Survival probability of an edge Majorana in a one-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-wave superconducting chain under sudden quenching of parameters

Rajak, Atanu; Dutta, Amit

doi:10.1103/physreve.89.042125

Cited by 56 publications

(49 citation statements)

References 52 publications

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“…Can the existence of topological order lead to a different realm in nonequilibrium dynamics? Studies of such synergy [30,31,38,39,61] have just begun to explore diverse and exciting phenomena with regards to dynamic evolution of topological features. In previous work by two of the authors of this article and co-workers, reference [62], the term 'topological blocking' was coined with regards to the role played by a highlighting feature of topological order-ground state degeneracies-in quench dynamics.…”

Section: Introductionmentioning

confidence: 99%

Quench dynamics and parity blocking in Majorana wires

et al. 2015

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We theoretically explore quench dynamics in a finite-sized topological fermionic p-wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick's theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities -the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term "parity blocking". This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.

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Section: Introductionmentioning

confidence: 99%

Quench dynamics and parity blocking in Majorana wires

et al. 2015

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“…On the one hand, in an equilibrium state with topological order, features like edge states are protected by a bulk gap [4], while such protection may not be effective in dynamical processes, especially in quench dynamics, where the sudden change inevitably induces high-energy excitations [37]. On the other hand, despite many recent studies on topological phases and edge states in quantum quenches, topology in a dynamical process is still an on-going area of research that needs further characterization [34][35][36][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin–orbit coupling

Wang

Xianlong

2015

New J. Phys.

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We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.

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“…Especially, the quenching dynamics of a topological insulator [27] and the p-wave superconducting chain [28][29][30] have been explored in this connection. We note that the dynamical generation [31], formation, and manipulation [32] of Majorana edge states for a driven system have also been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Possibility of adiabatic transport of a Majorana edge state through an extended gapless region

2014

Self Cite

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In the context of slow quenching dynamics of a p-wave superconducting chain, it has been shown that a Majorana edge state cannot be adiabatically transported from one topological phase to the other separated by a quantum critical line. On the other hand, the inclusion of a phase factor in the hopping term, which breaks the effective time-reversal invariance, results in an extended gapless region between two topological phases. We show that for a finite chain with an open boundary condition, there exists a nonzero probability that a Majorana edge state can be adiabatically transported from one topological phase to the other across this gapless region following a slow quench of the superconducting term; this happens for an optimum transit time, which is proportional to the system size and diverges for a thermodynamically large chain. We attribute this phenomenon to the mixing of the Majorana only with low-lying inverted bulk states. Remarkably, the Majorana state always persists with the same probability even after the quenching is stopped. For a periodic chain, on the other hand, we find a Kibble-Zurek scaling of the defect density with a renormalized rate of quenching.

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Survival probability of an edge Majorana in a one-dimensionalp-wave superconducting chain under sudden quenching of parameters

Cited by 56 publications

References 52 publications

Quench dynamics and parity blocking in Majorana wires

Quench dynamics and parity blocking in Majorana wires

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin–orbit coupling

Possibility of adiabatic transport of a Majorana edge state through an extended gapless region

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