Fate of Majorana fermions and Chern numbers after a quantum quench

Abstract

The stability of Majorana fermions at the edges of a two-dimensional topological supercondutor is studied, after quenches to either non-topological phases or other topological phases. Both instantaneous and slow quenches are considered. In general, the Majorana modes decay and, in the case of instantaneous quenches, their revival times scale to infinity as the system size grows. Considering fast quantum quenches within the same topological phase, leads, in some cases, to robust edge modes. Quenches to a topological $Z_2$ phase reveal some robustness of the Majorana fermions. Comparing strong spin-orbit coupling with weak spin-orbit coupling, it is found that the Majorana fermions are fairly robust, if the pairing is not aligned with the spin-orbit Rashba coupling. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number oscillates between increasing values. In some cases, the time average Chern number seems to converge to the appropriate value, but often the decay is very slow. The effect of varying the rate of change in slow quenches is also analysed. It is found that the defect production is non-universal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.

arXiv comment14 pages, 19 figures

References in corpus (82)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Berry Phase Effects on Electronic Properties
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• New directions in the pursuit of Majorana fermions in solid state systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Theory of Phase Ordering Kinetics
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Time-dependence of correlation functions following a quantum quench
• Cosmological Experiments in Condensed Matter Systems
• Dynamics of a Quantum Phase Transition
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Superconductivty without inversion symmetry: MnSi versus CePt_3Si
• Quantum Quench in the Transverse Field Ising Chain
• Quantum Quenches in Extended Systems
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• Universal adiabatic dynamics across a quantum critical point
• Prethermalization
• Interaction Quench in the Hubbard model
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Quantum quench dynamics of the Luttinger model
• Quantum quench dynamics of some exactly solvable models in one dimension
• Solitons and Rabi Oscillations in a Time-Dependent BCS Pairing Problem
• Floquet generation of Majorana end modes and topological invariants
• Constructing the generalized Gibbs ensemble after a quantum quench
• Quantum phase transitions across p-wave Feshbach resonance
• Effective thermal dynamics following a quantum quench in a spin chain
• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Quantum quenches and thermalization in one-dimensional fermionic systems
• Synchronization in the BCS Pairing Dynamics as a Critical Phenomenon
• Quench dynamics near a quantum critical point
• Oscillating Superfluidity of Bosons in Optical Lattices
• Defect production in non-linear quench across a quantum critical point
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Dynamical vanishing of the order parameter in a fermionic condensate
• Topology induced anomalous defect production by crossing a quantum critical point
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Entropy of isolated quantum systems after a quench
• Thermalization and Quantum Correlations in Exactly Solvable Models
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Quantum Quench from a Thermal Initial State
• Mode coupling induced dissipative and thermal effects at long times after a quantum quench
• Nonequilibrium Cooper pairing in the nonadiabatic regime
• Phase Transitions out of Equilibrium: domain formation and growth
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Quantum quenches from integrability: the fermionic pairing model
• Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
• Initial state dependence of the quench dynamics in integrable quantum systems
• Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas
• Non-adiabatic processes in Majorana qubit systems
• Quench dynamics near a quantum critical point: application to the sine-Gordon model
• Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench
• Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point
• Topological Order Following a Quantum Quench
• Survival probability of an edge Majorana in a 1-D p-wave superconducting chain under sudden quenching of parameters
• Topological Rényi entropy after a quantum quench
• Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons
• Dynamical formation and manipulation of Majorana fermions in driven quantum wires
• Dynamical Selection in Emergent Fermionic Pairing
• Quantum Spinodal Decomposition
• Thermalization in Systems with Bipartite Eigenmode Entanglement
• Hall conductivity as bulk signature of topological transitions in superconductors
• Anomalous Hall effect in superconductors with spin-orbit interaction

Cited by in corpus (49)

• Dynamical preparation of Floquet Chern insulators
• Mixed state dynamical quantum phase transition and emergent topology
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Dynamical topological invariant after a quantum quench
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Topology of one dimensional quantum systems out of equilibrium
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Classification of topological insulators and superconductors out of equilibrium
• Effects of periodic kicking on dispersion and wave packet dynamics in graphene
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model
• Quench dynamics and parity blocking in Majorana wires
• Selective Population of Edge States in a 2D Topological Band System
• Floquet engineering to exotic topological phases in systems of cold atoms
• Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions
• One-dimensional quantum many body systems with long-range interactions
• Kibble-Zurek behavior in disordered Chern insulators
• Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition
• Edge and bulk localization of Floquet topological superconductors
• Floquet topological phase of nondriven $p$-wave nonequilibrium excitonic insulators
• Edge mode dynamics of quenched topological wires
• Dynamical quantum correlations after sudden quenches
• Quench Dynamics Across Topological Quantum Phase Transitions
• Quenching in Chern insulators with satellite Dirac points: The fate of edge states
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Topological phase transitions in finite-size periodically driven translationally invariant systems
• Slow quenches in two-dimensional time-reversal symmetric Z2 topological insulators
• Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven SSH chain
• Exact results in Floquet coin toss for driven integrable models
• Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems
• Topological phase transition in the quench dynamics of a one-dimensional Fermi gas
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Detecting topological phases via survival probabilities of edge Majorana fermions
• Photoinduced anomalous Hall effect in the interacting Haldane model: targeting topological states with pump pulses
• Boundary-induced dynamics in 1D topological systems and memory effects of edge modes
• Survival probability in a quenched Majorana chain with an impurity
• Electron Interaction Effects in Periodically Driven Kitaev Model: Topology Breaking and Enhancement of Quantum Chaos
• Wavepacket dynamics on Chern band lattices in a trap
• Response of fermions in Chern bands to spatially local quenches
• Universal Landau-Zener regimes in dynamical topological phase transitions
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Quench dynamics of edge states in a finite extended Su-Schrieffer-Heeger system
• Interband coherence induced correction to Thouless pumping: possible observation in cold-atom systems
• Dynamically Induced Topology and Quantum Monodromies in a Proximity Quenched Gapless Wire
• Topology in the space-time scaling limit of quantum dynamics
• Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes