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arXiv:2006.13529 · Physical review. B./Physical review. B

Memory-critical dynamical buildup of phonon-dressed Majorana fermions

Oliver Kaestle, Yue Sun, Ying Hu, Alexander Carmele

Published Dec 11, 2020• 1 citation
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Abstract

We investigate the dynamical interplay between the topological state of matter and a non-Markovian dissipation, which gives rise to a crucial timescale into the system dynamics due to its quantum memory. We specifically study a one-dimensional polaronic topological superconductor with phonon-dressed $p$-wave pairing, when a fast temperature increase in surrounding phonons induces an open-system dynamics. We show that when the memory depth increases, the Majorana edge dynamics transits from relaxing monotonically to a plateau of substantial value into a collapse-and-buildup behavior, even when the polaron Hamiltonian is close to the topological phase boundary. Above a critical memory depth, the system can approach a new dressed state of the topological superconductor in dynamical equilibrium with phonons, with nearly full buildup of the Majorana correlation.

DOI
10.1103/physrevb.102.245115

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We investigate the dynamical interplay between the topological state of matter and a non-Markovian dissipation, which gives rise to a crucial timescale into the system dynamics due to its quantum memory. We specifically study a one-dimensional polaronic topological superconductor with phonon-dressed ppp-wave pairing, when a fast temperature increase in surrounding phonons induces an open-system dynamics. We show that when the memory depth increases, the Majorana edge dynamics transits from relaxing monotonically to a plateau of substantial value into a collapse-and-buildup behavior, even when the polaron Hamiltonian is close to the topological phase boundary. Above a critical memory depth, the system can approach a new dressed state of the topological superconductor in dynamical equilibrium with phonons, with nearly full buildup of the Majorana correlation.
Majorana bosons, that is, tight bosonic analogues of the Majorana fermionic quasi-particles of condensed-matter physics, are forbidden for gapped free bosonic matter within a standard Hamiltonian scenario. We show how the interplay between dynamical metastability and non-trivial bulk topology makes their emergence possible in non-interacting bosonic chains undergoing Markovian dissipation. This leads to a distinctive form of topological metastability whereby, consistent with the breakdown of Noether's theorem for open systems, a conserved Majorana boson localized on one edge is paired with a distinct symmetry generator localized on the opposite edge. We argue that Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum. Our results suggest that symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which are still stable over practical time scales.
Majorana bosons, that is, tight bosonic analogs of the Majorana fermionic quasiparticles of condensed-matter physics, are forbidden for gapped free bosonic matter within a standard Hamiltonian scenario. We show how the interplay between dynamical metastability and nontrivial bulk topology makes their emergence possible in noninteracting bosonic chains undergoing Markovian dissipation. This leads to a distinctive form of topological metastability, whereby a conserved Majorana boson localized on one edge is paired, in general, with a symmetry generator localized on the opposite edge. We argue that Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum. Our results suggest that symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which persist over practical timescales.
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We investigate the robustness of topological superconductors under the perturbing influence of a finite charge current. To this aim, we introduce a modified Kitaev Hamiltonian parametrically dependent on the quasiparticle momentum induced by the current. Using different quantifiers of the topological phase, such as the Majorana polarization and the edge state quantum conditional mutual information, we prove the existence of a finite critical value of the quasiparticle momentum below which edge modes and topological superconductivity survive. We also discuss how a finite current breaks time reversal symmetry and changes the topological class in the Altland-Zirnbauer classification scheme compared to the case of isolated systems. Our findings provide a nontrivial example of the interplay between topology and the nonequilibrium physics of open quantum systems, a relation of crucial importance in the quest to a viable topological quantum electronics.
The one-dimensional (1D) Kitaev model in the topological phase, with open boundary conditions, hosts Majorana zero modes. These are fermion parity-odd operators that almost commute with the Hamiltonian and manifest in long coherence times for edge degrees of freedom. We obtain higher-dimensional counterparts of such Majorana operators by explicitly computing their closed form expressions in models describing 2D and 3D higher-order superconductors. Due to the existence of such Majorana zero modes, the coherence time of the infinite temperature autocorrelation function of the corner Majorana operators in these models diverges with the linear system size. In the presence of a certain class of orbital-selective dissipative dynamics, the coherence times of half of the corner Majorana operators are enhanced, while the time correlations corresponding to the remaining corner Majoranas decay much faster as compared with the unitary case. We numerically demonstrate robustness of the coherence times to the presence of disorder.