Semiconductors with strong spin-orbit interactions can exhibit a helical gap with spin-momentum locking opened by a magnetic field. Such a gap is highly spin selective as a result of a topologically protected spin-momentum locking, which can be used for spin filtering. We experimentally demonstrate such a spin filtering effect in a quasi-ballistic p-type germanium/silicon core/shell nanowire (NW), which possesses a pseudo-helical gap without the application of magnetic field. Polarized hole spin injection to the NW is achieved using cobalt ferromagnetic contacts with controlled natural surface oxide on the NW as a tunnel barrier. Local and nonlocal spin valve effects are measured as the verification of polarized spin transport in the NW outside the helical gap. We electrically tune the NW into the helical gap by scanning its chemical potential with a gate. A hysteresis loop with three resistance states is observed in the local spin valve geometry, as an evidence of spin filtering in the helical gap.
We study spin polarized transport in silicon germanium nanowires using a semiclassical monte carlo approach. Spin depolarization in the channel is caused due to D'yakonov-Perel (DP) relaxation associated with Rashba spin orbit coupling and due to Elliott- Yafet (EY) relaxation. We investigate the dependence of spin dephasing on germanium mole fraction in silicon germanium nanowires. The spin dephasing lengths decrease with an increase in the germanium mole fraction. We also find that the temperature has a strong influence on the dephasing rate and spin relaxation lengths increase with decrease…
We use semiclassical Monte Carlo approach along with spin density matrix calculations to model spin polarized electron transport. The model is applied to germanium nanowires and germanium two dimensional channels to study and compare spin relaxation between them. Spin dephasing in germanium occurs because of Rashba Spin Orbit Interaction (structural inversion asymmetry) which gives rise to D'yakonov-Perel(DP) relaxation. In germanium spin flip scattering due to Elliot-Yafet(EY) mechanism also leads to spin relaxation. The spin relaxation tests for both 1-D and 2-D channels are carried out at d…
We have simultaneously measured conductance and thermoelectric power (TEP) of individual silicon and germanium/silicon core/shell nanowires in the field effect transistor device configuration. As the applied gate voltage changes, the TEP shows distinctly different behaviors while the electrical conductance exhibits the turn-off, subthreshold, and saturation regimes respectively. At room temperature, peak TEP value of $\sim 300 μ$V/K is observed in the subthreshold regime of the Si devices. The temperature dependence of the saturated TEP values are used to estimate the carrier doping of Si nano…
We report the optoelectrical characterisation of Eshelby twisted Germanium sulfide (GeS) nanowires with first experimental observation of ferroelectric order at room temperature in GeS which is an otherwise centrosymmetric molecule. The chemical composition and structure of these nanowires were confirmed by various spectroscopic, microscopic and diffractive techniques. In addition, the nanowires were found to be stable over time. From the optoelectronic measurements we found that these p-type semiconducting GeS nanowires have up to two orders higher charge carrier mobility than GeS nanosheets …
Electrical injection of spin-polarized electrons into a semiconductor, large spin diffusion length, and an integration friendly platform are desirable ingredients for spin-based devices. Here we demonstrate lateral spin injection and detection in germanium nanowires, by using ferromagnetic metal contacts and tunnel barriers for contact resistance engineering. Using data measured from over 80 samples, we map out the contact resistance window for which lateral spin transport is observed, manifestly showing the conductivity matching required for spin injection. Our analysis, based on the spin dif…
By using non-equilibrium molecular dynamics simulations, we demonstrated that thermal conductivity of Germanium nanowires can be reduced more than 25% at room temperature by atomistic coating. There is a critical coating thickness beyond which thermal conductivity of the coated nanowire is larger than that of the host nanowire. The diameter dependent critical coating thickness and minimum thermal conductivity are explored. Moreover, we found that interface roughness can induce further reduction of thermal conductivity in coated nanowires. From the vibrational eigen-mode analysis, it is found t…
We calculate the electronic structures of Germanium nanowires by taking the effective-mass theory. The electron and hole states at the G-valley are studied via the eight-band k.p theory. For the [111] L-valley, we expand the envelope wave function using Bessel functions to calculate the energies of the electron states for the first time. The results show that the energy dispersion curves of electron states at the L-valley are almost parabolic irrespective of the radius of Germanium nanowires. Based on the electronic structures, the density of states of Germanium nanowires are also obtained, an…
We have measured the terahertz response of oriented germanium nanowires using ultrafast optical-pump terahertz-probe spectroscopy. We present results on the time, frequency, and polarization dependence of the terahertz response. Our results indicate intraband energy relaxation times of photoexcited carriers in the 1.5-2.0 ps range, carrier density dependent interband electron-hole recombination times in the 75-125 ps range, and carrier momentum scattering rates in the 60-90 fs range. Additionally, the terahertz response of the nanowires is strongly polarization dependent despite the subwavelen…
We investigate spin polarized electron transport in ultra-thin Si-Core/Ge-Shell and Ge-Core/Si-Shell nanowire system using semi-classical Monte Carlo simulation method. Depolarization of electron's spin occurs in nanowire mainly due to D'yakonov-Perel dephasing (DP-mechanism) and Elliott-Yafet dephasing (EY-mechanism). We studied the dependence of spin dephasing on ultra-thin silicon core diameter in Si-Core/Ge-Shell nanowire and germanium core diameter in Ge-Core/Si-Shell nanowire. Variation in spin dephasing length with varying core diameter ranging from 1 nm to 9 nm indicate that spin depha…
The thermoelectric properties of a nanoscale germanium segment connected by aluminium nanowires are studied using scanning thermal microscopy. The germanium segment of 168\,nm length features atomically sharp interfaces to the aluminium wires and is surrounded by an Al$_2$O$_3$ shell. The temperature distribution along the self-heated nanowire is measured as a function of the applied electrical current, for both Joule and Peltier effects. An analysis is developed that is able to extract the thermal and thermoelectric properties including thermal conductivity, the thermal boundary resistance to…
We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.
Rashba nanowires in a magnetic field exhibit a helical regime when the spin-orbit momentum is close to the Fermi momentum, k_F \approx k_{SO}. We show that this regime is characterized by a strongly anisotropic electron spin susceptibility, with an exponentially suppressed signal along one direction in spin space, and that there are no low frequency spin fluctuations along this direction. Since the spin response in the gapless regime k_F \not \approx k_{SO} has a power law behavior in all three directions, spin measurements provide a signature of the helical regime that complements spin-insens…
Spin-momentum locking in a semiconductor device with strong spin-orbit coupling (SOC) is a fundamental goal of nanoscale spintronics and an important prerequisite for the formation of Majorana bound states. Such a helical state is predicted in one-dimensional (1D) nanowires subject to strong Rashba SOC and spin-mixing, its hallmark being a characteristic reentrant behaviour in the conductance. Here, we report the first direct experimental observations of the reentrant conductance feature, which reveals the formation of a helical liquid, in the lowest 1D subband of an InAs nanowire. Surprisingl…
Two-dimensional electron and hole gas systems, enabled through band structure design and epitaxial growth on planar substrates, have served as key platforms for fundamental condensed matter research and high performance devices. The analogous development of one-dimensional (1D) electron or hole gas systems through controlled growth on 1D nanostructure substrates, which could open up opportunities beyond existing carbon nanotube and nanowire systems, has not been realized. Here we report the synthesis and transport studies of a 1D hole gas system based on a free-standing germanium/silicon (Ge/S…
We study theoretically the low-energy hole states of Ge/Si core/shell nanowires. The low-energy valence band is quasidegenerate, formed by two doublets of different orbital angular momenta, and can be controlled via the relative shell thickness and via external fields. We find that direct (dipolar) coupling to a moderate electric field leads to an unusually large spin-orbit interaction of Rashba type on the order of meV which gives rise to pronounced helical states enabling electrical spin control. The system allows for quantum dots and spin qubits with energy levels that can vary from nearly …
A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interac…
The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the helical electron transport is a crucial step to both physics and device applications of topological insulators. Topological insulator nanowires, of which spin-textured surface electrons form 1D band manipulated by enclosed magnetic flux, offer a unique nanoscale platform to realize quantum transport of spin-momentum locking nature. Here, we report an observation o…
Nanowires with helical surface states represent key prerequisites for observing and exploiting phase-coherent topological conductance phenomena, such as spin-momentum locked quantum transport or topological superconductivity. We demonstrate in a joint experimental and theoretical study that gated nanowires fabricated from high-mobility strained HgTe, known as a bulk topological insulator, indeed preserve the topological nature of the surface states, that moreover extend phase-coherently across the entire wire geometry. The phase-coherence lengths are enhanced up to 5 $μ$m when tuning the wires…
The motion of an electron and its spin are generally not coupled. However in a one dimensional material with strong spin-orbit interaction (SOI) a helical state may emerge at finite magnetic fields, where electrons of opposite spin will have opposite momentum. The existence of this helical state has applications for spin filtering and Cooper pair splitter devices and is an essential ingredient for realizing topologically protected quantum computing using Majorana zero modes. Here we report electrical conductance measurements of a quantum point contact (QPC) formed in an indium antimonide nanow…
Helical spin chains, consisting of magnetic (ad-)atoms, on the surface of bulk superconductors are predicted to host Majorana bound states (MBSs) at the ends of the chain. Here, we investigate the prevalence of trivial zero-energy bound states in these helical spin chain systems. First, we show that the Hamiltonian of a helical spin chain on a superconductor can be mapped to an effective Hamiltonian reminiscent of a semiconductor nanowire with strong Rashba spin-orbit coupling. In particular, we show that a varying rotation rate between neighbouring magnetic moments maps to smooth non-uniform …
The integration of efficient, miniaturized group IV lasers into CMOS architecture holds the key to the realization of fully functional photonic-integrated circuits. Despite several years of progress, however, all group IV lasers reported to date exhibit impractically high thresholds owing to their unfavorable bandstructures. Highly strained germanium with its fundamentally altered bandstructure has emerged as a potential low-threshold gain medium, but there has yet to be any successful demonstration of lasing from this seemingly promising material system. Here, we demonstrate a low-threshold, …
We study normal transport and the sub-gap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance, Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field $B$ that removes a spin sector in the leads (\emph{helical} leads), but not in the central region. Conversely, a helical central r…
As the conventional silicon metal-oxide-semiconductor field-effect transistor (MOSFET) approaches its scaling limits; many novel device structures are being extensively explored. Among them, the silicon nanowire transistor (SNWT) has attracted broad attention. To understand device physics in depth and to assess the performance limits of SNWTs, simulation is becoming increasingly important. The objectives of this work are: 1) to theoretically explore the essential physics of SNWTs (e.g., electrostatics, transport and band structure) by performing computer-based simulations, and 2) to assess the…
Magnetization reversal mechanism of double-helix nanowires probed by dark-field magneto-optical Kerr effect
TU Wien（维也纳工业大学）；University of Loughborough（拉夫堡大学）；Instituto de Nanociencia y Materiales de Aragón, CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所，西班牙科学理事会-萨拉戈萨大学）；Synchrotron SOLEIL（SOLEIL同步辐射中心）；University of Vienna（维也纳大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Hiroshima University（广岛大学）
Transport properties of disordered quantum confined helical Dirac systems are investigated in the large energy limit. As long as the 2D transport length is larger than the perimeter of the nanowire, the conductance and the Fano factor are sensitive to disorder only when the Fermi energy is close to an opening of a transverse mode. In the limit of a large number of transverse modes, transport properties are insensitive to the geometry of the nanowire or the nature and strength of the disorder but, instead, are dominated by the properties of the interface between the ohmic contact and the nanowi…
We study ballistic hole transport through Ge/Si core/shell nanowires at low temperatures. We observe Fabry-P$\acute{e}$rot interference patterns as well as conductance plateaus at integer multiples of 2e$^2$/h at zero magnetic field. Magnetic field evolution of these plateaus reveals large effective Land$\acute{e}$ g-factors. Ballistic effects are observed in nanowires with silicon shell thicknesses of 1 - 3 nm, but not in bare germanium wires. These findings inform the future development of spin and topological quantum devices which rely on ballistic subband-resolved transport.
We study topological phase transitions in one dimensional (1-D) Rashba nanowire under a spatially varying Zeeman field when coupled to an $s$-wave superconductor substrate. We show that this system supports both Majorana bound states (MBS) and fractionally charged bound states (FBS) of Jackiw-Rebbi type. By disassembling Zeeman Hamiltonian into multiple helical components, we find that each helical component is relating to a corresponding topological region, characterized by the emergence of MBS. FBS arises in the overlapping gapped area created by any two helical components with topologically…
In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material scie…
We explore the effects of geometry on the thermal conductivity (kappa) of silicon and germanium nanowires, with lengths between 10-120 nm and diameters up to 5-6 nm. To this end we perform molecular dynamics simulations with the LAMMPS software, using Tersoff interatomic potentials. We consider nanowires with polygonal cross section and we discuss the effect of the transverse geometry on the thermal conductivity. We also consider tubular (hollow) nanowires and core/shell combinations of Si/Ge and Ge/Si, and we compare the heat transport of the core/shell structure with that of the separated co…
The spin-dependent electron transport has been studied in magnetic semiconductor waveguides (nanowires) in the helical magnetic field. We have shown that -- apart from the known conductance dip located at the magnetic field equal to the helical-field amplitude $B_h$ -- the additional conductance dips (with zero conductance) appear at magnetic field different from $B_h$. This effect occuring in the non-adiabatic regime is explained as resulting from the resonant Landau-Zener transitions between the spin-splitted subbands.
Using Ensemble Monte Carlo simulations the photocurrent in a 500nm long strained [110] silicon nanowire with diameter of 3.1 nm is investigated. It was observed that a phototransistor based on this nanowire can have responsivities in the order of 21.3 mA/W for an input light wavelength of 532 nm and intensity of 0.25-2.5 kW/cm2. The super-unity slope of 1.2 in photo conductance versus input light intensity suggests that the nanowire has a photoconductive gain and highlights its advantage over germanium nanowires with sub-unity slope (0.77). The generated photocurrents are in the 0.1 nA-1 nA ra…
Computationally efficient modeling of the thermal conductivity of materials is crucial to thorough experimental planning and theoretical understanding of thermal properties. We present a modeling approach in this work that utilizes frequency-dependent effective medium to calculate lattice thermal conductivity of nanostructured solids. The method accurately predicts a significant reduction in the thermal conductivity of nanostructured Si80Ge20 systems, along with previous reported thermal conductivities in nanowires and nanoparticles-in-matrix materials. We use our model to gain insight into th…
We study hybrid superconducting-semiconducting nanowires in the presence of Rashba spin-orbit interaction as well as helical magnetic fields. We show that the interplay between them leads to a competition of phases with two topological gaps closing and reopening, resulting in unexpected reentrance behavior. Besides the topological phase with localized Majorana fermions (MFs) we find new phases characterized by fractionally charged fermion (FF) bound states of Jackiw-Rebbi type. The system can be fully gapped by the magnetic fields alone, giving rise to FFs that transmute into MFs upon turning …
We study how the shape of a periodic magnetic field affects the presence of Majorana bound states (MBS) in a nanowire-superconductor system. Motivated by the field configurations that can be produced by an array of nanomagnets, we consider spiral fields with an elliptic cross-section and fields with two sinusoidal components. We show that MBS are robust to imperfect helical magnetic fields. In particular, if the amplitude of one component is tuned to the value determined by the superconducting order parameter in the wire, the MBS can exist even if the second component has a much smaller amplit…
Spin-helical states, which arise in quasi-one-dimensional (1D) channels with spin-orbital (SO) coupling, underpin efforts to realize topologically-protected quantum bits based on Majorana modes in semiconductor nanowires. Detecting helical states is challenging due to non-idealities present in real devices. Here we show by means of tight-binding calculations that by using ferromagnetic contacts it is possible to detect helical modes with high sensitivity even in the presence of realistic device effects, such as quantum interference. This is possible because of the spin-selective transmission p…
Helical states can be measured through the observation of the reentrant behaviour, which is a dip in the conductance probed in semiconducting nanowires (NWs) with strong spin-orbit coupling (SOC) under the presence of an external perpendicular magnetic field. We investigate the effects of deformations in the electronic transport in NWs considering the coupling between different transverse modes. Within this approach, we show that the dip in the conductance of a NW is affected by the presence of a local constriction. Moreover, we find that the reentrant feature in the conductance can appear in …
Cylindrical magnetic nanowires are promising systems for the development of three-dimensional spintronic devices. Here, we simulate the evolution of magnetic states during fabrication of strongly-coupled cylindrical nanowires with varying degrees of overlap. By varying the separation between wires, the relative strength of exchange and magnetostatic coupling can be tuned. Hence leading to the formation of six fundamental states as a function of both inter-wire separation and wire height. In particular, two complex three-dimensional magnetic states, a 3D Landau Pattern and a Helical Domain wall…
The characterization of helical states can be performed by checking the existence of the re-entrant behaviour, which appears as a dip in the conductance probed in nanowires (NWs) with strong spin-orbit coupling (SOC) and under perpendicular magnetic field. On the other hand, the experiment described in Ref. 1 observed the re-entrant behaviour in the absence of a magnetic field, which was explained through spin-flipping two-particle backscattering. We theoretically show that the observation of the re-entrant behaviour is due to a multi-channel scattering mechanism, which causes a reduction of t…
By modeling a Rashba nanowire contacted to leads via an inhomogeneous spin-orbit coupling profile, we investigate the equilibrium properties of the spin sector when a uniform magnetic field is applied along the nanowire axis. We find that the interplay between magnetic field and Rashba coupling generates a spin current, polarised perpendicularly to the applied field and flowing through the nanowire even at equilibrium. In the nanowire bulk such effect persists far beyond the regime where the nanowire mimics the helical states of a quantum spin Hall system, while in the leads the spin current i…
The helical state is a fundamental prerequisite for many spintronics applications and Majorana zero mode engineering in nanoscopic semiconductors. Its existence in quasi-one-dimensional nanowires was predicted to be detectable as a characteristic reentrant behavior in the conductance, which in a typical two-terminal architecture may be difficult to distinguish from other possible phenomena such as Fabry-Perot oscillations. Here we present an alternative method of helical gap detection free of the mentioned ambiguity, and based on the nonlocal conductance measurements in a three-terminal juncti…
We show a hard induced superconducting gap in a Ge-Si nanowire Josephson transistor up to in-plane magnetic fields of $250$ mT, an important step towards creating and detecting Majorana zero modes in this system. A hard induced gap requires a highly homogeneous tunneling heterointerface between the superconducting contacts and the semiconducting nanowire. This is realized by annealing devices at $180$ $^\circ$C during which aluminium inter-diffuses and replaces the germanium in a section of the nanowire. Next to Al, we find a superconductor with lower critical temperature ($T_\mathrm{C}=0.9$ K…
We theoretically investigate the D'yakonov-Perel' spin relaxation properties in diffusive wurtzite semiconductor nanowires and their impact on the quantum correction to the conductivity. Although the lifetime of the long-lived spin states is limited by the dominant $k$-linear spin-orbit contributions in the bulk, these terms show almost no effect in the finite-size nanowires. Here, the spin lifetime is essentially determined by the small $k$-cubic spin-orbit terms and nearly independent of the wire radius. At the same time, these states possess in general a complex helical structure in real sp…
We used density-functional theory based first principles simulations to study the effects of uniaxial strain and quantum confinement on the electronic properties of germanium nanowires along the [110] direction, such as the energy gap and the effective masses of the electron and hole. The diameters of the nanowires being studied are up to 50 Å. As shown in our calculations, the Ge [110] nanowires possess a direct band gap, in contrast to the nature of an indirect band gap in bulk. We discovered that the band gap and the effective masses of charge carries can be modulated by applying uniaxial s…
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying the electric field to a silicene sheet. In particular, the gap closes at a certain critical electric field. Examining the band structure of a silicene nanoribbon, we demonstrate that a topological phase transition occurs from a topol…
Spin waves are the low-energy excitations of magnetically ordered materials. They are key elements in the stability analysis of the ordered phase and have a wealth of technological applications. Recently, we showed that spin waves of a magnetic nanowire may carry a definite amount of orbital angular momentum components along the propagation direction. This helical, in addition to the chiral, character of the spin waves is related to the spatial modulations of the spin wave phase across the wire. It, however, remains a challenge to generate and control such modes with conventional magnetic fiel…
We compute analytically the weak (anti)localization correction to the Drude conductivity for electrons in tubular semiconductor systems of zinc blende type. We include linear Rashba and Dresselhaus spin-orbit coupling (SOC) and compare wires of standard growth directions $\langle100\rangle$, $\langle111\rangle$, and $\langle110\rangle$. The motion on the quasi-two-dimensional surface is considered diffusive in both directions: transversal as well as along the cylinder axis. It is shown that Dresselhaus and Rashba SOC similarly affect the spin relaxation rates. For the $\langle110\rangle$ growt…
We study theoretically the low-energy hole states in Si, Ge, and Ge/Si core/shell nanowires (NWs). The NW core in our model has a rectangular cross section, the results for a square cross section are presented in detail. In the case of Ge and Ge/Si core/shell NWs, we obtain very good agreement with previous theoretical results for cylindrically symmetric NWs. In particular, the NWs allow for an unusually strong and electrically controllable spin-orbit interaction (SOI) of Rashba type. We find that the dominant contribution to the SOI is the "direct Rashba spin-orbit interaction" (DRSOI), which…
