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Topological insulators (TIs) hold promise as a platform for spintronics applications due to the fascinating spin-momentum locking (SML) of the surface states. One particular interest lies in using TIs as spin-polarized sources for spintronics structures. Here, we propose the band tilt induced nonlinear Nernst effect (NLNE) in TIs as a clean and efficient route to generate high-performance spin polarization (SP). We show that in the presence of SML and hexagonal warping effect a finite band tilt can induce an imbalance of two spin carriers and effectively give rise to spin-polarized NLNE current in TIs. In our scheme, both the spin current and charge current regime can be achieved under the thermal drive. The obtainable SP can be efficiently tuned in either a smooth or rapid way, exhibiting highly flexible tunability. In addition, near-unity SP can be generated within a wide range of tunable parameters, which is also found to be robust against temperature. Therefore, our work provides a mechanism to realize controllable room-temperature high-degree SP based on TIs, which is of essential importance for future spintronics applications., The accepted version in PRB Letter

Andreev bound states (ABSs) are localized quantum states that contain both electron and hole components. They ubiquitously reside in inhomogeneous superconducting systems. Following theoretical analysis, we propose to probe the electron-hole weights of an ABS via a local tunneling measurement that detects the transient current under a steplike pulse bias. With our protocol, the ABS energy level can also be obtained from peaks of the Fourier spectrum of the transient current. Our protocol can be applied to detect robust zero-energy Majorana bound states (MBSs), which have equal electron-hole weights, in candidate platforms where local tunneling spectroscopy measurement is possible. In the 1D Majorana nanowire model, we numerically calculate the electron-hole weights for different types of low-energy bound states, including ABSs, quasi-MBSs, and MBSs., 14 pages, 5 figures

Chiral anomaly or Adler-Bell-Jackiw anomaly in Weyl semimetals (WSMs) has a significant impact on the electron transport behaviors, leading to remarkable longitudinal or planar electrical and thermoelectric transport phenomena in the presence of electromagnetic gauge fields. These phenomena are consequences of the imbalanced chiral charge and energy induced by chiral anomaly in the presence of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields ($\mathbf{E \cdot B }\neq 0$) or $(\mathbf{B \cdot \nabla }T\neq 0)$ ($\mathbf{\nabla}T$ is the thermal gradient). We here propose another two fascinating transport properties, namely, the nonlinear planar Nernst effect and nonlinear planar thermal Hall effect induced by chiral anomaly in the presence of $\mathbf{B \cdot \nabla}T\neq 0$ in WSMs. Using the semiclassical Boltzmann transport theory, we derive the analytical expressions for the chiral anomaly induced nonlinear Nernst and thermal Hall transport coefficients and also evaluate the fundamental mathematical relations among them in the nonlinear regime. The formulas we find in this current work are consistent with that predicted for the nonlinear anomalous electrical and thermoelectric effects induced by Berry curvature dipole recently. Additionally, in contrast to the recent work, by utilizing the lattice Weyl Hamiltonian with intrinsic chiral chemical potential, we find that the chiral anomaly induced nonlinear planar effects can exist even for a pair of oppositely tilted or non-tilted Weyl cones in both time reversal and inversion broken WSMs. The chiral anomaly induced nonlinear planar effects predicted here along with the related parameter dependencies are hence possible to be realized in realistic WSMs in experiment., Comment: Published version

Focusing on the implications of recent experiments on Majorana zero modes in semiconductor-superconductor (SM-SC) heterostructures, we critically examine the quantization of the zero-bias differential conductance as a possible unambiguous signature of Majorana physics in the presence of disorder. By numerically calculating the zero-bias conductance (ZBC) maps as function of Zeeman splitting and chemical potential for different disorder realizations, we show that the presence of quantized "islands" characterized by a ZBC value (approximately) equal to $2e^2/h$ and having a finite area/volume in a multi-dimensional parameter space represents a unique signature of Majorana physics supporting Majorana zero modes (MZMs) or partially-separated Majorana modes (ps-MMs). We find that in the presence of strong disorder Majorana physics only emerges locally and gives rise to ps-MMs, which, in turn, generate small quantized islands when one of the Majorana modes is located at the end of the system. Observing these small islands may require sample selection and the systematic scanning of a large volume in the control parameter space. Upon decreasing disorder, the quantized islands increase in size and eventually coalesce into large topological regions. Since the presence of MZMs localized at the opposite ends of the system is typically associated with large quantized islands, looking for MZM-induced edge-to-edge correlations is premature in the absence of convincing experimental evidence for (even small) quantized islands. We conclude that the observation of quantized islands demonstrates unambiguously the presence of the key ingredients necessary for Majorana physics, provides an excellent diagnostic tool for evaluating the disorder strength, and, consequently, represents the next natural milestone in the Majorana search., 12 pages, 10 figures. Published version

Topological Weyl semimetals (WSMs) have been predicted to be excellent candidates for detecting Berry curvature dipole (BCD) and the related non-linear effects in electronics and optics due to the large Berry curvature concentrated around the Weyl nodes. And yet, linearized models of isolated tilted Weyl cones only realize a diagonal non-zero BCD tensor which sum to zero in the model of WSM with multiple Weyl nodes in the presence of mirror symmetry. On the other hand, recent \textit{ab initio} work has found that realistic WSMs like TaAs-type or MoTe$_2$-type compounds, which have mirror symmetry, indeed show an off-diagonal BCD tensor with an enhanced magnitude for its non-zero components. So far, there is a lack of theoretical work addressing this contradiction for 3D WSMs. In this paper, we systematically study the BCD in 3D WSMs using lattice Weyl Hamiltonians, which go beyond the linearized models. We find that the non-zero BCD and its related important features for these WSMs do not rely on the contribution from the Weyl nodes. Instead, they are dependent on the part of the Fermi surface that lies \textit{between} the Weyl nodes, in the region of the reciprocal space where neighboring Weyl cones overlap. For large enough chemical potential such Fermi surfaces are present in the lattice Weyl Hamiltonians as well as in the realistic WSMs. We also show that, a lattice Weyl Hamitonian with a non-zero chiral chemical potential for the Weyl cones can also support dips or peaks in the off-diagonal components of the BCD tensor near the Weyl nodes themselves, consistent with recent \textit{ab initio} work., Published version

The recent experimental observations of decaying energy oscillations with increasing magnetic field in semiconductor-superconductor Majorana nanowires is in contrast with the theoretical expectations based on the presence of Majorana zero modes localized at the ends of the system. These observations have been recently theoretically justified by considering a position-dependent spin-orbit coupling that can emerge due to a tunnel gate. Here, we show that the window in parameter space where this phenomenology occurs is vanishingly small when compared to the parameter region where Majorana oscillations should increase in amplitude with the applied magnetic field. Further, including a position-dependent effective potential that is also induced due to a tunnel gate practically removes this small window. Using extensive numerical calculations, we show that, as expected, increasing amplitude oscillations of the hybridization energy represent a generic property of topological Majorana zero modes, while decreasing amplitude oscillations are a generic property of low-energy trivial Andreev bound states, recently called partially separated Andreev bound states. By averaging over several realistic parameter configurations, we identify robust features of the hybridization energy that can be observed in a typical differential conductance experiment without fine-tuning the control parameters.

We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime $-$ the topologically-trivial regime due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs), which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width $\e_w$ of the low-energy conductance peaks $\e_w$. However, the feasibility of measurement-based braiding depends on a different energy scale $\e_m$. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the $\e_m$ threshold, so that measurement-based braiding is possible in principle. Starting with ps-ABSs with energy below $\e_m$, we identify the maximum amplitudes of different types of perturbations that are consistent with perturbation-induced energy splittings not exceeding the $\e_m$ limit. We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for $\e_m$ cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs., Comment: 18 pages, 17 figures

Unlike the conventional (linear) anomalous Nernst effect, the non-linear anomalous Nernst effect (NLANE) can survive in an inversion symmetry broken system even in the presence of time-reversal symmetry. Using semiclassical Boltzmann transport theory, we derive the general expression of the non-linear anomalous Nernst coefficient as the second-order response function to the applied temperature gradient. We find that the non-linear Nernst current, which flows perpendicular to the temperature gradient even in the absence of a magnetic field, arises due to the Berry curvature of the states near the Fermi surface, and thus is associated with purely a Fermi surface contribution. We apply these results to bilayer WTe$_2$, which is an inversion broken but time reversal symmetric type-II Weyl semimetal supporting chiral Weyl fermions. By tuning the spin-orbit coupling, we show that the sign of the NLANE can change in this system. Together with the angular dependence, we calculate the temperature and chemical potential dependencies of NLANE in bilayer WTe$_2$, and predict specific experimental signatures that can be checked in experiments., PRB accepted version

We solve analytically the problem of a finite-length Kitaev chain coupled to a quantum dot (QD) which extends the standard Kitaev chain problem to the quantum dot-semiconductor-superconductor (QD-SM-SC) nanowire heterostructure currently under intense investigation for possible occurrence of Majorana zero modes (MZMs). As a first step we obtain the analytical solution of the finite-length Kitaev chain without the quantum dot which to the best of our knowledge has also not appeared before. Our full solution of the Kitaev chain coupled to a quantum dot reveals the emergence of a robust near-zero-energy Andreev bound state (ABSs) localized in the quantum dot region as the generic lowest energy solution in the topologically trivial phase. By contrast in the Kitaev chain without the quantum dot such a solution does not exist. The robustness of the ABS in the topologically trivial phase is due to a partial spatial decoupling of the component Majorana bound states (MBSs) over the length of the dot potential. As a result the signatures of the ABS in measurements that couple locally to the quantum dot e.g. tunneling measurements are identical to the signatures of topologically protected MZMs which arise only in the topological superconducting (TS) phase of the Kitaev chain.

Higher order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional (2D) quantum spin Hall insulator (QSHI) proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing Majorana corner modes and possible higher order topological superfluidity with conventional s-wave superfluids/superconductors., Comment: 5+ pages and 4 figures; Version accepted for publication in PRL

In a series of recent papers anomalous Hall and Nernst effects have been theoretically discussed in the non-linear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the non-linear regime. The formulae we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulae, an important byproduct of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments., Comment: 6 pages, 4 figures. Accepted version

We show that partially separated Andreev bound states (ps-ABSs), comprised of pairs of overlapping Majorana bound states (MBSs) emerging in quantum dot-semiconductor-superconductor heterostructures, produce robust zero bias conductance plateaus in end-of-wire charge tunneling experiments. These plateaus remain quantized at $2e^2/h$ over large ranges of experimental control parameters. In light of recent experiments reporting the observation of robust $2e^2/h$-quantized conductance plateaus in local charge tunneling experiments, we perform extensive numerical calculations to explicitly show that such quantized conductance plateaus, which are obtained by varying control parameters such as the tunnel barrier height, the super gate potential, and the applied magnetic field, can arise as a result of the existence of ps-ABSs. Because ps-ABSs can form rather generically in the topologically trivial regime, even in the absence of disorder, our results suggest that the observation of a robust quantized conductance plateau does not represent sufficient evidence to demonstrate the existence of non-Abelian topologically-protected Majorana zero modes localized at the opposite ends of a wire., Comment: 8 pages, 8 figures

Highly ordered TiO2 nanotube array (TNA) films were fabricated by anodic oxidation of Ti foil. Au nanoparticles (NPs) are decorated onto the top of TNA films with the aid of ion-sputtering and thermal annealing. The steady-state photoluminescence (PL) spectra, as well as x-ray photoelectron spectroscopy (XPS) and Raman analysis, confirm the presence of Ti3+ valence states in the prepared TNA films. The UV–vis absorption spectra show that the photo-response of as-prepared samples is extended from UV to the visible light region. From the nanosecond time-resolved transient photoluminescence (NTRT-PL) spectra, Ti3+-related PL intensity is observed to vary distinctly with the deposition time of Au NPs. Such a phenomenon could be explained by considering the modulation of oxygen vacancy densities and charge states in TNA films by surface loading Au NPs. The enhanced visible-light photocatalytic activities of the Au-TNA composite were evaluated through the photodegradation of methyl orange (MO) in aqueous solution by UV–vis absorption spectrometry. The decoration of Au NPs plays an essential role in enhancing visible-light photocatalytic activity, because energetic photoelectrons are able to inject to the conduction band of TiO2 owing to the surface plasmon resonance (SPR) effect. It is hoped that our current work will provide a simple strategy to synthesize defect-related composite for photocatalytic applications.