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Non-Hermitian topological systems have been shown to exhibit many interesting properties. However, due to the presence of complex energy spectra and non-Hermitian skin effect (NHSE), the topological edge states will be dynamically unstable and unresolvable from the bulk states which are also localized at the boundaries. Here we propose a one-dimensional nonreciprocal superlattice model in which topological phases are solely induced by the modulated asymmetric hopping amplitude. Most importantly, we can obtain robust real energy spectra, and in the meanwhile, eliminate the NHSE both in the commensurate and incommensurate lattices by tuning the modulation. Thus the topological zero and nonzero energy edge states are stable and distinguishable from the bulk states, which would definitely facilitate the experimental identifications of non-Hermitian topological phases. We further propose a practical scheme to realize this nonreciprocal model by exploiting electrical circuits.

Twisted bilayer graphene is one of the simplest van der Waals structures, and its inhomogeneous interlayer coupling can induce rich electronic properties. In twisted bilayer graphene nanoribbons (tBLGNRs), the interlayer coupling strengths are different for two ribbon edges due to the inhomogeneous bonding, which splits the edge states into two individuals in energy. The lower-energy state, localizing at the ribbon edge with the stronger interlayer coupling, is a good candidate to generate one-dimensional (1D) topological superconductivity in the presence of Rashba spin-orbit coupling, Zeeman field, and $s$-wave superconductivity. Majorana zero modes (MZMs) are found to be localized at both ends of this edge. The topological invariants of the system are explored by evaluating the Berry phase for infinite-length ribbons and Majorana polarization for quasi-1D ribbons, giving the same topological phase diagram. More importantly, by adjusting interlayer dislocation and uniaxial strain of tBLGNRs across the critical values, the lower-energy edge changes and 1D topological superconductivity can ``jump'' from one ribbon edge to the other one. Finally, by applying a gate voltage bias between bilayers or changing the interlayer distance, a MZM can transfer along the ribbon edge. The tBLGNRs provide an alternative platform to study 1D topological superconductivity and MZMs.

We investigate a generalized Aubry-Andr\'e-Harper (AAH) model with p-wave superconducting pairing. Both the hopping amplitudes between the nearest neighboring lattice sites and the on-site potentials in this system are modulated by a cosine function with a periodicity of $1/\alpha$. In the incommensurate case [$\alpha=(\sqrt{5}-1)/2$], due to the modulations on the hopping amplitudes, the critical region of this quasiperiodic system is significantly reduced and the system becomes more easily to be turned from extended states to localized states. In the commensurate case ($\alpha = 1/2$), we find that this model shows three different phases when we tune the system parameters: Su-Schrieffer-Heeger (SSH)-like trivial, SSH-like topological, and Kitaev-like topological phases. The phase diagrams and the topological quantum numbers for these phases are presented in this work. This generalized AAH model combined with superconducting pairing provides us with a useful testfield for studying the phase transitions from extended states to Anderson localized states and the transitions between different topological phases., Comment: 9 pages, 5 figures

We theoretically investigate the electronic properties of the interface between quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators. A robust chiral gapless state, which substantially differs from edge states of QSH or QAH insulators, is predicted at the QSH/QAH interface using an effective Hamiltonian model. We systematically reveal distinctive properties of interface states between QSH and single-valley QAH, multivalley high-Chern-number QAH and valley-polarized QAH insulators based on tight-binding models using the interface Green's function method. As an example, first-principles calculations are conducted for the interface states between fully and semihydrogenated bismuth (111) thin films, verifying the existence of interface states in realistic material systems. Due to the physically protected junction structure, the interface state is expected to be more stable and insensitive than topological boundary states against edge defects and chemical decoration. Hence our results of the interface states provide a promising route towards enhancing the performance and stability of low-dissipation electronics in real environment.

Based on the instanton technique in the spin-coherent-state path-integral representation, the spin-parity effects induced by the topological Wess-Zumino or Berry phase are studied theoretically in nanometer-scale single-domain ferromagnets in the presence of an external magnetic field along the hard anisotropy axis. We consider the magnetocrystalline anisotropy with the biaxial, trigonal, tetragonal, and hexagonal crystal symmetry, respectively. Both the Wentzel-Kramers-Brillouin (WKB) exponent and the preexponential factors are evaluated in the instanton's contribution to the ground-state tunnel splittings. The Euclidean transition amplitudes between energetically degenerate easy directions are obtained with the help of the dilute instanton gas approximation. The effective Hamiltonian approach is applied to present the final results of ground-state tunnel splittings for each kind of crystal symmetry. The Euclidean transition amplitudes and the ground-state tunnel splittings are found to depend on the parity of total spins of ferromagnets and oscillate with the external magnetic field for both the integer and half-integer total spins. We show that the topological phase interference or spin-parity effects can reflect in thermodynamic quantities of magnetic tunneling states. Possible relevance to experiments is also discussed.

Based on the two-sublattice model, the quantum interference effects induced by the topological phase term in the Euclidean action are studied in resonant quantum coherence of the N\'eel vector between energetically degenerate easy directions in single-domain antiferromagnetic nanoparticles with m-fold rotational symmetries around the z axis and reflection symmetry in the $x\ensuremath{-}y$ plane at zero magnetic field, where $m=3,$ $4$, and $6$, which corresponds to the trigonal, tetragonal, and hexagonal crystal symmetries, respectively. By applying the standard instanton technique in the spin-coherent-state path-integral representation, we evaluate both the Wentzel-Kramers-Brillouin exponent and the preexponential factors in the instanton's contribution to the tunneling level splitting. The Euclidean transition amplitudes between energetically degenerate easy directions are obtained by making use of the dilute instanton-gas approximation. The effective Hamiltonian approach is applied to give the final results of the ground-state tunneling level splittings for each kind of crystal symmetry. The low-lying tunneling level spectrum and the thermodynamic properties of magnetic tunneling states are found to depend significantly on the parity of the excess spin of single-domain antiferromagnet. The topological quenching of the ground-state tunneling level splitting for the half-integer excess spins obtained previously for the biaxial crystal symmetry (i.e., double-well system at zero magnetic field) can be recovered by a simple diagonalization of the effective Hamiltonian. It is shown that the effective Hamiltonian approach is equivalent to the dilute instanton-gas approximation. Possible relevance to experiments is also discussed.

Based on the two-sublattice model, we investigate the quantum tunneling behaviors of the N\'eel vector in single-domain antiferromagnetic nanoparticles placed in an external magnetic field at an arbitrarily directed angle in the ZX plane. We consider the magnetocrystalline anisotropy with biaxial, tetragonal, and hexagonal crystal symmetry, respectively. By applying the standard instanton technique in the spin-coherent-state path-integral representation, we calculate the tunneling level splittings, the tunneling rates, and the crossover temperatures in the low barrier limit for three angle ranges of the external applied magnetic field $({\ensuremath{\theta}}_{H}=\ensuremath{\pi}/2,$ $\ensuremath{\pi}\ensuremath{\ll}{\ensuremath{\theta}}_{H}\ensuremath{\ll}\ensuremath{\pi},$ and ${\ensuremath{\theta}}_{H}=\ensuremath{\pi}).$ Our results show that the tunneling level splittings, the tunneling rates, and the crossover temperatures depend on the orientation of the external applied magnetic field distinctly, which provides a possible experimental test for macroscopic quantum tunneling and coherence of the N\'eel vector in nanometer-scale single-domain antiferromagnets.

Based on the two-sublattice model, we study the topological phase interference effect in resonant macroscopic quantum coherence of the N\'eel vector in a single-domain antiferromagnetic nanoparticle with biaxial crystal symmetry placed in an external magnetic field applied along the medium axis. By applying the standard instanton technique in spin-coherent-state path integral, we evaluate both the Wentzel-Kramers-Brillouin exponent and the preexponential factors in the instanton's contribution to the tunneling-level splitting. The Euclidean transition amplitude is obtained by making use of the dilute instanton-gas approximation. The low-lying tunneling-level spectrum and the thermodynamic properties of magnetic tunneling states are found to depend on the parity of the excess spin of the antiferromagnetic nanoparticle significantly. Possible relevance to experiments is also discussed.

Strong electron and spin correlations are studied in parallel-coupled double quantum dots with interdot spin superexchange J. In the Kondo regime with degenerate dot energy levels, coherent transport occurs at zero temperature, where two entangled (bonding and antibonding) resonances are formed near the Fermi energy. When increasing J or the dot-lead parallel-coupling asymmetry ratio Gamma(2)/Gamma(1), a swap between two entangled resonances occurs and the line shapes of the transmission are interchanged. The linear conductance shows a peak at the critical values. Such a peculiar effect with the virtue of many-body coherence may be useful in future quantum computing.

On the basis of the nonequilibrium Green's function and nonperturbative canonical transformation for the local electron-phonon interaction (EPI), the quantum transport through a single-molecule transistor(SMT) has been investigated with a particular attention paid to the joint effect of the EPI and SMT-lead coupling on the spectral function and conductance. In addition to the usual EPI-induced renormalized effects (such as the red-shift, sharpening, and phonon-sidebands of the SMT level), owing to improved disentagling the electron-phonon system, it has been found that, the profile of the spectral function of the SMT electron is sensitive to lead chemical potentials, thus can readily be manipulated by tuning the bias as well as the SMT-gate voltage. As a consequence, the broken particle-hole symmetry in this system can be clearly recognized through the phonon sidebands in the spectral function. These EPI effects also manifest themselves in the nonequilibrium transport properties of the SMT, particularly at low temperature., Comment: 9 pages, 7 figures, final version accepted by PRB

An imaginary-time path integral study is presented for spin tunneling in the biaxial antiferromagnetic grain with noncompensated sublattices placed in a magnetic field with an arbitrary direction in the plane of easy and medium axes. Different structures of the tunneling barriers can be generated by the magnitude and the orientation of the magnetic field. By calculating the nonvacuum instantons or bounces, we analytically obtain the dependence of decay rates from excited levels as well as ground-state levels and the temperature of the crossover from the thermal to quantum regime on the direction and strength of the field in a wide range of angles of the applied magnetic field. It is found that the WKB exponent and the crossover temperature strongly depend on the orientation of the field, which can be tested with the use of existing experimental techniques. In the large noncompensation limit, our results reduce to spin tunneling in ferromagnetic particles.