中国物理B：英文版

Topological phase transitions driven by next-nearest-neighbor hopping in noncentrosymmetric cold Fermi gases

王瑞, 张存喜, 计青山

Published Jan 1, 2015• 0 citations

Abstract

We investigate the topological phase marked by the Thouless–Kohmoto–Nightingale–Nijs(TKNN) number and the phase transitions driven by the next nearest neighbor(NNN) hopping in noncentrosymmetric cold Fermi gases, both spinsinglet pairing and spin-triplet pairing are considered. There exists a critical t’c for the NNN hopping, at which the quantum phase transition occurs, and the system changes from an Abelian(non-Abelian) phase to a non-Abelian(Abelian) one. By numerically diagonalizing the Hamiltonian in the real space, the energy spectra with edge states for different topological phases and the Majorana zero modes are discussed. Although the spin-triplet pairing does not contribute to the gap closing and the phase diagram, it induces gapless states in the presence of a magnetic field, and the TKNN number in this region is still zero.

Related papers

Topological phase transitions driven by next-nearest-neighbor hopping in noncentrosymmetric cold Fermi gases

Rui Wang, Cunxi Zhang, Ji Qing-Shan

We investigate the topological phase marked by the Thouless–Kohmoto–Nightingale–Nijs (TKNN) number and the phase transitions driven by the next nearest neighbor (NNN) hopping in noncentrosymmetric cold Fermi gases, both spin-singlet pairing and spin-triplet pairing are considered. There exists a critical for the NNN hopping, at which the quantum phase transition occurs, and the system changes from an Abelian (non-Abelian) phase to a non-Abelian (Abelian) one. By numerically diagonalizing the Hamiltonian in the real space, the energy spectra with edge states for different topological phases and the Majorana zero modes are discussed. Although the spin-triplet pairing does not contribute to the gap closing and the phase diagram, it induces gapless states in the presence of a magnetic field, and the TKNN number in this region is still zero.

Chinese Physics BFeb 26, 20152 citations

Topological phase transitions driven by real next-nearest-neighbor hopping in cold fermi gases

R. Wang, Y.F. Zhang, C.X. Zhang

The strength t′ of the next-nearest-neighbor (NNN) hopping in most realized square optical lattices is much smaller than that of the nearest-neighbor hopping, and is usually seen as zero. Recently, both experimental and theoretical works have shown that the magnitude of the NNN hopping can be tuned in a wide range by shaking the optical lattice. In this paper, we study the effect of the real NNN term on topological phase transitions of the cold fermi gases in a two-dimensional square anisotropic optical lattice. We investigate the gapless condition of the system and the topological phase symbolized by the TKNN number. For the real NNN hopping, there exists a critical point tc′ as a function of μ, when 0<t′<tc′, there are only non-Abelian topological phases which are indicted by an odd TKNN number, and when t′>tc′ , the Abelian topological phase appears and the zone of the phase will be widened with the increase of t′. By numerically diagonalizing the Hamiltonian in the real space, the corresponding edge states for different topological phase and Majorana zero modes are discussed.

Results in PhysicsJan 1, 20142 citations

Topological superfluids on a square optical lattice with non-Abelian gauge fields: Effects of next-nearest-neighbor hopping in the BCS-BEC evolution

M. Iskin

We consider a two-component Fermi gas with attractive interactions on a square optical lattice, and study the interplay of Zeeman field, spin-orbit coupling, and next-nearest-neighbor hopping on the ground-state phase diagrams in the entire BCS-BEC evolution. In particular, we first classify and distinguish all possible superfluid phases by the momentum-space topology of their zero-energy quasiparticle-quasihole excitations, and then numerically establish a plethora of quantum phase transitions in between. These transitions are further signaled and evidenced by the changes in the corresponding topological invariant of the system, i.e., its Chern number. Lastly, we find that the superfluid phase exhibits a reentrant structure, separated by a fingering normal phase, the origin of which is traced back to the changes in the single-particle density of states.

arXiv:1509.08219Physical Review AJan 12, 20164 citations

Detecting topological phase transition in 1D superconducting systems with next nearest neighbor hopping

Lingli Zhu -, Qian Huang, Hui-Lin Dai +3 more

We investigate the effect of next-nearest-neighbor hopping on topological quantum phase transitions (QPTs) that are characterized by the number of Majorana zero modes in one-dimensional (1D) p-wave superconducting systems. We also numerically analyze the scaling behavior and the universality of the Berry phase (BP) of the ground state close to the critical point. For critical line (I), the derivative of the ground-state BP is nonanalytic at the phase boundaries. For the phase boundary (II), a noncontractible BP of the ground state itself is also a witness of quantum phase transition.

Laser Physics LettersDec 5, 20142 citations

Emergence of new topological gapless phases in the modified square-lattice Kitaev model

Jihyeon Park, Gun Sang Jeon

We investigate emergent topological gapless phases in the square-lattice Kitaev model with additional hopping terms. In the presence of nearest-neighbor hopping only, the model is known to exhibit gapless phases with two topological gapless points. When the strength of the newly added next-nearest-neighbor hopping is smaller than a certain value, qualitatively the same phase diagram persists. We find that further increase of the extra hopping results in a new topological phase with four gapless points. We construct a phase diagram to clarify the regions of emergent topological gapless phases as well as topologically trivial ones in the space of the chemical potential and the next-nearest-neighbor hopping strength. We examine the evolution of the gapless phases in the energy dispersions of the bulk as the chemical potential varies. The topological properties of the gapless phases are characterized by the winding numbers of the present gapless points. We also consider the ribbon geometry to examine the corresponding topological edge states. It is revealed that Majorana-fermion edge modes exist as flat bands in topological gapless phases. We also perform the analytical calculation as to Majorana-fermion zero-energy modes and discuss its implications on the numerical results.

arXiv:2311.11684Nov 20, 20230 citations

Successive Majorana topological transitions driven by a magnetic field in the Kitaev model

Joji Nasu, Yasuyuki Kato, Yoshitomo Kamiya +1 more

We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum---line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.

arXiv:1805.02423Physical review. B./Physical review. BAug 30, 201872 citations