We investigate the topological properties of a dimerized Kitaev chain with long-range interactions, including the intercell hopping and superconducting pairing terms. It is found that even only when the intercell hopping term appears, the size of the energy gap, the proportion of topological phases, and the topological phase transition can be modulated. The notable result is that they lead to a new Kitaev-like phase featured by the twofold-degenerated Majorana zero-energy edge states. Next in the presence of the intercell superconducting pairing term, this kind of Majorana phase can be magnified. This work provides new proposals to realize the twofold degenerated Majorana modes based on the intercell hopping and superconducting pairing terms of the dimerized Kitaev chain.
Motivated by the recent experimental observation of the topological Anderson insulator in disordered atomic wires based on the Su-Schrieffer-Heeger (SSH) model, we study disorder effects on a dimerized Kitaev superconductor chain which is regarded as the superconductor version of the SSH model. By computing the real-space winding number and the zero-bias differential conductance, we analyze the topological phase transitions occurring in a dimerized Kitaev superconductor chain with disorder. It is found that disorder can induce a topologically nontrivial superconductor phase hosting Majorana ze…
The one dimensional closed interacting Kitaev chain and the dimerized version are studied. The topological invariants in terms of Green's function are calculated by the density matrix renormalization group method and the exact diagonalization method. For the interacting Kitaev chain, we point out that the calculation of topological invariant in the charge density wave phase must consider the dimerized configuration of the ground states. The variation of topological invariant are attributed to the poles of eigenvalues of the zero-frequency Green's functions. For the interacting dimerized Kitaev…
We investigate localization and topological properties of a dimerized Kitaev chain with p-wave superconducting correlations and a quasiperiodically modulated chemical potential. With regard to the localization studies, we demonstrate the existence of distinct phases, such as, the extended phase, the critical (intermediate) phase, and the localized phase that arise due to the competition between the dimerization and the onsite quasiperiodic potential. Most interestingly, the critical phase comprises of two different mobility edges that are found to exist between the extended to the localized ph…
A moiré pattern occurs when two periodic structures in a system have a slight mismatch period, resulting the coexistence of distinct phases in different large-scale spacial regions of the same system. Two periodic structures can arise from periodic electric and magnetic fields, respectively. We investigated the moiré pattern via a dimerized Kitaev spin chain with a periodic transverse field, which can be mapped onto the system of dimerized spinless fermions with p-wave superconductivity. The exact solution for staggered field demonstrated that the ground state has two distinct phases: (i) Neel…
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice's hopping amplitudes can induce a series of bulk energy gap openings in the Hofstadter spectrum at certain fractional fillings, giving rise to various topological phases. In particular, we show that at $\frac{1}{2}$-filling the topological quadrupole insulator phase with a quadrupole moment quantized to $\frac{e}{2}$ and associated corner-localized mid-gap states exists in certain parameter regime for all magnetic fluxes. At $\frac…
We investigate the evolutions of edge Majorana fermions (MFs) and unveil that they can be used to char- acterize different topological phases and study the topological phase transitions. For some limiting cases of the evolution process for the one-dimensional Kitaev model and Su-Schrieffer-Heeger (SSH) model, we give analytical expressions of the survival probabilities of the edge MFs, which indicates that different topological phases correspond to different zero point numbers of the defined survival probabilities at some times. For a general case, we consider a dimerized Kitaev model and the …
We present an analytical solution for the full spectrum of Kitaev's one-dimensional p-wave superconductor with arbitrary hopping, pairing amplitude and chemical potential in the case of an open chain. We also discuss the structure of the zero-modes in the presence of both phase gradients and next nearest neighbor hopping and pairing terms. As observed by Sticlet et al., one feature of such models is that in a part of the phase diagram, zero-modes are present at one end of the system, while there are none on the other side. We explain the presence of this feature analytically, and show that it …
We study a non-Hermitian Kitaev chain model that contains three sources of non-Hermiticity: a constant imaginary potential, asymmetry between hopping amplitudes $t_{\rm R}$ and $t_{\rm L}$ in the right and left directions, and imbalance in pair potentials $Δ_{\rm c}$ and $Δ_{\rm a}$ for pair creation and annihilation, respectively. We show that bulk--boundary correspondence holds in this system; two topological invariants defined in bulk geometry under a modified periodic boundary condition correctly describe the presence or absence of a pair of boundary zero modes in boundary geometry under a…
We show how a recently proposed solid state Majorana platform comprising a planar Josephson junction proximitized to a 2D electron gas (2DEG) with Rashba spin-orbit coupling and Zeeman field can be viewed as an effectively one dimensional (1D) Kitaev chain with long-range pairing and hopping terms. We highlight how the couplings of the 1D system may be tuned by changing experimentally realistic parameters. We also show that the mapping is robust to disorder by computing the Clifford pseudospectrum index in real space for the long-range Kitaev chain across several topological phases. This mappi…
Poor man's Majorana bound states in quantum dot based Kitaev chain coupled to a photonic cavity
CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院）；Institute of Fundamental Physics IFF-CSIC（西班牙高等科学研究理事会基础物理研究所）；JEIP, UAR 3573 CNRS, Collège de France, PSL Research University（法兰西公学院）
We study local and non-local transport across a two-leg long-range Kitaev ladder connected to two normal metal leads. We focus on the role of the constituent Majorana fermions and the subgap Andreev states. The double degeneracy of Majorana fermions of the individual legs of the ladder gets lifted by a coupling between the two leading to the formation of Andreev bound states. The coupling can be induced by a superconducting phase difference between the two legs of the ladder accompanied by a finite inter-leg hopping. Andreev bound states formed strongly enhance local Andreev reflection. When t…
We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly degenerate ground states even for finite system sizes. We present analytical results for the strong Majorana zero modes, the phase diagram and the topological order. Furthermore, we generalise our results to include interactions.
We study a 1D chain of non-interacting bosonic cavities which are subject to nearest-neighbour parametric driving. With a suitable choice of drive phases, this model is strongly analogous to the celebrated Kitaev chain model of a 1D p-wave superconductor. The system exhibits phase-dependent chirality: photons propagate and are amplified in a direction that is determined by the phase of the initial drive or excitation. Further, we find a drastic sensitivity to boundary conditions: for a range of parameters, the boundary-less system has only delocalized, dynamically unstable modes, while a finit…
We consider granular quantum matter defined by Sachdev-Ye-Kitaev (SYK) dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, we identify a zero temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.
In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization properties of the Aubry-André-Harper model in the presence of long-range hopping and superconducting pairing amplitudes. These amplitudes decay with power-law exponents $ξ$ and $α$ respectively. To this end, we review and compare a toolbox of global and local characterization methods in order to investigate different types of transitions between ergodic, localized…
We show that the pair of Majorana modes at each end of a 1D spin triplet superconductor with total Cooper pair spin S_x=0 (i.e., Delta_{up,up} = -Delta_{down,down} = p*Delta_0; two uncoupled time reversed copies of the Kitaev p-wave chain) are topologically robust to perturbations such as mixing by the S_z=0 component of the order parameter (Delta_{up,down}=Delta_{down,up}), transverse hopping (in quasi-1D systems), non-magnetic disorder, and also, most importantly, to time reversal breaking perturbations such as applied Zeeman fields/magnetic impurities and the mixing by the S_y=0 component o…
We study the effects of disorder on a Kitaev chain with longer-range hopping and pairing terms which is capable of forming local zero energy excitations and, hence, serves as a minimal model for localization-protected edge qubits. The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes (MZMs) per edge. Using a semi-analytic approach corroborated by numerical calculations of the entanglement degeneracy, we show how phase boundaries evolve under the influence of disorder. While in general the 2 MZM region is stable with respect to moderate disorder, stronger values drive trans…
