Information: N.D. is grateful to S. Ruffo, A. Trombettoni, and G. Gori for useful discussions at the early stages of this work. N.D. and T.E. acknowledge financial support by Deutsche Forschungsgemeinschaft (DFG) via Collaborative Research Centre SFB 1225 (ISOQUANT) and under Germany’s Excellence Strategy EXC-2181/1-390900948 (Heidelberg STRUCTURES Excellence Cluster). L.D. acknowledges financial support from the BIRD2016 project of the University of Padova. G.M. is grateful for financial support by the DFG Priority Program No. 1929 GiRyd and by the German Ministry of Education and Research (BMBF) via the Quantera project NAQUAS. Project NAQUAS has received funding from the QuantERA ERA-NET Cofund in Quantum Technologies implemented within the European Union’s Horizon 2020 Programme.KeyWords: Quantum Phase-transition; Majorana Fermions; BreakdownDOI: 10.1103/PhysRevB.100.184306Citations: 18data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)