De Haas-van Alphen Oscillations Research Articles

Smell Sensors are Useful for Detecting de Haas–van Alphen Oscillations

Some kind of nanomechanical membrane-type surface stress sensors can be used for torque magnetometry of sub-millimeter-sized samples. Such sensors are sensitive enough to detect quantum oscillations.

Quantum oscillations without magnetic field

When magnetic field $B$ is applied to a metal, nearly all observable quantities exhibit oscillations periodic in $1/B$. Such quantum oscillations reflect the fundamental reorganization of electron states into Landau levels as a canonical response of the metal to the applied magnetic field. We predict here that, remarkably, in the recently discovered Dirac and Weyl semimetals quantum oscillations can occur in the complete absence of magnetic field. These zero-field quantum oscillations are driven by elastic strain which, in the space of the low-energy Dirac fermions, acts as a chiral gauge potential. We propose an experimental setup in which the strain in a thin film (or nanowire) can generate pseudomagnetic field $b$ as large as 15T and demonstrate the resulting de Haas-van Alphen and Shubnikov-de Haas oscillations periodic in $1/b$.

Fermi-surface topologies and low-temperature phases of the filled skutterudite compoundsCeOs4Sb12andNdOs4Sb12

MHz conductivity, torque magnetometer and magnetization measurements are reported on single crystals of CeOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ using temperatures down to 0.5~K and magnetic fields of up to 60~tesla. The field-orientation dependence of the de Haas-van Alphen and Shubnikov-de Haas oscillations is deduced by rotating the samples about the $[010]$ and $[0\bar{1}1]$ directions. The results indicate that NdOs$_4$Sb$_{12}$ has a similar Fermi surface topology to that of the unusual superconductor PrOs$_4$Sb$_{12}$, but with significantly smaller effective masses, supporting the importance of local phonon modes in contributing to the low-temperature heat capacity of NdOs$_4$Sb$_{12}$. By contrast, CeOs$_4$Sb$_{12}$ undergoes a field-induced transition from an unusual semimetal into a high-field, high-temperature state characterized by a single, almost spherical Fermi-surface section. The behavior of the phase boundary and comparisons with models of the bandstructure lead us to propose that the field-induced phase transition in CeOs$_4$Sb$_{12}$ is similar in origin to the well-known $\alpha-\gamma$ transition in Ce and its alloys.

Magnetic phase diagram of underdoped YBa2Cu3Oy inferred from torque magnetization and thermal conductivity

Strong evidence for charge-density correlation in the underdoped phase of the cuprate YBa2Cu3O y was obtained by NMR and resonant X-ray scattering. The fluctuations were found to be enhanced in strong magnetic fields. Recently, 3D charge-density-wave (CDW) formation with long-range order (LRO) was observed by X-ray diffraction in [Formula: see text] 15 T. To elucidate how the CDW transition impacts the pair condensate, we have used torque magnetization to 45 T and thermal conductivity [Formula: see text] to construct the magnetic phase diagram in untwinned crystals with hole density p = 0.11. We show that the 3D CDW transitions appear as sharp features in the susceptibility and [Formula: see text] at the fields [Formula: see text] and [Formula: see text], which define phase boundaries in agreement with spectroscopic techniques. From measurements of the melting field [Formula: see text] of the vortex solid, we obtain evidence for two vortex solid states below 8 K. At 0.5 K, the pair condensate appears to adjust to the 3D CDW by a sharp transition at 24 T between two vortex solids with very different shear moduli. At even higher H (41 T), the second vortex solid melts to a vortex liquid which survives to fields well above 41 T. de Haas-van Alphen oscillations appear at fields 24-28 T, below the lower bound for the upper critical field [Formula: see text].

Berry phase and band structure analysis of the Weyl semimetal NbP.

Weyl semimetals are often considered the 3D-analogon of graphene or topological insulators. The evaluation of quantum oscillations in these systems remains challenging because there are often multiple conduction bands. We observe de Haas-van Alphen oscillations with several frequencies in a single crystal of the Weyl semimetal niobium phosphide. For each fundamental crystal axis, we can fit the raw data to a superposition of sinusoidal functions, which enables us to calculate the characteristic parameters of all individual bulk conduction bands using Fourier transform with an analysis of the temperature and magnetic field-dependent oscillation amplitude decay. Our experimental results indicate that the band structure consists of Dirac bands with low cyclotron mass, a non-trivial Berry phase and parabolic bands with a higher effective mass and trivial Berry phase.

Quantum Hall conductance and de Haas–van Alphen oscillation in a tight-binding model with electron and hole pockets for(TMTSF)2NO3

Quantized Hall conductance and de Haas van Alphen (dHvA) oscillation are studied theoretically in the tight-binding model for (TMTSF)$_2$NO$_3$, in which there are small pockets of electron and hole due to the periodic potentials of anion ordering in the $a$-direction. The magnetic field is treated by hoppings as complex numbers due to the phase caused by the vector potential, i.e. Peierls substitution. In realistic values of parameters and the magnetic field, the energy as a function of a magnetic field (Hofstadter butterfly diagram) is obtained. It is shown that energy levels are broadened and the gaps are closed or almost closed periodically as a function of the inverse magnetic field, which are not seen in a semi-classical theory of the magnetic breakdown. Hall conductance is quantized with an integer obtained by Diophantine equation when the chemical potential lies in an energy gap. When electrons or holes are doped in this system, Hall conductance is quantized in some regions of a magnetic field but it is not quantized in other regions of a magnetic field due to the broadening of the Landau levels. The amplitude of the dHvA oscillation at zero temperature decreases as the magnetic field increases, while it is constant in the semi-classical Lifshitz Kosevich formula.

Specific features of quantum oscillations of magnetization in quasi-two-dimensional antiferromagnetic semimetals

The specific features of quantum oscillations of the magnetization in quasi-two-dimensional wide-band-gap antiferromagnetic semimetals with a low concentration of charge carriers have been considered theoretically. It has been shown that, in these systems, the Fermi energy determined from the analysis of the frequency of the de Haas–van Alphen oscillations according to the standard procedure can differ significantly from the true value. For the correct determination of the Fermi energy in the canted phase, it has been proposed to analyze quantum oscillations of the magnetization M not as a function of the inverse magnetic field 1/H, but as a function of 1/cosγ, where the angle γ characterizes the inclination angle of the magnetic field with respect to the plane of the quasi-two-dimensional semimetal.

New insights on frequency combinations and ‘forbidden frequencies’ in the de Haas–van Alphen spectrum of κ-(ET)2Cu(SCN)2

de Haas–van Alphen oscillations of the organic metal κ-(ET)2Cu(SCN)2 have been measured up to 55 T at liquid helium temperatures. The Fermi surface of this charge transfer salt is a textbook example of a linear chain of orbits coupled by magnetic breakdown. Accordingly, the oscillation spectrum is composed of linear combinations of the frequencies linked to the α and magnetic breakdown-induced β orbits. The field and temperature dependence of all the observed Fourier components, in particular the ‘forbidden frequency’ which cannot correspond to a classical orbit, are quantitatively accounted for by analytical calculations based on a second order development of the free energy, i.e. beyond the first order Lifshitz–Kosevich formula.

Quantum oscillations in the surface states of topological Kondo insulators

SmB has been predicted to be a strong topological Kondo insulator and experimentally it has been confirmed that at low temperatures the electrical conductivity only takes place at the surfaces of the crystal. Quantum oscillations and ARPES measurements revealed several Dirac cones on the (0 0 1) and (1 0 1) surfaces of the crystal. We considered four models for surface Dirac cones with an additional parabolic dispersion and studied their Landau quantization and the expectation value of the spin of the electrons. The Landau quantization is quite similar in all four cases and would give rise to similar de Haas-van Alphen oscillations. The spin-momentum locking, on the other hand, differs dramatically. Without the additional parabolic dispersion the spins are locked in the plane of the surface. The parabolic dispersion, however, produces a gradual canting of the spins out of the surface plane. The NMR Korringa relaxation and Knight shift of B nuclei in the topological Kondo insulator SmB are discussed and we explore the possibility of microwave transitions among the surface states.

Effect of structural disorder on quantum oscillations in graphite

We have studied the effect of structural disorder on the de Haas van Alphen and Shubnikov de Haas quantum oscillations measured in natural, Kish, and highly oriented pyrolytic graphite samples at temperatures down to 30 mK and at magnetic fields up to 14 T. The measurements were performed on different samples characterized by means of x-ray diffractometry, transmission electron microscopy, and atomic-force microscopy techniques. Our results reveal a correlation between the amplitude of quantum oscillations and the sample surface roughness.

Rotating ideal Fermi gases under a harmonic potential

We present a numerical analysis on thermodynamics of a harmonically trapped ideal Fermi gases subjected to either rotating frame or synthetic magnetic field. We discuss the rotation frequency dependency of chemical potential, specific heat, magnetization, particle flow and density profile. Our results demonstrate that the magnetization displays three characteristic regions: mesoscopic fluctuation, de Haas–van Alphen oscillation and Landau diamagnetism. The center and amplitude of oscillation peaks in particle flow in rotating frame exhibit much stronger dependence on rotation frequency than those in synthetic magnetic field.

Effect of electronic band dispersion curvature on de Haas-van Alphen oscillations

The effect of electronic band curvature, i.e. the deviation from parabolicity of electronic dispersion, on de Haas-van Alphen oscillations spectra is studied. Although the oscillations amplitude remain unaffected, it is demonstrated that non-quadratic terms of the Landau bands dispersion, which is particularly relevant in the case of Dirac fermions, induces a field- and temperature-dependent Onsager phase. As a result, a temperature-dependent shift of the de Haas-van Alphen oscillations frequency is predicted.

Non-Lifshitz–Kosevich field- and temperature-dependent amplitude of quantum oscillations in the quasi-two dimensional metal θ-(ET)4ZnBr4(C6H4Cl2)

According to band structure calculations, the Fermi surface of the quasi-two dimensional metal -(ET)4ZnBr4(C6H4Cl2) illustrates the linear chain of coupled orbits model. Accordingly, de Haas–van Alphen oscillations spectra recorded in pulsed magnetic field of up to 55 T evidence many Fourier components, the frequency of which are linear combinations of the frequencies relevant to the closed and the magnetic breakdown orbits. The field and temperature dependence of their amplitude are quantitatively accounted for by analytic calculations including, beyond the Lifshitz–Kosevich formula, second-order terms in damping factors due to the oscillation of the chemical potential as the magnetic field varies. Whereas these second-order terms are negligible for the orbits , and , they are solely responsible for the ‘forbidden orbit’ and its harmonic and have a significant influence on Fourier components such as and , yielding strongly non-Lifshitz–Kosevich behaviour in the latter case.

Magnetic properties of Dirac fermions in a buckled honeycomb lattice

We calculate the magnetic response of a buckled honeycomb lattice with intrinsic spin-orbit coupling (such as silicene) which supports valley-spin polarized energy bands when subjected to a perpendicular electric field $E_z$. By changing the magnitude of the external electric field, the size of the two band gaps involved can be tuned, and a transition from a topological insulator (TI) to a trivial band insulator (BI) is induced as one of the gaps becomes zero, and the system enters a valley-spin polarized metallic state (VSPM). In an external magnetic field ($B$), a distinct signature of the transition is seen in the derivative of the magnetization with respect to chemical potential ($\mu$) which gives the quantization of the Hall plateaus through the Streda relation. When plotted as a function of the external electric field, the magnetization has an abrupt change in slope at its minimum which signals the VSPM state. The magnetic susceptibility ($\chi$) shows jumps as a function of $\mu$ when a band gap is crossed which provides a measure of the gaps' variation as a function of external electric field. Alternatively, at fixed $\mu$, the susceptibility displays an increasingly large diamagnetic response as the electric field approaches the critical value of the VSPM phase. In the VSPM state, magnetic oscillations exist for any value of chemical potential while for the TI, and BI state, $\mu$ must be larger than the minimum gap in the system. When $\mu$ is larger than both gaps, there are two fundamental cyclotron frequencies (which can also be tuned by $E_z$) involved in the de-Haas van-Alphen oscillations which are close in magnitude. This causes a prominent beating pattern to emerge.

Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5

Conventional, thermally driven continuous phase transitions are described by universal critical behavior that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behavior remain open issues. Here we report measurements of heat capacity and de Haas-van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B0* ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn5 suggest that the Fermi-surface change at B0* is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn5, a significant step toward the derivation of a universal phase diagram for QCPs.

Orbital magnetism of graphene nanostructures: Bulk and confinement effects

We consider the orbital magnetic properties of non-interacting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both, frombulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility $\chi$ of bulk graphene in a magnetic field for the different regimes arising from the relative magnitudes of the energy scales involved, i.e. temperature, Landau level spacing and chemical potential. We show that for finite temperature or chemical potential, $\chi$ is not divergent although the diamagnetic contribution $\chi_{0}$ from the filled valance band exhibits the well-known $-B^{-1/2}$ dependence. We further derive oscillatory modulations of $\chi$, corresponding to de Haas-van Alphen oscillations of conventional two-dimensional electron gases. These oscillations can be large in graphene, thereby compensating the diamagnetic contribution $\chi_{0}$ and yielding a net paramagnetic susceptibility for certain energy and magnetic field regimes. Second, we predict and analyze corresponding strong, confinement-induced susceptibility oscillations in graphene-based quantum dots with amplitudes distincly exceeding the corresponding bulk susceptibility. Within a semiclassical approach we derive generic expressions for orbital magnetism of graphene quantum dots with regular classical dynamics. Graphene-specific features can be traced back to pseudospin interference along the underlying periodic orbits. We demonstrate the quality of the semiclassical approximation by comparison with quantum mechanical results for two exemplary mesoscopic systems, a graphene disk with infinite mass-type edges and a rectangular graphene structure with armchair and zigzag edges, using numerical tight-binding calculations in the latter case.

De Haas-van Alphen oscillations in the compensated organic metal α-‵pseudo-κ′-(ET)4H3O[Fe(C2O4)3]·(C6H4Br2)

Field-, temperature- and angle-dependent Fourier amplitude of de Haas-van Alphen (dHvA) oscillations are calculated for compensated two-dimensional (2D) metals with textbook Fermi surface (FS) composed of one hole and two electron orbits connected by magnetic breakdown. It is demonstrated that, taking into account the opposite sign of electron and hole orbits, a given Fourier component involves combination of several orbits, the contribution of which must be included in the calculations. Such FS is observed in the strongly 2D organic metal alpha-'pseudo-kappa'-(ET)4H3O[Fe(C2O4)3].(C6H4Br2), dHvA oscillations of which have been studied up to 55 T for various directions of the magnetic field with respect to the conducting plane. Calculations are in good quantitative agreement with the data.

Quantum oscillations of magnetization in tight-binding electrons on a honeycomb lattice

We show that the new quantum oscillations of the magnetization can occur when the Fermi surface consists of points (massless Dirac points) or even when the chemical potential is in a energy gap by studying the tight-binding electrons on a honeycomb lattice in a uniform magnetic field. The quantum oscillations of the magnetization as a function of the inverse magnetic field are known as the de Haas-van Alphen (dHvA) oscillations and the frequency is proportional to the area of the Fermi surface. The dominant period of the new oscillations corresponds to the area of the first Brillouin zone and its phase is zero. The origin of the new quantum oscillations is the characteristic magnetic field dependence of the energy known as the Hofstadter butterfly and the Harper broadening of Landau levels. The new oscillations are not caused by the crossing of the chemical potential and Landau levels, which is the case in the dHvA oscillations. The new oscillations can be observed experimentally in systems with large supercell such as graphene antidot lattice or ultra cold atoms in optical lattice at an external magnetic field of a few Tesla when the area of the supercell is ten thousand times larger than that of graphene.

Effects of AMM on the EoS of magnetized dense systems

AbstractWe investigate the effects of the anomalous magnetic moment (AMM) in the EoS of a fermion system in the presence of a magnetic field. In the region of strong magnetic fields (B > m2) the AMM is found from the one‐loop fermion selfenergy. In contrast to the weak‐field AMM found by Schwinger, in the strong magnetic field case, the AMM depends on the Landau level (LL) and decreases with it. The effects of the AMM in the EoS at intermediate‐to‐large fields can be found introducing the one‐loop, LL‐dependent AMM in the effective Lagrangian that is then used to find the thermodynamical potential of the system. We compare the plots of the parallel and perpendicular pressures versus the magnetic field in the strong field region considering the LL‐dependent AMM, the Schwinger AMM, and no AMM at all. The results clearly show a separation between the physical magnitudes found using the Schwinger AMM and the LL‐dependent AMM. This is an indication of the inconsistency of considering the Schwinger AMM beyond the weak field region B < m2 where it was originally found. The curves for the EoS, pressures and magnetization at different fields give rise to the well‐known de Haas van Alphen oscillations, associated to the change in the number of LL contributing at different fields. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermodynamics of electrons in the graphene bilayer

Some problems of the thermodynamics of electrons in a doped graphene bilayer are considered. Analytical expressions are derived for chemical potential and specific heat in the limiting cases of low and high temperatures. The Seebeck and Thomson coefficients are estimated. Landau levels are studied using a semi-classical approach. An expression for thermodynamic potential is obtained and the de Haas-van Alphen oscillations are studied. The oscillations of magnetic entropy and electron temperature in a magnetic field, i.e., the oscillating magnetocaloric effect, are investigated. For all parameters, the cases of graphene bilayer and monolayer are compared.