Majorana zero modes in a ladder of density-modulated Kitaev superconductor chains

Zhou, Bozhen; Xu, Dong-Hui; Zhou, Bin

doi:10.1016/j.physleta.2017.05.035

Cited by 9 publications

(7 citation statements)

References 47 publications

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“…Various generalizations of the single Kitaev chain have recently appeared [13,14,15,16,17,18], the simplest one being obtained by coupling two single Kitaev chains with transversal hopping and pairing terms to form a Kitaev ladder (KL) [19]. The Hamiltonian of the system is given by:H=HK1+HK2+HK1,K2, where HK1 and HK2 are the Hamiltonians of the isolated Kitaev chains given in Equation (1), while HK1,K2 describes the interchain coupling whose expression is given by:HK1,K2=∑j=1L[−t1aj,1†aj,2+Δ1aj,1aj,2+h.c.].…”

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

“…The topological phase diagram can be obtained by the calculation of the winding number [18,21]. Using the chiral basis, the Hamiltonian (8) assumes the following off-diagonal form [21] H˜(k)=UH(k)U†=0AkAk†0, where U is the basis change matrix and Ak is the 2×2 matrix Ak=−ϵk−iΔk−t1−Δ1−t1+Δ1−ϵk−iΔk.…”

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

“…Following Zhou et al [18], we calculate the winding number as W=Tr∫−ππdk2πi4pt4ptAk−1∂kAk=−∫−ππdk2πi4pt4pt∂kprefixlnDetAk and compute the topological phase diagram, which is systematically analyzed in the following discussion. To provide evidence of the richness of the topological phases of the model, in the following, we present our results using an extended parameters range, which in principle could be completely explored in cold atoms experiments rather than in condensed matter systems.…”

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

“…Various generalization of the single Kitaev chain have recently appeared [13][14][15][16][17][18] , the simplest one being obtained by coupling two single Kitaev chains with transversal hopping and pairing terms to form a Kitaev ladder (KL) 19 . The Hamiltonian of the system is given by:…”

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

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Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders

et al. 2019

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In this work, the general problem of the characterization of the topological phase of an open quantum system is addressed. In particular, we study the topological properties of Kitaev chains and ladders under the perturbing effect of a current flux injected into the system using an external normal lead and derived from it via a superconducting electrode. After discussing the topological phase diagram of the isolated systems, using a scattering technique within the Bogoliubov–de Gennes formulation, we analyze the differential conductance properties of these topological devices as a function of all relevant model parameters. The relevant problem of implementing local spectroscopic measurements to characterize topological systems is also addressed by studying the system electrical response as a function of the position and the distance of the normal electrode (tip). The results show how the signatures of topological order affect the electrical response of the analyzed systems, a subset of which being robust also against the effects of a moderate amount of disorder. The analysis of the internal modes of the nanodevices demonstrates that topological protection can be lost when quantum states of an initially isolated topological system are hybridized with those of the external reservoirs. The conclusions of this work could be useful in understanding the topological phases of nanowire-based mesoscopic devices.

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Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

Section: Ladder Of Two Kitaev Chainsmentioning

confidence: 99%

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Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders

et al. 2019

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“…On the theoretical side, we are not aware of similar studies of the spin ladders with the anisotropy and dimerization, however there has been work done on the groundstate phases and entanglement in the Kitaev fermionic ladders with modulations and anomalous terms [21][22][23][24][25][26][27][28][29]. Such fermionic models are the closest counteparts of the spin ladders in question, since the models with 1 2 -spins or spinless fermions can be mapped onto each other by a judiciously chosen Jordan-Wigner transformation.…”

Section: Introductionmentioning

confidence: 99%

Brane order and quantum magnetism in modulated anisotropic ladders

Pandey¹,

Chitov²

2021

Preprint

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Two-leg spin-1 2 ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to a sum of two (even/odd) XY quantum chains in the alternating transverse fields. The mapping between the effective Hamiltonian of the ladder and the pair of the dual XY chains considerably simplifies calculations the order parameters and analysis of the hidden symmetry breaking. The ground-state phase diagram of the staggered ladder contains nine phases, four of them are conventional antiferromagnets, while the other five possess non-local brane orders. Using the dualities and the newly found exact results for the local and string order parameters of the transverse XY chains, we were able to find analytically all the magnetizations and the brane order parameters for the staggered case, as functions of the renormalized couplings of the effective Hamiltonian. The columnar ladder has three ground-state phases and does not possess magnetic long-ranged order. The brane order parameters for these three phases are calculated numerically from the Toeplitz determinants. We expect this study to motivate the search for the real spin-Peierls anisotropic ladder compounds which can undergo the predicted quantum phase transitions with gap closures and distinct brane orders.

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Topological Phase Transition and Phase Diagrams in a Two‐Leg Kitaev Ladder System

Yan

Wang

et al. 2020

Annalen der Physik

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A scheme to investigate the topological properties in a two‐leg Kitaev ladder system composed of two Kitaev chains is proposed. In the case of two identical Kitaev chains, it is found that the interchain hopping amplitude plays a significant role in the separation of the energy spectrum and in inducing a topologically nontrivial phase, while the interchain pairing strength only affects the size of the energy gap. Moreover, another situation that the system consists of two non‐identical Kitaev chains is also investigated and the corresponding phase diagram is calculated. It is found that two pairs of degenerate nonzero edge modes will, respectively, appear in the upper and lower energy gaps when the interchain hopping amplitude or the interchain pairing strength is large enough. Furthermore, it is pointed out that the winding number is quantitatively equivalent to half of the number of zero energy edge modes in our system.

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Majorana zero modes in a ladder of density-modulated Kitaev superconductor chains

Cited by 9 publications

References 47 publications

Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders

Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders

Brane order and quantum magnetism in modulated anisotropic ladders

Topological Phase Transition and Phase Diagrams in a Two‐Leg Kitaev Ladder System

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