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Quasi-one-dimensional (1D) materials provide a superior platform for characterizing and tuning topological phases for two reasons: i) existence for multiple cleavable surfaces that enables better experimental identification of topological classification, and ii) stronger response to perturbations such as strain for tuning topological phases compared to higher dimensional crystal structures. In this paper, we present experimental evidence for a room-temperature topological phase transition in the quasi-1D material Bi$_4$I$_4$, mediated via a first order structural transition between two distinct stacking orders of the weakly-coupled chains. Using high resolution angle-resolved photoemission spectroscopy on the two natural cleavable surfaces, we identify the high temperature $\beta$ phase to be the first weak topological insulator with gapless Dirac cones on the (100) surface and no Dirac crossing on the (001) surface, while in the low temperature $\alpha$ phase, the topological surface state on the (100) surface opens a gap, consistent with a recent theoretical prediction of a higher-order topological insulator beyond the scope of the established topological materials databases that hosts gapless hinge states. Our results not only identify a rare topological phase transition between first-order and second-order topological insulators but also establish a novel quasi-1D material platform for exploring unprecedented physics., Comment: 9 pages, 4 figures, accepted for publication in Phys. Rev. X

Chiral Majorana edge modes are theoretically proposed to perform braiding operations for the potential quantum computation. Here, we suggest a scheme to regulate trajectories of the chiral Majorana fermion based on a quantum anomalous Hall insulator (QAHI)-topological superconductor heterostructure. An applied external gate voltage to the QAHI region introduces a dynamical phase so that the outgoing Majorana fermions can be prominently tuned to different leads. The trajectory is mechanically analyzed and the electrical manipulation is represented by the oscillating transmission coefficients versus the gate voltage. Through the optimization of devices, the conductance is likewise detectable to be periodically oscillating, which means an experimental control of chiral Majorana edge modes. Besides, this oscillating period which is robust against disorder also provides an attainable method of observing the energy dispersion relation of the edge mode of the QAHI. Furthermore, the oscillating behavior of conductance serves as smoking-gun evidence of the existence of the chiral Majorana fermion, which could be experimentally confirmed., Comment: 14 pages, 11 figures

The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin-orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. By using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method, the three elements of the spin current in the transverse leads and then spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has the essential difference with the traditional one: The z direction spin currents is zero without the magnetic field while it appears under the magnetic field, and the x and y direction spin currents in the two transverse leads flows out or flows in together, in contrary to the traditional spin Nernst effect, in which the spin current is induced by the spin-orbit coupling and flows out from one lead and flows in on the other. So we call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have the center-reversal-type symmetry, the mirror-reversal-type symmetry and the electron-hole-type symmetry, which lead to the spin Nernst coefficients being odd function or even function of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals., Comment: 12 pages, 11 figures

The non-Abelian braiding of Majorana fermions is one of the most promising operations providing a key building block for the realization of topological quantum computation. Recently, the chiral Majorana fermions were observed in a hybrid junction btween a quantum anomalous Hall insulator and an s-wave superconductor. Here we show that if a quantum dot or Majorana zero mode couples to the chiral Majorana fermions, the resulting resonant exchange of chiral Majorana fermions can lead to the non-Abelian braiding. Remarkably, any operation in the braid group can be achieved by this scheme. We further propose electrical transport experiments to observe the braiding of four chiral Majorana fermions and demonstrate the non-Abelian braiding statistics in four-terminal devices of the hybrid junctions. Both a conductance peak due to the braiding and the braiding-order dependent conductance are predicted. These findings pave a way to perform any braiding operation of chiral Majorana fermions by electrically controllable quantum dots., Comment: 11 pages, 9 figures

The 3D topological insulator (TI) PN junction under magnetic fields presents a novel transport property which is investigated both theoretically and numerically in this paper. Transport in this device can be tuned by the axial magnetic field. Specifically, the scattering coefficients between incoming and outgoing modes oscillate with axial magnetic flux at the harmonic form. In the condition of horizontal mirror symmetry, the initial phase of the harmonic oscillation is dependent on the parities of incoming and outgoing modes. This symmetry is broken when a vertical bias is applied which leads to a kinetic phase shift added to the initial phase. On the other hand, the amplitude of oscillation is suppressed by the surface disorder while it has no influence on the phase of oscillation. Furthermore, with the help of the vertical bias, a special (1,-2) 3D TI PN junction can be achieved, leading to a novel spin precession phenomenon.

We study the transport on the domain wall (DW) in a magnetic topological insulator. The low-energy behaviors of the magnetic topological insulator are dominated by the chiral edge states (CESs). Here, we find that the spectrum and transport of the CESs at the DW are strongly dependent on the DW configuration. For a Bloch wall, two co-propagating CESs at the DW are doubly degenerate and the incoming electron is totally reflected. However, for a N\'{e}el wall, the two CESs are split and the transmission is determined by the interference between the CESs. Moreover, the effective Hamiltonian for the CESs indicates that the component of magnetization perpendicular to the wall leads to the distinct transport behavior. These findings may pave a way to realize the low-power-dissipation spintronics devices based on magnetic DWs., Comment: 8 pages, 5 figures

We study the transport of chiral Majorana edge modes (CMEMs) in a hybrid quantum anomalous Hall insulator-topological superconductor (QAHI-TSC) system in which the TSC region contains a Josephson junction and a cavity. The Josephson junction undergoes a topological transition when the magnetic flux through the cavity passes through half-integer multiples of magnetic flux quantum. For the trivial phase, the CMEMs transmit along the QAHI-TSC interface as without magnetic flux. However, for the nontrivial phase, a zero-energy Majorana state appears in the cavity, leading that a CMEM can resonantly tunnel through the Majorana state to a different CMEM. These findings may provide a feasible scheme to control the transport of CMEMs by using the magnetic flux and the transport pattern can be customized by setting the size of the TSC., Comment: 5 pages, 4 figures

We study the influence of step defect on surface states in three-dimensional topological insulators subject to a perpendicular magnetic field. By calculating the energy spectrum of the surface states, we find that Landau levels (LLs) can form on flat regions of the surface and are distant from the step defect, and several subbands emerge at side surface of the step defect. The subband which connects to the two zeroth LLs is spin-polarized and chiral. In particular, when the electron transports along the side surface, the electron spin direction can be manipulated arbitrarily by gate voltage. And no reflection occurs even if the electron spin direction is changed. This provides a fascinating avenue to control the electron spin easily and coherently. In addition, regarding the subbands with high LL index, there exist spin-momentum locking helical states and the quantum spin Hall effect can appear., Comment: 6 pages, 5 figures

The thermoelectric properties of the surface states in three-dimensional topological insulator nanowires are studied. The Seebeck coefficients $S_c$ and the dimensionless thermoelectrical figure of merit $ZT$ are obtained by using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method. They are strongly dependent on the gate voltage and the longitudinal and perpendicular magnetic fields. By changing the gate voltage or magnetic fields, the values of $S_c$ and $ZT$ can be easily controlled. At the zero magnetic fields and zero gate voltage, or at the large perpendicular magnetic field and nonzero gate voltage, $ZT$ has the large value. Owing to the electron-hole symmetry, $S_c$ is an odd function of the Fermi energy while $ZT$ is an even function regardless of the magnetic fields. $S_c$ and $ZT$ show peaks when the quantized transmission coefficient jumps from one plateau to another. The highest peak appears while the Fermi energy is near the Dirac point. At the zero perpendicular magnetic field and zero gate voltage, the height of $n$th peak of $S_C$ is $\frac{k_B}{e}\texttt{ln}2/(|n|+1/2)$ and $\frac{k_B}{e}\texttt{ln}2/|n|$ for the longitudinal magnetic flux $\phi_{\parallel} = 0 $ and $\pi$, respectively. Finally, we also study the effect of disorder and find that $S_c$ and $ZT$ are robust against disorder. In particular, the large value of $ZT$ can survive even if at the strong disorder. These characteristics (that $ZT$ has the large value, is easily regulated, and is robust against the disorder) are very beneficial for the application of the thermoelectricity., Comment: 9 pages,10 figures

We theoretically study the electronic transport through a ferromagnet-Ising superconductor junction. A tight-binding Hamiltonian describing the Ising superconductor is presented. Then by combing the non-equilibrium Green's function method, the expressions of Andreev reflection coefficient and conductance are obtained. A strong magnetoanisotropic spin-triplet Andreev reflection is shown, and the magnetoanisotropic period is $\pi$ instead of $2\pi$ as in the conventional magnetoanisotropic system. We demonstrate a significant increase of the spin-triplet Andreev reflection for the single-band Ising superconductor. Furthermore, the dependence of the Andreev reflection on the incident energy and incident angle are also investigated. A complete Andreev reflection can occur when the incident energy is equal to the superconductor gap, regardless of the Fermi energy (spin polarization) of the ferromagnet. For the suitable oblique incidence, the spin-triplet Andreev reflection can be strongly enhanced. In addition, the conductance spectroscopies of both zero bias and finite bias are studied, and the influence of gate voltage, exchange energy, and spin-orbit coupling on the conductance spectroscopy are discussed in detail. The conductance reveals a strong magnetoanisotropy with period $\pi$ as the Andreev reflection coefficient. When the magnetization direction is parallel to the junction plane, a large conductance peak always emerges at the superconductor gap. This work offers a comprehensive and systematic study of the spin-triplet Andreev reflection, and has underlying application of $\pi$-periodic spin valve in spintronics., Comment: 10 pages, 9 figures

The Majorana fermion can be described by a real wave function with only two phases (0 and {\pi}) which provide a controllable degree of freedom. We propose a strategy to regulate the phase of the chiral Majorana state by coupling with a scanning tunneling microscope tip in a system consisting of quantum anomalous Hall insulator coupled with a superconductor. With the change of the chemical potential, the chiral Majorana state can be tuned alternately between 0 and {\pi}, in which, correspondingly, the perfect normal tunneling and perfect crossed Andreev reflection appear. The perfect crossed Andreev reflection, by which a Cooper pair can be split into two electrons going into different terminals completely, leads to a pumping current and distinct quantized resistances. These findings may provide a signature of Majorana fermions and pave a feasible avenue to regulate the phase of Majorana state., Comment: 9 pages, 7 figures

The surface states in three-dimensional (3D) topological insulators (TIs) can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the Fermion doubling problem when putting the continuous 2D Dirac equation into a lattice model. In this letter, we introduce a Wilson term with a zero bare mass into the 2D lattice model to overcome the difficulty. By comparing with a 3D Hamiltonian, we show that the modified 2D lattice model can faithfully describe the low-energy electrical and transport properties of surface states of 3D TIs. So this 2D lattice model provides a simple and cheap way to numerically simulate the surface states of 3D TI nanostructures. Based on the 2D lattice model, we also establish the wormhole effect in a TI nanowire by a magnetic field along the wire and show the surface states being robust against disorder. The proposed 2D lattice model can be extensively applied to study the various properties and effects, such as the transport properties, Hall effect, universal conductance fluctuations, localization effect, etc.. So it paves a new way to study the surface states of the 3D topological insulators., Comment: 7 pages, 5 figures