We study one dimensional (1D) and quasi-1D periodic structures as possible platforms for the emergence of Majorana bound states with enhanced robustness against disorder and system inhomogeneity. First, using a simple 1D model, we analytically derive the effective parameters characterizing the minibands generated by the periodic potential. We show that, for strong enough periodic potentials, the higher energy minibands hosting Majorana bound states have significant advantages compared to their counterparts in uniform systems, including increased topological gaps, enhanced robustness against disorder, and enlarged parameter space regions consistent with the presence of topological superconductivity. We identify the problem of engineering a strong enough periodic potential as a key roadblock to realizing efficient periodic 1D structures. To address this challenge, we propose an efficient implementation of the periodic potential based on quasi-1D channels realized in 2D semiconductor heterostructures proximity coupled to superconductor strips of periodically modulated width. Our numerical study of the modulated channel device shows excellent agreement with the simple 1D model, reveals a topological phase diagram that is quite insensitive to the details of the confining potential associated with screening by the superconductor, and demonstrates that engineering patterned 2D structures represents a powerful and versatile approach to realizing robust Majorana bound states.
Conductance Quantization in a Periodically Modulated Quantum Channel: backscattering and mode mixing
已知量子点接触的电导以$2e^2/h$为单位被量化，并且由于反向散射，该量化被点接触中的非绝热散射体破坏。最近，它被展示[Phys. Rev. Lett. 71，137（1993）]，在量子信道中周期性地取许多非绝热散射体，可以恢复量子化。我们研究这种电导量子化的周期系统中存在的一个强缺陷。双短截线的周期性排列给出了电导的显著量子化。双收缩的周期性排列也只有在收缩之间的间隔很小时才能给出非常好的量化。我们得出结论，电导量化的周期性调制的通道是强大的。
Microwave photoconductivity of a periodically modulated two-dimensional electron system: Striped states and overlapping Landau levels
我们研究了微波辐射下条纹态的直流响应。在单向周期调制电势的影响下，条纹态可以通过二维电子系统来建模，这在[J.Dietel et al.Phys.Rev.B（71），045329（2005）]中进行了研究。我们进一步将我们对周期调制系统的研究扩展到朗道能级强重叠的情况，并计算了暗电导和光电导。的调制电位的强度作为一个额外的参数，它允许改变的重叠的朗道水平独立的填充分数。
We have experimentally and numerically investigated the dispersion of collective spin waves prop-agating through arrays of longitudinally magnetized nanowires with periodically modulated width. Two nanowire arrays with single-side modulation and different periodicity of modulation were studied and compared to the nanowires with homogeneous width. The spin-wave dispersion, meas-ured up to the third Brillouin zone of the reciprocal space, revealed the presence of two dispersive modes for the width-modulated NWs, whose amplitude of magnonic band depends on the modula-tion periodicity, and a set o…
This article presents theoretical results for the dynamic response of periodically surface-modulated ferromagnetic thin films. For such system, the role of the periodic dipolar field induced by the modulation is addressed by using the plane-wave method. By controlling the geometry of the modulated volumes within the film, the frequency modes and spatial profiles of spin waves can be manipulated. The angular dependence of the frequency band-gaps unveils the influence of both dynamic and static magnetic charges, which reside in the edges of the etching periodic zones, and it is stablished that b…
Transverse-electric (TE) surface plasmon polaritons are unique eigenmodes of a homogeneous graphene layer that are tunable with the chemical potential and temperature. However, as their dispersion curve spectrally lies just below the light line, they cannot be resonantly excited by an externally incident wave. Here, we propose a way of exciting the TE modes and tuning their peaks in the transmission by introducing a one-dimensional graphene grating. Using the scattering-matrix formalism, we show that periodic modulations of graphene make the transmission more pronounced, potentially allowing f…
We propose to study the transition from a nodal loop to nodal chain phase in a tunable two-dimensional $π$-flux lattice with periodical modulation potential. The Hamiltonian describes a periodically modulated optical lattice system under artificial magnetic fluxes and the tunable modulation phase factor provides additionally an artificial dimension of external parameter space. We demonstrate that this lattice system is able to describe a semimetal with either nodal loop or nodal chain Fermi surface in the extended three-dimensional Brillouin zone. By changing the strength of modulation potenti…
We explore the transport properties of a periodically modulated $α$-$\mathcal{T}_3$ lattice in the presence of a perpendicular magnetic field. The effect of the Berry phase on electrical conductivity oscillation, so-called Weiss oscillation, caused by the modulation induced non-zero drift velocity of charge carriers is investigated. Employing linear response theory within the low temperature regime, we analyze Weiss oscillation as a function of the external magnetic field for both electrically and magnetically modulated $α$-$\mathcal{T}_3$ lattice numerically as well as analytically. The Berry…
We investigate the dispersion topology of elastic lattices characterized by spatial stiffness modulation. The modulation is defined by the sampling of a two-dimensional surface, which provides the lattices with topological properties that are usually attributed to two-dimensional crystals. We show that the cyclic variation of the phase of the stiffness modulation leads to a Berry phase accumulation for the Bloch eigenmodes, which is characterized by integer valued Chern numbers for the bands and associated gap labels. The resulting non-trivial gaps are spanned by edge modes localized at one of…
The linear response of two-dimensional electron gas in a perpendicular magnetic field in the presence of a spatially dependent classically smooth electrostatic potential is studied theoretically, by application of the Kubo formula for nonlocal conductivity tensor. In the classical transport regime, a general expression for the conductivity tensor through the correlation functions of the homogeneous electron gas is derived. The quantum transport regime, when Landau quantization is essential, is studied for the case of unidirectional periodic potential modulation. Apart from the Shubnikov-de Haa…
Beating of the oscillations in the transport coefficients of a one-dimensionally periodically modulated two-dimensional electron gas in the presence of spin-orbit interaction
Diameter-modulated nanowires offer an important paradigm to design the magnetization response of 3D magnetic nanostructures by engineering the domain wall pinning. With the aim to understand its nature and to control the process, we analyze the magnetization response in FeCo modulated polycrystalline two-segment nanowires varying the minor diameter. Our modelling indicates a very complex behavior with a strong dependence on the disorder distribution and an important role of topologically non-trivial magnetization structures. We demonstrate that modulated nanowires with a small diameter differe…
Photonic crystals and metamaterials are two overarching paradigms for manipulating light. Combining the two approaches leads to hypercrystals: hyperbolic dispersion metamaterials that undergo periodic modulation and mix photonic-crystal-like aspects with hyperbolic dispersion physics. So far, there has been limited experimental realization of hypercrystals due to various technical and design constraints. Here, we create nanoscale hypercrystals with lattice constants ranging from 25 nm to 160 nm and measure their collective Bloch modes and dispersion with scattering nearfield microscopy. We dem…
We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two parameters - detuning between the clocks and the repump rate. There are three main phases - trivial steady state (Phase I), where all atoms are maximally pumped, nontrivial steady state corresponding to monochromatic superradiance (Phase II), and amplitude-modulated superradiance (Phase III). Phases I and II are fixed points of the mean-field dynamics, wh…
The effect of spatially modulated interaction on quantum phase transition in one-dimensional interacting spinless fermion system is theoretically investigated by exact diagonalization and density matrix renormalization group method. Our calculations show that the periodically modulated interaction can drive the spinless fermion system into topological charge density wave state. The topological state is encoded by quasiparticle end states and the fractional quantized $e/2$ end charges, and characterized by Berry phase and Chern number. The quasiparticle energy spectra as a function of modulated…
Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture
Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics, South China Normal University（华南师范大学物理学院）；Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University（华南师范大学前沿物理研究院）
We explore a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductor-semiconductor dev…
