Effect of incommensurate disorder on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev's chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of $e^2/h$, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate disorder suppresses the current at finite voltage bias, and then narrows the linear response regime of the $I-V$ curve which exhibits two plateaus corresponding to the superconducting gap and the band edge respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value $2+2\Delta$ with $\Delta$ the p-wave pairing amplitude, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage will also cause an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose $I-V$ curve exhibits an exponential shape.Comment: 9 pages, 7 figure

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas

We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential 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.Comment: 7 pages, 5 figure

The Shi arrangement of the type DℓD_\ell

In this paper, we give a basis for the derivation module of the cone over the Shi arrangement of the type $D_\ell$ explicitly

Two-particle dark state cooling of a nanomechanical resonator

The steady-state cooling of a nanomechanical resonator interacting with three coupled quantum dots is studied. General conditions for the cooling to the ground state with single and two-electron dark states are obtained. The results show that in the case of the interaction of the resonator with a single-electron dark state, no cooling of the resonator occurs unless the quantum dots are not identical. The steady-state cooling is possible only if the energy state of the quantum dot coupled to the drain electrode is detuned from the energy states of the dots coupled to the electron source electrode. The detuning has the effect of unequal shifting of the effective dressed states of the system that the cooling and heating processes occur at different frequencies. For the case of two electrons injected to the quantum dot system, the creation of a two-particle dark state is established to be possible with spin-antiparallel electrons. The results predict that with the two-particle dark state, an effective cooling can be achieved even with identical quantum dots subject of an asymmetry only in the charging potential energies coupling the injected electrons. It is found that similar to the case of the single-electron dark state, the asymmetries result in the cooling and heating processes to occur at different frequencies. However, an important difference between the single and two-particle dark state cases is that the cooling process occurs at significantly different frequencies. This indicates that the frequency at which the resonator could be cooled to its ground state can be changed by switching from the one-electron to the two-electron Coulomb blockade process.Comment: Published versio