Quantum Interference Oscillations Research Articles

Gate-Modulated Quantum Interference Oscillations in Sb-Doped Bi2Se3 Topological Insulator Nanoribbon

Topological insulator nanoribbons (TI NRs) provide a useful platform to explore the phase-coherent quantum electronic transport of topological surface states, which is crucial for the development of topological quantum devices. When applied with an axial magnetic field, the TI NR exhibits magnetoconductance (MC) oscillations with a flux period of h/e, i.e., Aharonov-Bohm (AB) oscillations, and h/2e, i.e., Altshuler-Aronov-Spivak (AAS) oscillations. Herein, we present an extensive study of the AB and AAS oscillations in Sb doped Bi$_2$Se$_3$ TI NR as a function of the gate voltage, revealing phase-alternating topological AB oscillations. Moreover, the ensemble-averaged fast Fourier transform analysis on the Vg dependent MC curves indicates the suppression of the quantum interference oscillation amplitudes near the Dirac point, which is attributed to the suppression of the phase coherence length within the low carrier density region. The weak antilocalization analysis on the perpendicular MC curves confirms the idea of the suppressed coherence length near the Dirac point in the TI NR.

Adjustable Quantum Interference Oscillations in Sb-Doped Bi2Se3 Topological Insulator Nanoribbons.

Topological insulator (TI) nanoribbons (NRs) provide a platform for investigating quantum interference oscillations combined with topological surface states. One-dimensional subbands formed along the perimeter of a TI NR can be modulated by an axial magnetic field, exhibiting Aharonov-Bohm (AB) and Altshuler-Aronov-Spivak (AAS) oscillations of magnetoconductance (MC). Using Sb-doped Bi2Se3 TI NRs, we found that the relative amplitudes of the two quantum oscillations can be tuned by varying the channel length, exhibiting crossover from quasi-ballistic to diffusive transport regimes. The AB and AAS oscillations were discernible even for a 70 μm long channel, while only the AB oscillations were observed for a short channel. Analyses based on ensemble-averaged fast Fourier transform of MC curves revealed exponential temperature dependences of the AB and AAS oscillations, from which the circumferential phase-coherence length and thermal length were obtained. Our observations indicate that the channel length in a TI NR can be a useful control knob for tailored quantum interference oscillations, especially for developing topological hybrid quantum devices.

Repelling, binding, and oscillating of two-particle discrete-time quantum walks

In this paper, we investigate the effects of particle–particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle–particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.

Nanoscale Mach-Zehnder interferometer with spin-resolved quantum Hall edge states

We realize a nanoscale-area Mach-Zehnder interferometer with co-propagating quantum Hall spin-resolved edge states and demonstrate the persistence of gate-controlled quantum interference oscillations, as a function of an applied magnetic field, at relatively large temperatures. Arrays of top-gate magnetic nanofingers are used to induce a resonant charge transfer between the pair of spin-resolved edge states. To account for the pattern of oscillations measured as a function of magnetic field and gate voltage, we have developed a simple theoretical model which satisfactorily reproduces the data.

Determination of time-reversal symmetry breaking lengths in an InGaAs interferometer array

Quantum interference oscillations due to the Aharonov–Bohm phase were measured in a ring interferometer array fabricated on a two-dimensional electron system in an InGaAs/InAlAs heterostructure. Coexisting oscillations with magnetic flux periodicity h/e and h/2e were observed and their amplitudes compared as function of applied magnetic field. The h/2e oscillations originate in time-reversed trajectories with the ring interferometers operating in Sagnac-type mode, while the h/e oscillations result from Mach–Zehnder operation. The h/2e oscillations require time-reversal symmetry and hence can be used to quantify time-reversal symmetry breaking, more particularly the fundamental mesoscopic dephasing length associated with time-reversal symmetry breaking under applied magnetic field, an effective magnetic length. The oscillation amplitudes were investigated over magnetic fields spanning 2.2 T, using Fourier transforms over short segments of 40 mT. As the magnetic field increased, the h/2e oscillation amplitude decreased due to time-reversal symmetry breaking by the local magnetic flux in the interferometer arms. A dephasing model for quantum-coherent arrays was used to experimentally quantify effective magnetic lengths. The data was then compared with analytical expressions for diffusive, ballistic and confined systems.

Tomonaga-Luttinger Liquid Features in Ballistic Single-Walled Carbon Nanotubes: Conductance and Shot Noise

We study the electrical transport properties of well-contacted ballistic single-walled carbon nanotubes in a three-terminal configuration at low temperatures. We observe signatures of strong electron-electron interactions: the conductance exhibits bias-voltage-dependent amplitudes of quantum interference oscillation, and both the current noise and Fano factor manifest bias-voltage-dependent power-law scalings. We analyze our data within the Tomonaga-Luttinger liquid model using the nonequilibrium Keldysh formalism and find qualitative and quantitative agreement between experiment and theory.

Quantum interference in the quasi-one-dimensional organic conductor(Per)2Au(mnt)2

The quantum interference (QI) of charge carriers in a magnetic field is obtained in the organic conductor ${(\mathrm{Per})}_{2}\mathrm{Au}{(\mathrm{mnt})}_{2}$ by suppressing the charge-density-wave (CDW) state with pressure. The QI oscillation amplitude exhibits a temperature-dependent scattering rate, indicative of an inhomogeneous metal-CDW ground state. The QI oscillation frequency reveals a Fermi-surface topology in close agreement with band-structure predictions. The value of the frequency is quite small, making the limit of constructive interference experimentally accessible.

Quantum interference and population swapping in single quantum dots with V-type three-level

The quantum interference and Rabi oscillation of a V-type three-level system with two orthogonal sub-states in an elongated semiconductor quantum dot are discussed theoretically with optical Bloch equations when the system is driven by pulse-pair. Numerical calculations from the optical Bloch equations reveal that the quantum interference in the system is enhanced with the increasing of the energy decay or splitting. Furthermore, the populations swapping in two orthogonal sub-states can be realized though the direct transition is prohibited.

De Haas–van Alphen effect in two-dimensional and quasi-two-dimensional systems

We study the de Haas-van Alphen (dHvA) oscillation in two-dimensional and quasi-two-dimensional systems. We give a general formula of the dHvA oscillation in two-dimensional multi-band systems. By using this formula, the dHvA oscillation and its temperature-dependence for the two-band system are shown. By introducing the interlayer hopping $t_z$, we examine the crossover from the two-dimension, where the oscillation of the chemical potential plays an important role in the magnetization oscillation, to the three-dimension, where the oscillation of the chemical potential can be neglected as is well know as the Lifshitz and Kosevich formula. The crossover is seen at $4 t_z \sim 8 ta b H /\phi_0$, where a and b are lattice constants, $\phi_0$ is the flux quantum and 8t is the width of the total energy band. We also study the dHvA oscillation in quasi-two-dimensional magnetic breakdown systems. The quantum interference oscillations such as $\beta-\alpha$ oscillation as well as the fundamental oscillations are suppressed by the interlayer hopping $t_z$, while the $\beta+\alpha$ oscillation gradually increases as $t_z$ increases and it has a maximum at $t_z/t\approx 0.025$. This interesting dependence on the dimensionality can be observed in the quasi-two-dimensional organic conductors with uniaxial pressure.

Quantum interference oscillation and effect of spin in de Haas van Alphen effect in the quantum-well materials

In the heterojunction GaAs/Al 0.3Ga 0.7As with the two-dimensional (2D) one-band system and In x Ga 1− x As and GaAs/AlAs with 2D multi-band system, the de Haas van Alphen (dHvA) oscillation has been observed recently. The Lifshitz and Kosevich formula used conventionally in the dHvA effect is not appropriate to the 2D system. Therefore, we analytically give a formula on the dHvA oscillation in the 2D multi-band system. It is possible to obtain the cyclotron effective mass and the effective g-value exactly.

Competing types of quantum oscillations in the two-dimensional organic conductor(BEDT−TTF)8Hg4Cl12(C6H5Cl)2

Interlayer magnetoconductance of the quasi-two dimensional organic metal (BEDT-TTF)8Hg4Cl12(C6H5Cl)2 has been investigated in pulsed magnetic fields extending up to 36 T and in the temperature range from 1.6 to 15 K. A complex oscillatory spectrum, built on linear combinations of three basic frequencies only is observed. These basic frequencies arise from the compensated closed hole and electron orbits and from the two orbits located in between. The field and temperature dependencies of the amplitude of the various oscillation series are studied within the framework of the coupled orbits model of Falicov and Stachowiak. This analysis reveals that these series result from the contribution of either conventional Shubnikov-de Haas effect (SdH) or quantum interference (QI), both of them being induced by magnetic breakthrough. Nevertheless, discrepancies between experimental and calculated parameters indicate that these phenomena alone cannot account for all of the data. Due to its low effective mass, one of the QI oscillation series - which corresponds to the whole first Brillouin zone area - is clearly observed up to 13 K.

Quantum Interference Oscillation in DHvA Effect in the Two- and Three-dimensional Systems

We study the behavior of the dHvA oscillation from the two-dimension to the three-dimension by changing the interlayer hopping t z . We show that the oscillation of the chemical potential is gradually suppressed as t z increases. It results from the broadening of the width of the Landau level. In the quasi-two-dimensional magnetic breakdown system such as κ-(BEDT-TTF) 2 Cu(NCS) 2 , the quantum interference oscillation such as β-α oscillation is suppressed, while the amplitude of the β+α oscillation has a maximum as a function of t z . This interesting dependence on the dimensionality can be observed in quasi-two-dimensional metals under the uniaxial pressure.

Quantum interference in artificial band structures.

Magnetotransport experiments on two-dimensional electron systems with an atomically precise, one-dimensional potential modulation reveal striking quantum interference oscillations. Within a semiclassical framework, they are recognized either as self-interference along closed orbits, many of them rendered possible by magnetic breakdown between Fermi contour segments of the artificial band structure, or as interference-enhanced backscattering. The known commensurability oscillations appear as a special case of the latter mechanism.

Hot-electron effects and oxide degradation in MOS structures studied with ballistic electron emission microscopy

The application of the STM-based technique of ballistic electron emission microscopy (BEEM) to the study of transport properties of SiO2 gate oxide layers is reviewed. Oxide degradation observed on a local scale of nanometer dimensions ranges from the filling of electron traps with low-kinetic-energy electrons injected just above the oxide barrier, to trap generation and filling triggered by electrons with kinetic energies ≥2 eV. BEEM provides means to determine the spatial distributions of the traps. Only positively charged traps are observed for thin (≤4 nm) SiO2 layers upon electrical stressing. Oxide breakdown is seldom induced by local stressing, suggesting that it occurs at extrinsic defect sites that are widely separated. BEEM also provides unique opportunities to address fundamental issues. In that regard, examples of the dynamic response of the SiO2 dielectric to a moving electron are presented, as well as the determination of the dispersion of the electron mass of the conduction-band electrons. The latter is achieved by modeling quantum interference oscillations in the BEEM current.

Determination of the energy-dependent conduction band mass in SiO2

The energy dependence of the conduction band mass in amorphous SiO2 was deduced from quantum interference oscillations in the ballistic electron emission microscope current, and separately from Monte Carlo simulations of the electron mean free paths obtained by internal photoemission. The results imply a strong nonparabolicity of the conduction band of SiO2.

Energy-dependent conduction band mass of SiO2 determined by ballistic electron emission microscopy

Quantum interference oscillations in ballistic electron emission microscopy (BEEM) spectra were observed for metal–oxide–semiconductor structures with 23 and 30 Å SiO2 interlayers. Maxima in the transmission coefficients, obtained from solutions of the one-dimensional Schrödinger equation that included image force corrections, could be matched to the spectral maxima provided that the effective electron mass mox, an adjustable parameter, was increased at each of the consecutive higher energy maxima. The resulting energy dependence or dispersion of mox(E) showed a dependence on the oxide thickness. The 23 and 30 Å oxides exhibit initial (zero kinetic energy) mox values of 0.52 m0 and 0.45 m0, respectively, that disperse upward with energy by ≈0.3 m0 over a 0–2.5 eV range in kinetic energies. The range of mox values observed is substantially lower than the average mox values deduced from quantum interference in Fowler–Nordheim tunneling experiments. The origin of these differences are discussed, and it is argued that BEEM is an inherently simpler and less error prone technique to evaluate mox.

Quantum Interference in the Spin-Polarized Heavy Fermion CompoundCeB6: Evidence for Topological Deformation of the Fermi Surface in Strong Magnetic Fields

We report susceptibility experiments in magnetic fields up to 60thinspthinspT and show conclusively that the de Haas{endash}van Alphen oscillations originate from a single spin Fermi surface. New observed frequencies present in magnetic breakdown and quantum interference oscillations indicate that the Fermi-surface topology changes as a function of the applied field while maintaining a constant volume. These results are not expected from the Anderson lattice model. {copyright} {ital 1998} {ital The American Physical Society}

Current oscillations in thin metal–oxide–semiconductor structures observed by ballistic electron emission microscopy

Quantum interference oscillations of electrons in a thin SiO2 layer were observed by ballistic electron emission microscopy (BEEM). With BEEM, electrons are injected across the gate of a metal–oxide–semiconductor (MOS) structure and directly into the conduction band of the SiO2. The MOS capacitor consisted of a 5 nm thick Pd film deposited on a 2.8±0.2 nm oxide thermally grown on Si(100). Oscillations with up to four peaks in an energy range of 0–3 eV above the injection threshold were noted. Their magnitude is of the order of 30% of the underlying BEEM current. The oscillations were most salient and their energy location repeatable at points of the sample that were previously not exposed to the electron beam. Even modest exposures caused a buildup of positive charge. This charge resulted in energy shifts, as well as a weakening of the oscillations, both of which are a consequence of the added scattering and local field inhomogeneities associated with the random distribution of the positive charge. Solutions of the Schrödinger equation that included a built-in oxide potential of 0.20 V and image force effects at both interfaces gave excellent fits to the experimental data for an effective electron mass in the oxide mox=0.63±0.09mo. The uncertainty in mox arises from an uncertainty of ±0.2 nm in the determination of the oxide thickness by ellipsometric methods. Nevertheless, the obtained value is well above the generally accepted value of 0.5mo.

The Quantum Interference Oscillation due to the Magnetic Breakdown

The Quantum Interference Oscillation due to the Magnetic Breakdown

DHvA Effect with Quantum Interference Oscillation due to Magnetic Breakdown

The effect of the magnetic breakdown on the dHvA oscillation is studied by full-quantum numerical calculation for a two-dimensional model. We demonstrate that the interference difference oscillation, usually designated as β-α , exists even in the thermodynamic quantity; this result is contrary to the conventional semi-classical picture. In addition, the dependencies of various oscillations of the magnetization on the field, temperature and band gap are examined thoroughly and compared with the semi-classical theory by Falicov and Stachoviak, which is based on the Pippard's coupled network model and the Lifshitz-Kosevich formula. We discuss the relevance of our calculation to the observed interference difference frequencies in the dHvA oscillation of magnesium and in the SdH oscillation of two-dimensional organic conductors.