Dingle Temperature Research Articles

Transport Properties of Topological Insulator Bi0.83Sb0.17 Nanowires

ABSTRACTWe have investigated the transport properties of topological insulator based on single-crystal Bi0.83Sb0.17 nanowires. The single-crystal nanowire samples in the diameter range 200 nm – 1.1 μm were prepared by the high frequency liquid phase casting in a glass capillary using an improved Ulitovsky technique; they were cylindrical single-crystals with (1011) orientation along the wire axis. In this orientation, the wire axis makes an angle of 19.5o with the bisector axis C1 in the bisector-trigonal plane. Bi0.83Sb0.17 is a narrow gap semiconductor with energy gap at L point of Brillouin zone ΔE= 21 meV. In accordance with the measurements of the temperature dependence of the resistivity of the samples resistance increases with decreasing temperature, but at low temperatures decrease in the resistance is observed. This effect, decrease in the resistance, is a clear manifestation of the interesting properties of topological insulators - the presence on its surface of a highly conducting zone. The Arrhenius plot of resistance R in samples with diameter d=1.1 µm and d=200 nm indicates a thermal activation behavior with an activation gap ΔE= 21 and 35 meV, respectively, which proves the presence of the quantum size effect in these samples. We found that in the range of diameter 1100 nm - 200 nm when the diameter decreases the energy gap is growing as 1/d. We have investigated magnetoresistance of Bi0.83Sb0.17 nanowires at various magnetic field orientations. From the temperature dependences of Shubnikov de Haas oscillation amplitude for different orientation of magnetic field we have calculated the cyclotron mass mc and Dingle temperature TD for longitudinal and transverse (B||C3 and B||C2) directions of magnetic fields, which equal 1.96*10-2m0, 9.8 K, 8.5*10-3m0 , 9.4 K and 1.5*10-1m0 , 2.8 K respectively. The observed effects are discussed.

Probing electron interactions in a two-dimensional system by quantum magneto-oscillations

We have experimentally studied the renormalized effective mass ${m}^{*}$ and Dingle temperature ${T}_{D}$ in two spin subbands with essentially different electron populations. Firstly, we found that the product ${m}^{*}{T}_{D}$ that determines the damping of quantum oscillations, to the first approximation, is the same in the majority and minority subbands even at a spin polarization degree as high as 66%. This result confirms the theoretical predictions that the interaction takes place at high energies $\ensuremath{\sim}{E}_{F}$ rather than within a narrow strip of energies ${E}_{F}\ifmmode\pm\else\textpm\fi{}{k}_{B}T$. Secondly, to the next approximation, we revealed a difference in the damping factor of the two spin subbands, which causes skewness of the oscillation line shape. In the absence of the in-plane magnetic field ${B}_{\ensuremath{\parallel}}$, the damping factor ${m}^{*}{T}_{D}$ is systematically smaller in the spin-majority subband. The difference, quantified with the skew factor $\ensuremath{\gamma}=({T}_{D\ensuremath{\downarrow}}\ensuremath{-}{T}_{D\ensuremath{\uparrow}})/2{T}_{D0}$ can be as large as 20%. The skew factor tends to decrease as ${B}_{\ensuremath{\parallel}}$ or temperature grow, or ${B}_{\ensuremath{\perp}}$ decreases; for low electron densities and high in-plane fields, the skew factor even changes sign. Finally, we compared the temperature and magnetic field dependencies of the magneto-oscillation amplitude with predictions of the interaction correction theory, and found, besides some qualitative similarities, several quantitative and qualitative differences. To explain qualitatively our results, we suggested an empirical model that assumes the existence of easily magnetized triplet scatterers on the Si/${\mathrm{SiO}}_{2}$ interface.

Dynamics of Condon domain walls

A new nonlinear partial differential equation is used for description of the dynamics of domain walls of magnetic domains of the non-spin type (Condon domains). This equation is derived on the basis of the exact expression for the thermodynamic potential density enabling to take into account the oscillating behavior of the magnetization. The inhomogeneity is included in the generalized equation of state. The derived equation is solved analytically. A new shape of the moving domain wall is presented by the new kink solution of the obtained equation. It is shown that the moving domain wall preserves its profile in the wide range of magnetic fields and temperatures far from the diamagnetic phase transition. This shape coincides with the profile of the static domain wall found in our previous article, which was derived based on a new exact equation of state taking into account the oscillating behavior of the magnetization without expansion of the thermodynamic potential density into a power series. The dependence of the domain wall velocity and thickness on the magnetic field strength, temperature, and Dingle temperature is calculated.

Probing the surface states in Bi2Se3using the Shubnikov–de Haas effect

Shubnikov--de Haas oscillations are observed in Bi${}_{2}$Se${}_{3}$ flakes with high carrier concentration and low bulk mobility. These oscillations probe the protected surface states and enable us to extract their carrier concentration, effective mass, and Dingle temperature. The Fermi momentum obtained is in agreement with angle-resolved photoemission spectroscopy measurements performed on crystals from the same batch. We study the behavior of the Berry phase as a function of magnetic fields. The standard theoretical considerations fail to explain the observed behavior.

Static properties of Condon domains

A new nonlinear differential equation is used for description of the static properties of domain walls of magnetic domains of the non-spin type (Condon domains). This equation is derived on the basis of the exact expression for the thermodynamic potential density, enabling taking into account the oscillating behavior of the magnetization. Inhomogeneity is included in the generalized equation of state. The derived equation is solved analytically. A new shape of the domain wall is presented by the new kink solution of the obtained equation. The width and surface tension of the domain wall is presented as a function of the magnetic field strength, temperature, and Dingle temperature. They exhibit the critical behavior typical of the mean-field theory of second-order phase transitions. The calculated critical exponents are in agreement with nuclear magnetic resonance, muon spin-rotation spectroscopy and Hall probes measurements.

New features of magnetoresistance in highly anisotropic layered metals

The angular and magnetic-field variations of the interlayer magnetoresistance calculated in the limits of high magnetic field and very high anisotropy manifest several unusual properties. The monotonic part of the interlayer magnetoresistance increases with rising magnetic field along the current, which contradicts the standard theory and changes the angular dependence of the magnetoresistance. The Dingle temperature increases with magnetic field, dampens the magnetic quantum oscillations, and changes the field dependence of their amplitudes.

Weakly incoherent regime of interlayer conductivity in a magnetic field

We investigate the conductivity in layered metals in magnetic field in the weakly incoherent limit, when the interlayer transfer integral is smaller than the Landau level broadening due to the impurity potential, but the interlayer electron tunnelling conserves the intralayer momentum. It is shown that the impurity potential has much stronger effect in this regime, than in the quasi-2D metals in the coherent limit. The weakly incoherent regime has several new qualitative features, not found in the previous theoretical approaches. The background interlayer magnetoresistance in this regime monotonically grows with increasing of magnetic field perpendicular to the conducting layers. The effective electron mean free time is considerably shorter than in the coherent regime and decreases with magnetic field. This enhances the role of higher harmonics in the angular magnetoresistance oscillations and increases the Dingle temperature, which damps the magnetic quantum oscillations.

Metal–insulator transition in Si/SiGe heterostructures: mobility, spin polarization and Dingle temperature

For zero temperature we calculate the mobility of the two-dimensional electron gas in Si/SiGe heterostructures for charged-impurity scattering and interface-roughness scattering. Multiple-scattering effects lead to a metal–insulator transition (MIT) at low electron density, in agreement with experiment. Comparing the electron density dependence of the calculated mobility with experimental data of a recently developed insulator-gate field-effect transistor we conclude that (i) many remote charged impurities are present at the SiGe/Al2O3 interface (zi = 490 Å) and (ii) interface-roughness scattering (Λ ≈ 100 Å) is important at higher electron density or (iii) few nearby charged impurities are present at the Si/SiGe interface (zi = 0 Å). We calculate the mobility of the fully spin-polarized electron gas and compare the critical densities of the MIT of the non-polarized and the fully spin-polarized electron gas. The Dingle temperature (single-particle scattering time) is discussed. The temperature dependence of the mobility is also considered.

Fermi surface of the electron-doped cuprate superconductor Nd2−xCexCuO4 probed by high-field magnetotransport

We report on the study of the Fermi surface of the electron-doped cuprate superconductor Nd2−xCexCuO4 by measuring the interlayer magnetoresistance as a function of the strength and orientation of the applied magnetic field. We performed experiments in both steady and pulsed magnetic fields on high-quality single crystals with Ce concentrations of x=0.13–0.17. In the overdoped regime of x>0.15, we found both semiclassical angle-dependent magnetoresistance oscillations (AMROs) and Shubnikov–de Haas (SdH) oscillations. The combined AMROs and SdH data clearly show that the appearance of fast SdH oscillations in strongly overdoped samples is caused by magnetic breakdown. This observation provides clear evidence for a reconstructed multiply connected Fermi surface up to the very end of the overdoped regime at x≃0.17. The strength of the superlattice potential responsible for the reconstructed Fermi surface is found to decrease with increasing doping level and likely vanishes at the same carrier concentration as superconductivity, suggesting a close relation between translational symmetry breaking and superconducting pairing. A detailed analysis of the high-resolution SdH data allowed us to determine the effective cyclotron mass and Dingle temperature, as well as to estimate the magnetic breakdown field in the overdoped regime.

Effect of Disorder on Fermi Surface in Heavy Electron Systems

The Kondo lattice model with substitutional disorder is studied with attention to the size of the Fermi surface and the associated Dingle temperature. The model serves for understanding heavy-fermion Ce compounds alloyed with La according to substitution Ce{x}La{1-x}. The Fermi surface is identified from the steepest change of the momentum distribution of conduction electrons, and is derived at low enough temperature by the dynamical mean-field theory (DMFT) combined with the coherent potential approximation (CPA). The Fermi surface without magnetic field increases in size with decreasing x from x=1 (Ce end), and disappears at such x that gives the same number of localized spins as that of conduction electrons. From the opposite limit of x=0 (La end), the Fermi surface broadens quickly as x increases, but stays at the same position as that of the La end. With increasing magnetic field, a metamagnetic transition occurs, and the Fermi surface above the critical field changes continuously across the whole range of x. The Dingle temperature takes a maximum around x=0.5. Implication of the results to experimental observation is discussed.

Acoustoelectric effects in very high-mobility p-SiGe/Ge/SiGe heterostructure

Measurement results of the acoustoelectric effects [surface acoustic waves (SAW) attenuation and velocity] in a high-mobility p-SiGe/Ge/SiGe structure are presented. The structure was low-energy plasma-enhanced chemical vapor deposition grown with a two-dimensional (2D) channel buried in the strained Ge layer. The measurements were performed as a function of temperature (1.5–4.2 K) and magnetic field (up to 8.4 T) at different SAW intensities at frequencies 28 and 87 MHz. Shubnikov–de Haas-like oscillations of both SAW attenuation and the velocity change have been observed. Hole density and mobility, effective mass, quantum and transport relaxation times, as well as the Dingle temperature were measured with a method free of electric contacts. The effect of heating of the 2D hole gas by the electric field of the SAW was investigated. Energy relaxation time τε and the deformation potential constant determined.

Scattering of electrons in graphene by clusters of impurities

It is shown that formation of clusters of charged impurities on graphene can suppress their contribution to the resistivity by a factor of the order of the number of impurities per cluster. The dependence of conductivity on carrier concentration remains linear. In the regime where the cluster size is large in comparison to the Fermi wavelength, the scattering cross section shows sharp resonances as a function of incident angle and electron wave vector. In this regime, due to the dominant contribution of scattering by small angles, the transport cross section can be much smaller than the total one, which may be checked experimentally by comparison of the Dingle temperature to the electron mean-free path.

Magnetic oscillations amplitude of a dirty quasi two-dimensional organic metal

Magnetoresistance of dirty crystals of the organic metal (BEDO) 5Ni(CN) 4·3C 2H 4(OH) 2 (where BEDO stands for the bis(ethylenedioxy)tetrathiafulvalene molecule) has been measured up to 54 T at liquid helium temperatures. Quantum oscillations are clearly observed in a large field range even though a Dingle temperature as high as about 13 K is deduced from the field dependence of the oscillations amplitude. This value corresponds to scattering time as low as τ D ∼ 0.1 ps, leading to ω c τ D values (where ω c is the cyclotron pulsation) smaller than 1. Possible origins of the observed low scattering time value are discussed.

Influence of the hybridization of impurity electron states on the quantum magneto-oscillation phenomena in mercury selenide with iron impurities

Experimental study of the concentration dependence of the parameters of the Shubnikov–de Haas and de Haas–van Alphen oscillations in mercury selenide crystals containing iron impurities under conditions where the donor resonance energy level of the impurities falls into the conduction band and hybridization of the electronic states occurs. The observed concentration dependence of the Dingle temperature and g factor of the electrons exhibit minima correlated in position with the maximum of the electronic mobility. It is shown that the observed anomalies can be explained on the basis of a previously developed theory of hybridization effects.

Interface-roughness parameters in InAs quantum wells determined from mobility

For zero temperature we present theoretical results for the transport properties of the electron gas in InAs quantum wells in the presence of interface-roughness scattering. We show how to analyze experimental data in connection with interface-roughness scattering. By comparison with recent experimental results obtained for the mobility of InAs quantum wells, we determine the interface roughness parameters as Δ=3.2Å and Λ=14Å. We predict the single-particle relaxation time (Dingle temperature) and a possible metal-insulator transition in these InAs quantum well structures.

AlAs quantum wells: Transport properties of the two-dimensional electron gas

We present a theory of the transport properties at zero temperature of the electron gas in AlAs. The two-dimensional electron gas in AlAs has a valley degeneracy gv=1 for a quantum well width L<Lc=55Å and a valley degeneracy of gv=2 for L>Lc. We calculate the mobility for interface-roughness scattering and for impurity scattering. In addition we discuss the single-particle relaxation time (Dingle temperature) and the magnetoresistance in a parallel magnetic field. We discuss how transport measurements can be used to get information about microscopic parameters of disorder and many-body effects. Experimental results obtained for the mobility, the magnetoresistance, and the metal-insulator transition are discussed and compared with our theory.

Subband mobilities and dingle temperatures within a two-subband model in the presence of localized states

The transport time and the single-particle relaxation times in a two subband system of a two-dimensional electron gas have been calculated. Screening and density of states effects have been taken into account under the assumption that disorder leads to localized states in both subbands. It has been found that the single-particle relaxation time of the second subband is always larger than that for the first subband. The transport time of the second subband can be smaller or larger than the transport time of the first subband.

Two-band model for transport properties of silicon (1 1 1) MOSFET structures with high mobility

For zero temperature we present theoretical results for the mobility of a two-dimensional electron gas on the surface of silicon (1 1 1) in the case of impurity scattering and compare with experiments. We use a two-band model (7K-model) for valley degeneracy g v=2 and 4, which was proposed recently in the literature. A comparison between theory and recent experimental results shows reasonable agreement. Within the two-band model we predict the magnetoresistance in a parallel magnetic field and the Dingle temperatures of the two bands as function of the carrier density.

Dingle temperatures for a two-band model: Application to the two-dimensional electron gas on silicon (111)

For zero temperature, we present theoretical results for the Dingle temperatures of a two-dimensional electron gas with two occupied bands. For impurity scattering, we apply their calculation to a two-band model for valley degeneracy gv=2 and gv=4 proposed recently for silicon (111). Taking into account the density of states and screening effects of the two electron gases, we predict huge differences for the Dingle temperature of the two bands and a strong density dependence for the Dingle temperature of the first band due to screening by the second band. The mobility of the two-band model shows a strong density dependence.

Resonance modulation of the intersubband electron-electron interaction in an AlSb(δ-Te)/InAs/AsSb(δ-Te) quantum well by magnetic field

The amplitude-frequency modulation of oscillations of the magnetoresistance of 2D electrons in an AlSb(δ-Te)/InAs/AsSb(δ-Te) quantum well is studied. In the dependence of the amplitude of the oscillations δ(1/B) T = const, regions of negative Dingle temperature are observed. The anomalies in the dependence δ(1/B) T = const are attributed to the fact that the quantizing magnetic field resonantly induces intersubband electron-electron interaction between the 2D electrons of the ground size-quantization subband and excited subband. The resonance fields B and the times corresponding to the collision-related broadening of the Landau levels are estimated. The concentration threshold of filling of the excited size-quantization subband is established at a level of n s ≈ 8 × 1011 cm−2.