Quantizing Magnetic Field Research Articles

Influence of a Quantum Magnetic Field on the Heating of Charge Carriers in Pure Germanium

The results of an experimental study of charge-carrier heating by an electric field E in pure n- and p-type germanium samples in a quantizing magnetic field H, at E ⊥ H and under carrier photoexcitation conditions, are considered in detail. The results obtained are in qualitative agreement with the predictions of the theory of charge-carrier capture in crossed electric and magnetic fields.

Влияние квантового магнитного поля на разогрев носителей заряда в чистом Ge

AbstractThe results of an experimental study of charge-carrier heating by an electric field E in pure n - and p -type germanium samples in a quantizing magnetic field H , at E ⊥ H and under carrier photoexcitation conditions, are considered in detail. The results obtained are in qualitative agreement with the predictions of the theory of charge-carrier capture in crossed electric and magnetic fields.

Spin-orbit coupling effects in the quantum Hall regime probed by electron spin resonance

The spin resonance of two-dimensional (2D) electrons confined in a high-quality 4.5-nm AlAs quantum well was studied in the regime of the integer quantum Hall effect. The electron $g$-factor extracted from the magnetic field position of the spin resonance at a fixed microwave frequency demonstrated a strong nonlinear dependence on the magnetic field with discontinuities around even filling factors. The value of the $g$-factor tended to increase with a decrease of the magnetic field around each odd filling. Furthermore, the $g$-factor at the exactly odd filling factor $\ensuremath{\nu}$ turned out to be dependent on $\ensuremath{\nu}$, suggesting the entanglement between the spin degree of freedom and the orbital motion of the electrons in the regime of the integer quantum Hall effect. This suggestion is further supported, as all the experimental data are well described, when a Dresselhaus-type spin-orbit interaction is introduced into the Hamiltonian of a single electron in the quantizing magnetic field. Surprisingly, such excellent agreement was observed even in the case of tilted magnetic fields. The fitting procedure allowed us to determine the strength of the Dresselhaus spin-orbit term in a 2D electron system and to extract the fundamentally important Dresselhaus constant for bulk AlAs. Unexpectedly, not only was single spin resonance observed around even fillings, it tended to split into two well-resolved lines. Yet this finding remains a mystery and highlights the need for further experimental and theoretical efforts.

Phase transitions induced by a lateral superlattice potential in a two-dimensional electron gas

We study the phase transitions induced by a lateral superlattice potential (a metallic grid) placed on top of a two-dimensional electron gas (2DEG)formed in a semiconductor quantum well. In a quantizing magnetic field and at filling factor $\nu =1,$ the ground state of the 2DEG depends on the strength $V_{g}$ of the superlattice potential as well as on the number of flux quanta piercing the unit cell of the external potential. It was recently shown[1] that in the case of a square lateral superlattice, the potential modulates both the electronic and spin density and in some range of $V_{g}$, the ground state is a two-sublattice spin meron crystal where adjacent merons have the global phase of their spin texture shifted by $\pi$, i.e. they are "antiferromagnetically" ordered. In this work, we evaluate the importance of Landau-level mixing on the phase diagram obtained previously for the square lattice [1] and derive the phase diagram of the 2DEG modulated by a triangular superlattice. When Landau level mixing is considered, we find in this case that, in some range of $V_{g},$ the ground state is a three-sublattice spin meron crystal where adjacent merons of the same vorticity have the global phase of their spin texture rotated by $120^{\circ }$ with respect to one another. This meron crystal is preceded in the phase diagram by another meron lattice phase with a very different spin texture that does not appear, at first glance, to resolve the spin frustration inherent to an antiferromagnetic ordering on a triangular lattice. [1] R. C\^ot\'e and Xavier Bazier-Matte, Phys. Rev. B 94, 205303 (2016).

Three-particle electron-hole complexes in two-dimensional electron systems

Three-particle complexes consisting of two holes in the completely filled zero electron Landau level and an excited electron in the unoccupied first Landau level are investigated in a quantum Hall insulator. The distinctive features of these three-particle complexes are an electron-hole mass symmetry and the small energy gap of the quantum Hall insulator itself. Theoretical calculations of the trion energy spectrum in a quantizing magnetic field predict that, besides the ground state, trions feature a hierarchy of excited bound states. In agreement with the theoretical simulations, we observe new photoluminescence lines related to the excited trion states. A relatively small energy gap allows the binding of three-particle complexes with magnetoplasma oscillations and formation of plasmarons. The plasmaron properties are investigated experimentally.

Influence of temperature on the oscillations of longitudinal magnetoresistance in semiconductors with a nonparabolic dispersion law

The density of energy states were obtained in a quantizing magnetic field at different temperature and for nonquadratic dispersion law. The dependence of the density of energy states on temperature in quantizing magnetic fields is studied with the nonquadratic dispersion law. The continuous spectrum of the energy density of states at low temperature is transformed into discrete Landau levels. The theory of the temperature dependence of the oscillation Shubnikov–de Haas in semiconductors with a nonparabolic dispersion law is constructed, taking into account the thermal broadening of the Landau levels. The cyclotron effective mass of the electrons is determined from the Shubnikov–de Haas data. The theoretical results are compared with experimental data in Bi1.99Tl0.01Se3.

Nonlinear ion acoustic waves in a relativistic degenerate plasma with Landau diamagnetism and electron trapping

We consider the effects of trapping in a relativistic degenerate plasma with quantizing magnetic field. The linear dispersion relation for such an ion acoustic wave is derived and the propagation characteristics of these waves are discussed. The Sagdeev potential for the formation of arbitrary amplitude solitary structures is obtained and it is seen that only compressive solitary structures are formed for the relativistic degenerate quantized magnetoplasma. The dependence of the linear and nonlinear propagation characteristics of ion acoustic waves on different plasma parameters is explored. A comparison is also made with the previous studies. The useful applications of the present investigation in dense astrophysical environments like white dwarf stars and neutron stars, in semiconductor physics, in high-energy density physics, in inertial confinement fusion and in next generation laser–plasma interaction experiments are pointed out.

Magnetooptics of HgTe/CdTe Quantum Wells with Giant Rashba Splitting in Magnetic Fields up to 34 T

The electron cyclotron resonance spectra in classical and quantizing magnetic fields in asymmetric heterostructures with HgCdTe/CdHgTe quantum wells with selective barrier doping are investigated. Self-consistent calculations of the energy spectra at B = 0 and Landau levels in the framework of the 8-band Kane model using the Hartree approximation are made. The strong (~10%) splitting of the cyclotron resonance line observed in weak fields is attributed to the Rashba effect in samples with inverted and normal band structures. The evolution of absorption lines upon a variation in the magnetic field is investigated up to 34 T, when the magnetic quantization already dominates over Rashba splitting.

Circular and magnetoinduced photocurrents in Weyl semimetals

We develop a theory of the direct interband and indirect intraband photogalvanic effects in Weyl semimetals belonging to the gyrotropic classes with improper symmetry operations. At zero magnetic field, an excitation of such a material with circularly polarized light leads to a photocurrent whose direction depends on the light helicity. We show that in the semimetals of the C$_{2v}$ symmetry, an allowance for the tilt term in the effective Hamiltonian is enough to prevent cancellation of the photocurrent contributions from the Weyl cones of opposite chiralities. In the case of the C$_{4v}$ symmetry, in addition to the tilt it is necessary to include terms of the second- or third-order in the electron quasi-momentum. For indirect intraband transitions, the helicity-dependent photocurrent generated within each Weyl node takes on a universal value determined by the fundamental constants, the light frequency and electric field. We have complementarily investigated the magneto-gyrotropic photogalvanic effect, i.e. an appearance of a photocurrent under unpolarized excitation in a magnetic field. In quantized magnetic fields, the photocurrent is caused by optical transitions between the one-dimensional magnetic subbands. A value of the photocurrent is particularly high if one of the photocarriers is excited to the chiral subband with the energy below the cyclotron energy.

Ion-acoustic Gardner solitons in multi-ion degenerate plasma with the effect of polarization and trapping in the presence of a quantizing magnetic field

A theoretical investigation is presented for ion-acoustic Gardner solitons (GSs) and double layers (DLs) in a multi-ion plasma system. The plasma consists of inertial positively and negatively charged ions and negatively charged immobile heavy ions and electrons which are in trapping distribution, all existing in a quantizing magnetic field. The reductive perturbation method is used to derive Korteweg-de Vries (KdV), modified KdV (mKdV), and Gardner equations. It is found that the KdV solitons and Gardner solitons (GSs) are either compressive or rarefactive depending on the plasma parameters, whereas only compressive solitons are obtained in the mKdV case, wherever Gardner positive DLs exist. These solitons are significantly modified due to the introduction of the trapping parameter and polarization coefficient. The presented results are considered to be beneficial in understanding the solitary structures in dense quantum plasmas such as those existing in white dwarfs.

‘Forbidden’ intersubband optical transitions in quantum well structures in a tilted magnetic field

In this paper, we report on the behavior of intersubband optical absorption and emission spectrum in quantum well structures with an asymmetrical potential profile in a quantizing magnetic field tilted with respect to the layers in the considered structure. The analysis of the effect of both the magnetic field value and orientation and potential profile of a quantum well structure on the intensity of the ‘forbidden’ ( ) intersubband optical transitions is presented. We also present the approximate analytical expression for the estimation of the contribution to the absorption/emission coefficient of intersubband transitions with different

Shubnikov–de Haas Oscillations in the Magnetoresistance of Layered Conductors in Proximity to the Topological Lifshitz Transition

The dependence of the resistance of a layered conductor with a quasi-two-dimensional charge carrier energy spectrum on the strength and orientation of a quantizing magnetic field is studied. The case of an organic conductor with a multisheet Fermi surface consisting of a weakly warped cylinder and two adjoining planar sheets is considered. By applying an external pressure to the conductor or doping it with impurity atoms, the gap between the cylinder and the planar sheets of the Fermi surface (FS) may be reduced so that electrons start wandering on the FS, tunneling between its different parts due to magnetic breakdown. If an electron can pass through all the different sheets of the FS several times during the mean free time, its motion in the plane orthogonal to the magnetic field becomes finite. This leads to Shubnikov–de Haas oscillations with a period determined by the area enclosed by the closed breakdown orbit of an electron in momentum space. However, even at a slight tilting of the field from the normal to the layers by an angle ϑ, the equidistance is broken and at certain angles ϑk the probability of the magnetic breakdown to one of the planar FS sheets may become so low that the electron cannot complete the magnetic-breakdown orbit and its motion over the other planar sheet and the cylindrical part of the FS becomes infinite. As a result, magnetic-breakdown quantum oscillations of magnetization and all kinetic properties vanish. This vanishing repeats periodically as a function of tan ϑ with changing the tilt angle. Possibilities for experimental observation and investigation of the influence of magnetic breakdown on quantum oscillation phenomena are discussed.

Kinetics of intrasubband electron energy relaxation in quantum wells in a quantizing magnetic field

Herein we report the intrasubband relaxation of electron energy in the Landau level system of quantum well as a function of magnetic field strength. The relative role of scattering processes contributing to relaxation kinetics, the electron-electron scattering which redistributes the electrons between Landau levels and the optical phonon emission by the electrons reaching the Landau levels lying near and above the optical phonon energy is revealed. It was shown the most important factor determining the kinetics of energy relaxation is the electron-electron scattering processes, delivering electrons to Landau levels close to optical phonon energy. The flux of these electrons depends on the number of the Landau levels lying below the energy of the optical phonon and increases substantially with a decrease in this number. On the contrary, the electron-phonon scattering rate dependence of the energy relaxation time was found to be much weaker.

Nonlocal superconducting correlations in graphene in the quantum Hall regime

We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-B\"{u}ttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance.

Large, nonsaturating thermopower in a quantizing magnetic field.

The thermoelectric effect is the generation of an electrical voltage from a temperature gradient in a solid material due to the diffusion of free charge carriers from hot to cold. Identifying materials with a large thermoelectric response is crucial for the development of novel electric generators and coolers. We theoretically consider the thermopower of Dirac/Weyl semimetals subjected to a quantizing magnetic field. We contrast their thermoelectric properties with those of traditional heavily doped semiconductors and show that, under a sufficiently large magnetic field, the thermopower of Dirac/Weyl semimetals grows linearly with the field without saturation and can reach extremely high values. Our results suggest an immediate pathway for achieving record-high thermopower and thermoelectric figure of merit, and they compare well with a recent experiment on Pb1-x Sn x Se.

Vacuum Bloch–Siegert shift in Landau polaritons with ultra-high cooperativity

A two-level system resonantly interacting with an a.c. magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrodinger’s equation for this seemingly simple system can be solved exactly only under the rotating-wave approximation, which neglects the counter-rotating field component. When the a.c. field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch–Siegert shift. Here, we report the vacuum Bloch–Siegert shift, which is induced by the ultra-strong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility two-dimensional electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum Bloch–Siegert shift up to 40 GHz. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field. The Bloch–Siegert shift—a strong-field phenomenon that implies a failure of the rotating-wave approximation—is observed in the polariton dispersion diagram of a two-dimensional electron gas system inside a high-Q terahertz photonic crystal cavity.

Large, nonsaturating thermopower of nodal semimetals in a quantizing magnetic field

Large, nonsaturating thermopower of nodal semimetals in a quantizing magnetic field

Ideal Quantum Wires in a Magnetic Field: Self-Organization Energy, Critical Sizes, and Controllable Conductivity

The concept of an ideal quantum wire as a one-dimensional heterostructure whose spectrum contains exactly one bound level of the transverse dimension-quantized motion is introduced. The admissible range of the radii of such a wire is calculated. It is shown that only the quantization of longitudinal levels of motion makes it possible to calculate the energy released (absorbed) upon the fusion of two wires of the same material. In the traditional approach of a continuous longitudinal spectrum, this effect cannot be determined in principle. The influence of a longitudinal magnetic field on the spectrum of ideal wires is considered. It is established that a quantizing magnetic field destroys the unique level with negative energy (relative to the bottom of the continuous spectrum of the environment) but creates a family of positive bound Landau levels. In this case, the density of states in the wire is completely determined by the magnetic field, which makes it possible to control its spectrum and conductivity.

Dynamics of Electronic States and Magnetoabsorption in 3D Topological Insulators in a Quantizing Magnetic Field

Quantum states have been calculated analytically; the dynamics of a wave packet in a magnetic field has been investigated, and the optical absorption coefficient has been calculated for surface states in 3D topological insulators of the Bi2Te3 family. We have detected a qualitative effect of the hexagonal warping of the spectrum on the structure of wavefunctions at the Landau levels, its manifestation in the features of the wave packet dynamics in a quantizing magnetic field, as well as in the frequency dependence of the optical absorption coefficient, in which new peaks that are absent in the isotropic model of the spectrum appear depending on the polarization of the incident wave. The effects considered here can be manifested in the optical and transport experiments with topological insulators, which makes it possible to determine the parameters of their band structure.

Statistical thermodynamics and magnetic moments of Landau quantized group VI dichalcogenides

This work is focused on the determination of the Helmholtz free energy and the magnetic moments of the ‘Dirac-like’ group VI dichalcogenides subject to Landau quantization. We employ a technique described by Wilson to relate the free energy to the Green’s function for the dichalcogenides in a high magnetic field, which was recently evaluated explicitly in terms of elementary functions. In the course of this analysis, the partition function is determined as a function of the magnetic field as well. The results exhibit the role of the quantizing magnetic field in the Helmholtz free energy at arbitrary temperature, and they are also employed to obtain the magnetic moments of the dichalcogenides. Explicit analytic formulas characteristic of de Haas–van Alphen oscillatory phenomenology are presented in the degenerate limit, and nondegenerate Landau quantization effects are also presented for the dichalcogenide magnetic moments.