The Landau band effects in the quantum magnetic oscillations and the deviations from the quasiclassical Lifshitz–Kosevich theory in quasi-two-dimensional conductors

The quantum magnetic oscillations (QMO) in the layered and quasi-two-dimensional (2D) conductors deviate from the quasiclassical Lifshitz–Kosevich (LK) theory developed for 3D conventional metals. We discuss deviations related to the broadening of the Landau levels into Landau bands by various mechanisms (layer-stacking, magnetic breakdown, incoherence, disorder, localization etc.). Each mechanism yields a specific factor modulating the QMO amplitudes depending on the density of states and electron velocities within the Landau bands. In contrast to the LK theory, these factors differ for the thermodynamic (de Haas–van Alphen (dHvA)) and kinetic (Shubnikov–de Haas (SdH)) oscillations. We calculated the magnetic breakdown damping factors for the SdH and dHvA oscillations in the 2D conductors and analyzed their difference as well as the analogy between the bandwidth and Weiss oscillations. In case of an isotropic 3D metals the kinetic factors become proportional to the thermodynamic ones as is assumed in the LK theory

Shubnikov—de Haas oscillations, peaks and different temperature regimes of the diagonal conductivity in the integer quantum Hall conductor

A theory for the Shubnikov—de Haas oscillations in the diagonal conductivity σxx of a 2D conductor is developed for the case when electron states within the broaden Landau levels are localized except the narrow stripe in the center. The standard Shubnikov—de Haas oscillations take place only in the low-field region which at higher magnetic fields crosses over into peaks. In the limit Ωτ >> 1 peaks in the σxx became sharp and between them σxx → 0 (Ω is the cyclotron frequency, τ is the electron scattering time). The conductivity peaks display different temperature behavior with the decrease of temperature, T: a thermal activation regime, σxx exp(-Δ/T), which holds at higher temperatures, crosses over into the variable-range-hopping regime at lower temperatures with σxx 1/T exp(-√(Т₀/Т) (the prefactor 1/T is absent in the conductance)

Incoherent interlayer electron hopping as a possible reason for enhanced magnetic quantum oscillations in the mixed state of a layered organic superconductor

We present a theory which is able to explain enhanced magnetic quantum-oscillation amplitudes in the superconducting state of a layered organic metal with incoherent electronic transport across the layers. The incoherence acts through the deformation of the layer-stacking factor which becomes complex and decreases the total scattering rate in the mixed state. This novel mechanism restores the coherence by establishing a long-range order across the layers and can compensate the usual decrease of the Dingle factor below the upper critical magnetic field caused by the intralayer scattering

Helicons and magnetoimpurity waves in layered conductors

It is shown that local electron states, caused by impurities in a layered conductor placed in an external magnetic field, give rise to resonant corrections Δσαβ(ω) to the high-frequency conductivity tensor Δσαβ(ω) of the layers. These corrections appear due to the resonant transitions of electrons between the Landau levels and the local states and change dramatically the spectrum of collective electromagnetic oscillations in the system because of the "branch crossing" nearby the frequency ω₀(ħω₀ is the local state energy). As a result, a new magnetoimpurity wave, ω₋k, appears in the spectrum in addition to the helicon mode,ω₊k, which is known to exist in a pure layered conductor in a perpendicular magnetic field (k is the wave vector along the magnetic field). In the long wavelength limit, kα<<1 the helicon-like mode w₊k has a gap of the order of w₀ , whereas the magnetoimpurity mode in this limit goes to zero w₋k~(kα)² (a is the distance between adjacent layers). The small damping of these modes due to the broadening of the Landau levels and the magnetoimpurity levels are also calculated

Magnetic Quantum Oscillations of the Longitudinal Conductivity σzz\sigma_{zz} in Quasi two-dimensional Metals

We derive an analytical expression for the longitudinal magnetoconductivity $\sigma_{zz}$ in layered conductors in presence of a quantizing magnetic field perpendicular to the layers and for short-range in-plane impurity scattering in frame of the quantum transport theory. Our derivation points out quite unusual temperature and magnetic field dependences for Shubnikov-de Haas oscillations in the two-dimensional limit, i.e. $\hbar \omega_{c} \gg 4 \pi t$, where $t$ is the interlayer hopping integral for electrons, and $\omega_{c}$ the cyclotron frequency. In particular, when $\hbar \omega_{c} \gg 4 \pi t$ and $\hbar \omega_{c} \geq 2 \pi \Gamma_{\mu}$ (here $\Gamma_{\mu}$ is the value of the imaginary part of the impurity self-energy at the chemical potential $\mu$), a pseudo-gap centered on integer values of $\mu/\hbar\omega_{c}$ appears in the zero-temperature magnetoconductivity function $\sigma_{zz}(\mu/\hbar\omega_{c})$. At low temperatures, this high-field regime is characterized by a thermally activated behavior of the conductivity minima (when chemical potential $\mu$ lies between Landau levels) in correspondence with the recent observation in the organic conductor $\beta''\text{-(BEDT-TTF)}_{2}\text{SF}_{5}\text{CH}_{2}\text{CF}_{2}\text{SO}_ {3}$.Comment: 16 pages, 4 figures, to be published in Phys. Rev.

A crossover in the temperature behavior of the perpendicular upper critical magnetic field of layered superconductors and thin films

A mechanism which relates the upturn of the perpendicular upper critical magnetic field H┴с₂ (T) in layered superconductors and thin films with the structural inhomogeneity in the bulk of the sample, provided that the local critical temperature Tc* inside the inhomogeneity is higher than in the rest of the sample (Tc) is proposed. Within the Ginzburg-Landau approach an equation whic h describes two types of experimentally observed nonlinearities in H┴с₂ (T) near Tc for ISN (insulator-superconductor-normal metal) and NSN layer configurations, is found. In the NSN case a crossover from the linear branch H┴с₂ (T) ⋉ (Tc-T), for fields H ≤ Hₘ, to the nonlinear branch with the upturn, if H > Hₘ, takes place. The crossover field Hₘ is inversely proportional to the local enhancement of the critical temperature (Tc*-Tc) and the distance R to the surface (the nearest surface, in case of a thin film). In the ISN case the upturn holds for H<Hₘ, whereas for higher fields H┴с₂ (T) crosses over to the linear branch. In the ISI case the H┴с₂ (T) is a linear function

Shubnikov-de Haas oscillations in layered conductors with stacking faults

The Shubnikov-de Haas (SdH) oscillations of the in-plane conductivity of layered 2D electron gas is calculated. It is shown that layer stacking faults, magnetoimpurity bound states, and electron scattering modulate the SdH oscillations via the specific factors which bear the structural information. At zero temperature the 2D SdH oscillations are strongly nonsinusoidal in shape and related by simple equation to the derivative of the de Haas-van Alphen magnetization oscillations with respect to the magnetic field

Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime

The Aharonov–Bohm (AB) oscillations of the free energy, critical temperature Tc, magnetization M, and magnetic susceptibility χ as functions of the magnetic flux Φ through the hollow in a stack of mesoscopic superconducting cylinders are studied both analytically and numerically. The shape of these oscillations at low temperature T and small level broadening ν is generally nonsinusoidal and has singularities that depend on the superconducting order parameter Δ and stacking sequence. The period of the oscillations is equal to the normal flux quantum Φ₀. The harmonic amplitudes of the AB oscillations decrease exponentially if the diameter 2R of the cylinders becomes greater than the coherence length. Further increase of R results in a complete suppression of the AB oscillations and the development of parabolic Little–Parks (LP) oscillations of Tc(Φ) with half the period, Φs=Φ₀/2. Therefore a crossover from the AB to LP oscillations takes place as the diameter 2R is increased. It is shown that the temperature behavior of the magnetic susceptibility below the superconducting transition is χ ∝ exp(−T/T*), where T*=ℏv₀/2π²R (v₀ is the Fermi velocity, and ℏ is Planck’s constant). Such dependence of χ(T) has been observed recently in Ag wires coated with thin Nb layers in a weak external field [R. Frassanito et al., Czech. J. Phys. 46, 2317 (1996)]

Surface electromagnetic modes in layered conductors in a magnetic field

A transfer-matrix approach is developed for studies of the collective electromagnetic modes in a semi-infinite layered conductor subjected to a quantizing external magnetic field perpendicular to the layers. The dispersion relations for the surface and bulk modes are derived. It is shown that the surface mode has a gap in the long-wavelength limit and exists only if the absolute value of the in-plane wave vector q exceeds the threshold value q*=−1/(a ln|Δ|). Depending on the sign of the parameter Δ=(ε−ε₀)/(ε₀+ε), the frequency of the surface mode ωs(q,Δ) goes either above (for Δ>0) or below (for Δ0 and Δ<0 (a is the interlayer separation; ε0 and ε stand for the dielectric constants of the media outside the sample and between the layers; q and k are the components of the wave vector in the plane and perpendicular to the layers, respectively)

Magnetic quantum oscillations of diagonal conductivity in a two-dimensional conductor with a weak square superlattice modulation under conditions of the integer quantum Hall effect

We report on analytical and numerical studies of the magnetic quantum oscillations of the diagonal conductivity σxx in a two-dimensional conductor with a weak square superlattice modulation under conditions of the integer quantum Hall (IQHE) effect. The quantum Hall effect in such a system differs from the conventional IQHE, in which the finite width of the Landau bands is due to disorder only. The superlattice modulation potential yields a fractal splitting of the Landau levels into Hofstadter minibands. For rational flux through a unit cell, the minibands have a finite width and intrinsic dispersion relations. We consider a regime, now accessible experimentally, in which disorder does not wash out the fractal internal gap structure of the Landau bands completely. We found the following distinctions from the conventional IQHE produced by the superlattice: (i) the peaks in diagonal conductivity are split due to the Hofstadter miniband structure of Landau bands; (ii) the number of split peaks in the bunch, their positions and heights depend irregularly on the magnetic field and the Fermi energy; (iii) the gaps between the split Landau bands (and related quantum Hall plateaus) become narrower with the superlattice modulation than without it