Electron Phase Coherence Length Research Articles

One-dimensional antilocalization of electrons from spin disorder probed by nonlinear Hall effect

In recent years, nonreciprocal transport measurement has emerged as a probe of spin orbit interaction, spin texture, superconductivity, and other fundamental properties of materials. Here, we study the nonlinear Hall effect (NLHE) in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}/\mathrm{CoFeB}$ heterostructures measured by second harmonic voltage method. Magneto-optical Kerr effect measurements demonstrate the origin of the NLHE to be the asymmetric magnon scattering mechanism. Moreover, a linear relation between the nonlinear Hall resistance and the electron phase coherence length of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is observed between 5 and 50 K. We propose a phenomenological model that explains the enhancement of the NLHE below 50 K as a result of one-dimensional antilocalization of electrons from spin disorder, enabled by spin-momentum locking and conservation of angular momentum.

Anomalous Temperature Dependence of Quantum Correction to the Conductivity of Magnetic Topological Insulators.

Quantum transport in magnetic topological insulators reveals a strong interplay between magnetism and topology of electronic band structures. A recent experiment on magnetically doped topological insulator Bi_{2}Se_{3} thin films showed the anomalous temperature dependence of the magnetoconductivity while their field dependence presents a clear signature of weak antilocalization [Tkac etal., Phys. Rev. Lett. 123, 036406 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.036406]. Here, we demonstrate that the tiny mass of the surface electrons induced by the bulk magnetization leads to a temperature-dependent correction to the π Berry phase and generates a decoherence mechanism to the phase coherence length of the surface electrons. As a consequence, the quantum correction to conductivity can exhibit nonmonotonic behavior by decreasing the temperature. This effect is attributed to the close relation of the Berry phase and quantum interference of the topological surface electrons in quantum topological materials.

Unraveling the effect of electron-electron interaction on electronic transport in La-doped SrSnO3 films

We demonstrate that the electron-electron interaction effect is primarily responsible for an increase in the Hall coefficient in the La-doped SrSnO3 films below 50 K accompanied by an increase in the sheet resistance. The quantitative analysis of the magnetoresistance data yielded a large phase coherence length of electrons exceeding 450 nm at 1.8 K and revealed the electron-electron interaction being accountable for the breaking of electron phase coherency in La-doped SrSnO3 films. These results while providing critical insights into the fundamental transport behavior in doped stannates also indicate the potential applications of stannates in quantum coherent electronic devices owing to their large phase coherence length.

Coherent Resonant Tunneling through Double Metallic Quantum Well States.

Study of resonant tunneling through multimetallic quantum well (QW) structure is not only important for the fundamental understanding of quantum transport but also for the great potential to generate advanced functionalities of spintronic devices. However, it remains challenging to engineer such a structure due to the short electron phase coherence length in metallic QW system. Here, we demonstrate the successful fabrication of double-QW structure in a single fully epitaxial magnetic tunnel junction (MTJ) heterostructure, where two Fe QW layers are sandwiched between three MgAlO x tunnel barriers. We show clear evidence of the coherent resonant tunneling through the discrete QW states in the two QWs. The coherent resonant tunneling condition is fulfilled only when the middle barrier between the two QWs is thin enough and available QW states are present simultaneously in both QWs under a certain bias. Compared to the single QW structure, the resonant tunneling in double-QW MTJ produces strong conductivity oscillations with much narrower peak width (about half) owing to the enhanced energy filtering effect. This study presents a comprehensive understanding of the resonant tunneling mechanism in MTJ with multiple QWs, which is essential for future development of new spintronic devices operating in the quantum tunneling regime.

Observation of long phase-coherence length in epitaxial La-doped CdO thin films

The search for long electron phase-coherence length, which is the length that an electron can keep its quantum wavelike properties, has attracted considerable interest in the last several decades. Here, we report the long phase-coherence length of \ensuremath{\sim}3.7 \ensuremath{\mu}m in La-doped CdO thin films at 2 K. Systematical investigations of the La doping and the temperature dependences of the electron mobility and the electron phase-coherence length reveal contrasting scattering mechanisms for these two physical properties. Furthermore, these results show that the oxygen vacancies could be the dominant scatters in CdO thin films that break the electron phase coherence, which would shed light on further investigation of phase-coherence properties in oxide materials.

Defect-driven localization crossovers in MBE-grown La-doped SrSnO3 films

Through systematic control of cation stoichiometry using a hybrid molecular beam epitaxy method, we show a crossover from weak to strong localization of electronic carriers in La-doped $\mathrm{SrSn}{\mathrm{O}}_{3}$ films on $\mathrm{LaAl}{\mathrm{O}}_{3}$(001). We demonstrate that substrate-induced dislocations in these films can have a strong influence on the electron phase coherence length resulting in two-dimensional to three-dimensional weak localization crossover. We discuss the correlation between electronic transport, and defects associated with nonstoichiometry and dislocations.

Hot Electrons Regain Coherence in Semiconducting Nanowires

The higher the energy of a particle is above equilibrium the faster it relaxes due to the growing phase-space of available electronic states it can interact with. In the relaxation process phase coherence is lost, thus limiting high energy quantum control and manipulation. In one-dimensional systems high relaxation rates are expected to destabilize electronic quasiparticles. We show here that the decoherence induced by relaxation of hot electrons in one-dimensional semiconducting nanowires evolves non-monotonically with energy such that above a certain threshold hot-electrons regain stability with increasing energy. We directly observe this phenomenon by visualizing for the first time the interference patterns of the quasi-one-dimensional electrons using scanning tunneling microscopy. We visualize both the phase coherence length of the one-dimensional electrons, as well as their phase coherence time, captured by crystallographic Fabry-Perot resonators. A remarkable agreement with a theoretical model reveals that the non-monotonic behavior is driven by the unique manner in which one dimensional hot-electrons interact with the cold electrons occupying the Fermi-sea. This newly discovered relaxation profile suggests a high-energy regime for operating quantum applications that necessitate extended coherence or long thermalization times, and may stabilize electronic quasiparticles in one dimension.

Highly Conductive Polycrystalline Metallic Ring in a Magnetic Field

Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ∼ I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction. Keywords—Electrical Conduction, Electron Phase Coherence, Polycrystalline Metal, Magnetic Field.

Doping-Induced Universal Conductance Fluctuations in GaN Nanowires.

The transport properties of Ge-doped single GaN nanowires are investigated, which exhibit a weak localization effect as well as universal conductance fluctuations at low temperatures. By analyzing these quantum interference effects, the electron phase coherence length was determined. Its temperature dependence indicates that in the case of highly doped nanowires electron-electron scattering is the dominant dephasing mechanism, while for the slightly doped nanowires dephasing originates from Nyquist-scattering. The change of the dominant scattering mechanism is attributed to a modification of the carrier confinement caused by the Ge-doping. The results demonstrate that the phase coherence length can be tuned by the donor concentration making Ge-doped GaN nanowires an ideal model system for studying the influence of impurities on quantum-interference effects in mesoscopic and nanoscale systems.

Interfacial Coupling and Electronic Structure of Two-Dimensional Silicon Grown on the Ag(111) Surface at High Temperature.

Freestanding silicene, a monolayer of Si arranged in a honeycomb structure, has been predicted to give rise to massless Dirac fermions, akin to graphene. However, Si structures grown on a supporting substrate can show properties that strongly deviate from the freestanding case. Here, combining scanning tunneling microscopy/spectroscopy and differential conductance mapping, we show that the electrical properties of the phase of few-layer Si grown on Ag(111) strongly depend on film thickness, where the electron phase coherence length decreases and the free-electron-like surface state gradually diminishes when approaching the interface. These features are presumably attributable to the inelastic inter-band electron-electron scattering originating from the overlap between the surface state, interface state and the bulk state of the substrate. We further demonstrate that the intrinsic electronic structure of the as grown phase is identical to that of the R30° reconstructed Ag on Si(111), both of which exhibit the parabolic energy-momentum dispersion relation with comparable electron effective masses. These findings highlight the essential role of interfacial coupling on the properties of two-dimensional Si structures grown on supporting substrates, which should be thoroughly scrutinized in pursuit of silicene.

Long phase coherence length and anisotropic magnetoresistance in MgZnO thin film

We comprehensively investigate magnetotransport properties of MgZnO thin film grown on ZnO substrate by molecular-beam epitaxy. We measure the weak localization effect and extract the electron phase coherence length by fitting to a three-dimensional weak localization theory and by analyzing the different changing rate of the magnetoresistance, results of which are in good agreement with each other. The phase coherence length ranges from 38.4±1 nm at 50 K to 99.8±3.6 nm at 1.4 K, almost the same as that of ZnO nanoplates and In-doped ZnO nanowires, and its temperature dependence is found to scale as T−3/4. Meanwhile, we study the anisotropic magnetoresistance resulting from the geometric effect as well as the Lorentz force induced path-length effect, which will be enhanced in higher magnetic fields.

Dirac fermions and superconductivity in the homologous structures(AgxPb1−xSe)5(Bi2Se3)3m(m=1,2)

A newly discovered topological insulator (TI) $({\mathrm{Ag}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x}\mathrm{Se}{)}_{5}({\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}{)}_{3m}$ ($m=2$) has a band gap of 0.5 eV, the largest value reported in topological insulators. We present a magnetotransport study of the Dirac electrons of this compound in the quantum diffusion regime. Two-dimensional weak antilocalization due to the destructive interference of the Dirac electrons was observed. The phase coherence length of the Dirac electrons is independent of doping and disorder levels. This provides an indication of the backscattering immunity under the protection of time reversal invariance of the TI. We further report that the homologous compound $({\mathrm{Ag}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x}\mathrm{Se}{)}_{5}({\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}{)}_{3m}$ ($m=1$) is a superconductor with a transition temperature ${T}_{C}=1.7$ K. The related structures of these two phases allow lateral intergrowth of crystals to occur naturally, offering a potential platform to observe the Majorana fermion state at the boundary of two intergrown crystals.

Impact of Si growth rate on coherent electron transport in Si:P delta-doped devices

We address the impact of Si growth rate on electron transport in Si:P δ-doped devices encapsulated by low temperature Si molecular beam epitaxy. Si growth rates ranging from 0.05 to 2.2 Å s−1 were used in conjunction with 250 °C Si overgrowth. Using a combination of scanning tunneling microscopy and 4.2 K magnetotransport measurements, we find that high growth rates tend to degrade the crystal quality of the Si cap layer resulting in shorter electron mean free path and phase coherence length in such devices.

One-Dimensional Weak Localization of Electrons in a Single InAs Nanowire

We report on low temperature (2-30K) electron transport and magneto-transport measurements of a chemically synthesized InAs nanowire. Both the temperature, T, and transverse magnetic field dependences of the nanowire conductance are consistent with the functional forms predicted in one-dimensional (1D) weak localization theory. By fitting the magneto-conductance data to theory, the phase coherence length of electrons is determined to be tens of nanometers with a T(-1/3) dependence. Moreover, as the electron density is increased by a gate voltage, the magneto-conductance shows a possible signature of suppression of weak localization in multiple 1D subbands.

Effect of phase‐breaking events on electron transport in mesoscopic and nanodevices

AbstractExisting ballistic models for electron transport in mesoscopic and nanoscale systems break down as the size of the device becomes longer than the phase coherence length of electrons in the system. Krstic et al. experimentally observed that the current in single‐wall carbon nanotube systems can be regarded as a combination of a coherent part and a noncoherent part. In this article, we discuss the use of Büttiker phase‐breaking technique to address partially coherent electron transport, generalize that to a multichannel problem, and then study the effect of phase‐breaking events on the electron transport in two‐terminal graphene nanoribbon devices. We also investigate the difference between the pure‐phase randomization and phase/momentum randomization boundary conditions. While momentum randomization adds an extra resistance caused by backward scattering, pure‐phase randomization smooths the conductance oscillations because of interference. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

One-dimensional conduction properties of highly phosphorus-doped planar nanowires patterned by scanning probe microscopy

We present a detailed study of the cryogenic temperature conduction properties of a low resistivity, highly P-doped nanowire lithographically defined by a scanning tunneling microscope. Temperature-dependent magnetotransport measurements allow us to determine the dominant scattering mechanism as one-dimensional (1D) Nyquist phase breaking. We extract quantum corrections to the Drude conductivity arising from both 1D weak localization and 1D electron-electron interactions for this quasi-1D system. Below $450\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$, the electron phase coherence length is observed to saturate consistent with a Thouless crossover into the strong localization regime.

Direct Measurementof the Phase-Coherence Length in aGaAs/GaAlAsSquareNetwork

The low temperature magnetoconductance of a large array of quantum coherent loops exhibits Altshuler-Aronov-Spivak oscillations with a periodicity corresponding to 1/2 flux quantum per loop. We show that the measurement of the harmonics content provides an accurate way to determine the electron phase-coherence length L(phi) in units of the lattice length with no adjustable parameters. We use this method to determine L(phi) in a square network realized from a 2D electron gas in a GaAs/GaAlAs heterojunction, with only a few conducting channels. The temperature dependence follows a power law T(-1/3) from 1.3 K to 25 mK with no saturation, as expected for 1D diffusive electronic motion and electron-electron scattering as the main decoherence mechanism.

Phenomenology of conduction in incoherent layered crystals

A novel phenomenological approach to the analysis of the conductivities of incoherent layered crystals is presented. It is based on the fundamental relationship between the resistive anisotropy $\sigma_{ab}/\sigma_c$ and the ratio of the phase coherence lengths in the respective directions. We explore the model-independent consequences of a general assumption that the out-of-plane phase coherence length of single electrons is a short fixed distance of the order of interlayer spacing. Several topics are discussed: application of the scaling theory, magnetoresistivity, the effects of substitutions and the intermediate regime of conduction when both coherence lengths change with temperature, but at different rate.

Phase Coherence and Temperature Dependence of Current–Voltage Characteristics at Low-Current and Low-Voltage Region of Double-Barrier Resonant-Tunneling Diode

At sufficiently low temperatures, e.g., below 10 K, current in current–voltage (I–V) characteristics of double-barrier resonant-tunneling diodes (DBRTDs) in the low-current and low-voltage region is inversely proportional to the phase coherence length. However, with increasing temperature, this proportional behavior no longer holds due to thermal energy spread around the Fermi energy in the emitter. In this study, the temperature range in which current amplitude is inversely proportional to the phase coherence length is theoretically derived. The temperature range is dependent on the structural parameters of DBRTDs. By choosing appropriate device parameters, we can make the current amplitude inversely proportional to the phase coherence length even at relatively high temperatures, e.g., 77 K. These results are highly useful for estimating electron phase coherence length over a wide temperature range and for studying the temperature dependence of the phase coherence length using DBRTDs.

Aharonov-Bohm oscillation of resistance observed in a ferromagnetic Fe-Ni nanoring

The magnetoresistance of a ferromagnetic Fe–Ni nanoring with 420 nm in inner diameter and 500 nm in outer diameter was measured at very low temperatures below 100 mK. When a magnetic field is applied to the ring, the magnetoresistance exhibits oscillations whose period varies according to the field direction. This demonstrates the Aharonov–Bohm effect of the conduction electrons in the ferromagnetic nanoring. The amplitude of the oscillations can be regarded from the viewpoint of competition between the system size and the phase coherence length of the conduction electrons.