scholarly journals Landau levels, response functions and magnetic oscillations from a generalized Onsager relation

2018 ◽  
Vol 4 (5) ◽  
Author(s):  
Jean-Noël Fuchs ◽  
Frédéric Piéchon ◽  
Gilles Montambaux
Keyword(s):  
Magnetic Field ◽  
Phase Shift ◽  
Landau Levels ◽  
Field Energy ◽  
Magnetic Response ◽  
Zero Field ◽  
Response Functions ◽  
Field Phase ◽  
Onsager Relation ◽  
Magnetic Oscillations

A generalized semiclassical quantization condition for cyclotron orbits was recently proposed by Gao and Niu , that goes beyond the Onsager relation . In addition to the integrated density of states, it formally involves magnetic response functions of all orders in the magnetic field. In particular, up to second order, it requires the knowledge of the spontaneous magnetization and the magnetic susceptibility, as was early anticipated by Roth . We study three applications of this relation focusing on two-dimensional electrons. First, we obtain magnetic response functions from Landau levels. Second we obtain Landau levels from response functions. Third we study magnetic oscillations in metals and propose a proper way to analyze Landau plots (i.e. the oscillation index nn as a function of the inverse magnetic field 1/B1/B) in order to extract quantities such as a zero-field phase-shift. Whereas the frequency of 1/B1/B-oscillations depends on the zero-field energy spectrum, the zero-field phase-shift depends on the geometry of the cell-periodic Bloch states via two contributions: the Berry phase and the average orbital magnetic moment on the Fermi surface. We also quantify deviations from linearity in Landau plots (i.e. aperiodic magnetic oscillations), as recently measured in surface states of three-dimensional topological insulators and emphasized by Wright and McKenzie .

scholarly journals Zero-field magnetic response functions in Landau levels

2017 ◽  
Vol 114 (28) ◽  
pp. 7295-7300 ◽  
Author(s):  
Yang Gao ◽  
Qian Niu
Keyword(s):  
Landau Level ◽  
Berry Phase ◽  
Higher Order ◽  
Landau Levels ◽  
Magnetic Response ◽  
Zero Field ◽  
Response Functions ◽  
Zero Temperature ◽  
Quantization Rule ◽  
Higher Order Corrections

We present a fresh perspective on the Landau level quantization rule; that is, by successively including zero-field magnetic response functions at zero temperature, such as zero-field magnetization and susceptibility, the Onsager’s rule can be corrected order by order. Such a perspective is further reinterpreted as a quantization of the semiclassical electron density in solids. Our theory not only reproduces Onsager’s rule at zeroth order and the Berry phase and magnetic moment correction at first order but also explains the nature of higher-order corrections in a universal way. In applications, those higher-order corrections are expected to curve the linear relation between the level index and the inverse of the magnetic field, as already observed in experiments. Our theory then provides a way to extract the correct value of Berry phase as well as the magnetic susceptibility at zero temperature from Landau level fan diagrams in experiments. Moreover, it can be used theoretically to calculate Landau levels up to second-order accuracy for realistic models.

scholarly journals Temperature−field phase diagram of extreme magnetoresistance

2016 ◽  
Vol 113 (25) ◽  
pp. E3475-E3481 ◽  
Author(s):  
Fazel Fallah Tafti ◽  
Quinn Gibson ◽  
Satya Kushwaha ◽  
Jason W. Krizan ◽  
Neel Haldolaarachchige ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Temperature Field ◽  
Residual Resistivity ◽  
Chemical Compositions ◽  
Zero Field ◽  
Field Phase ◽  
Linear Band ◽  
Topological Semimetals ◽  
Band Crossing

The recent discovery of extreme magnetoresistance (XMR) in LaSb introduced lanthanum monopnictides as a new platform to study this effect in the absence of broken inversion symmetry or protected linear band crossing. In this work, we report XMR in LaBi. Through a comparative study of magnetotransport effects in LaBi and LaSb, we construct a temperature−field phase diagram with triangular shape that illustrates how a magnetic field tunes the electronic behavior in these materials. We show that the triangular phase diagram can be generalized to other topological semimetals with different crystal structures and different chemical compositions. By comparing our experimental results to band structure calculations, we suggest that XMR in LaBi and LaSb originates from a combination of compensated electron−hole pockets and a particular orbital texture on the electron pocket. Such orbital texture is likely to be a generic feature of various topological semimetals, giving rise to their small residual resistivity at zero field and subject to strong scattering induced by a magnetic field.

scholarly journals Geometric characterization of anomalous Landau levels of isolated flat bands

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yoonseok Hwang ◽  
Jun-Won Rhim ◽  
Bohm-Jung Yang
Keyword(s):  
Wave Function ◽  
Landau Level ◽  
Landau Levels ◽  
Zero Magnetic Field ◽  
Flat Band ◽  
Field Energy ◽  
Zero Field ◽  
Quantization Rule ◽  
Flat Bands ◽  
Ideal System

AbstractAccording to the Onsager’s semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.

scholarly journals Modified Fermi energy of electrons in a superhigh magnetic field

2016 ◽  
Vol 31 (11) ◽  
pp. 1650070 ◽  
Author(s):  
Cui Zhu ◽  
Zhi Fu Gao ◽  
Xiang Dong Li ◽  
Na Wang ◽  
Jian Ping Yuan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Landau Level ◽  
Fermi Energy ◽  
Landau Levels ◽  
Exclusion Principle ◽  
Index Formula ◽  
Field Energy ◽  
Relativistic Electrons ◽  
Level Number ◽  
The Magnetic Field

In this paper, we investigate the electron Landau level stability and its influence on the electron Fermi energy, [Formula: see text], in the circumstance of magnetars, which are powered by magnetic field energy. In a magnetar, the Landau levels of degenerate and relativistic electrons are strongly quantized. A new quantity [Formula: see text], the electron Landau level stability coefficient is introduced. According to the requirement that [Formula: see text] decreases with increasing the magnetic field intensity [Formula: see text], the magnetic field index [Formula: see text] in the expression of [Formula: see text] must be positive. By introducing the Dirac-[Formula: see text] function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to [Formula: see text] in a superhigh magnetic field (SMF). This solution has a low magnetic field index of [Formula: see text], compared with the previous one, and works when [Formula: see text] and [Formula: see text] Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density [Formula: see text], and decrease the maximum of electron Landau level number, which results in a redistribution of electrons. According to Pauli exclusion principle, the degenerate electrons will fill quantum states from the lowest Landau level to the highest Landau level. As [Formula: see text] increases, more and more electrons will occupy higher Landau levels, though [Formula: see text] decreases with the Landau level number [Formula: see text]. The enhanced [Formula: see text] in a SMF means an increase in the electron Fermi energy and an increase in the electron degeneracy pressure. The results are expected to facilitate the study of the weak-interaction processes inside neutron stars and the magnetic-thermal evolution mechanism for magnetars.

OBSERVATION OF A SECOND ENERGY SCALE IN YbAl3 ABOVE 40 T

2002 ◽  
Vol 16 (20n22) ◽  
pp. 2992-2997
Author(s):  
A. L. CORNELIUS ◽  
T. EBIHARA ◽  
J. M. LAWRENCE ◽  
P. S. RISEBOROUGH ◽  
J. D. THOMPSON
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Fermi Surface ◽  
Characteristic Temperature ◽  
Large Change ◽  
Energy Scale ◽  
Kondo Temperature ◽  
Field Energy ◽  
Zero Field ◽  
Effective Masses

YbAl 3 is an intermediate valent compound with a Kondo temperature T K in excess of 500 K and a rather low conduction electron density of ~0.5/atom. Recent measurements are suggestive of a second energy scale T coh of order 50 K that dominates the low temperature ( T ≪ T coh ) thermodynamic properties. Previous de Haas-van Alphen (dHvA) measurements on YbAl 3 in magnetic fields to 17 T reveal a fairly simple Fermi surface with 6 branches having effective masses m* ranging from 8 to 24 m0 (see Refs. [2-3]). We report magnetization and dHvA results on YbAl 3 in pulsed magnetic fields up to 60 T. For T ≪ T coh we indeed find that the magnetization 'crosses' over from the zero field energy scale T coh to the high temperature energy scale T K at a magnetic field B * ≈ 40 T (≈ K B T coh /μB). For B > B *, we find dHvA oscillations when magnetic field is applied along the <100>, <110> and <111> directions. For magnetic field applied along <111>, the Fermi surface changes very little for B > B*, and the effective masses are all reduced by a factor of 2-3 relative to their low field values. This is due to the large change in the characteristic temperature, which goes from T coh below B * to T K above B *. We believe this is the first work to directly observe the two energy scales and to observe the crossover in the dominant energy scale as a function of magnetic field.

MATHEMATICAL MODELING OF TEMPERATURE EFFECT ON THE FAN CHART OF MAGNETOABSORPTION SPECTRUM IN SEMICONDUCTORS

2019 ◽  
pp. 104-115
Author(s):  
G. Gulyamov ◽  
U. I. Erkaboev ◽  
A. G. Gulyamov
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Temperature Dependence ◽  
Density Of States ◽  
Landau Levels ◽  
Joint Density ◽  
Narrow Gap ◽  
Narrow Gap Semiconductors ◽  
Dispersion Law ◽  
The Magnetic Field

The article considers the oscillations of interband magneto-optical absorption in semiconductors with the Kane dispersion law. We have compared the changes in oscillations of the joint density of states with respect to the photon energy for different Landau levels in parabolic and non-parabolic zones. An analytical expression is obtained for the oscillation of the combined density of states in narrow-gap semiconductors. We have calculated the dependence of the maximum photon energy on the magnetic field at different temperatures. A theoretical study of the band structure showed that the magnetoabsorption oscillations decrease with an increase in temperature, and the photon energies nonlinearly depend on a strong magnetic field. The article proposes a simple method for calculating the oscillation of joint density of states in a quantizing magnetic field with the non-quadratic dispersion law. The temperature dependence of the oscillations joint density of states in semiconductors with non-parabolic dispersion law is obtained. Moreover, the article studies the temperature dependence of the band gap in a strong magnetic field with the non-quadratic dispersion law. The method is applied to the research of the magnetic absorption in narrow-gap semiconductors with nonparabolic dispersion law. It is shown that as the temperature increases, Landau levels are washed away due to thermal broadening and density of states turns into a density of states without a magnetic field. Using the mathematical model, the temperature dependence of the density distribution of energy states in strong magnetic fields is considered. It is shown that the continuous spectrum of the density of states, measured at the temperature of liquid nitrogen, at low temperatures turns into discrete Landau levels. Mathematical modeling of processes using experimental values of the continuous spectrum of the density of states makes it possible to calculate discrete Landau levels. We have created the three-dimensional fan chart of magneto optical oscillations of semiconductors with considering for the joint density of energy states. For a nonquadratic dispersion law, the maximum frequency of the absorbed light and the width of the forbidden band are shown to depend nonlinearly on the magnetic field. Modeling the temperature  dependence allowed us to determine the Landau levels in semiconductors in a wide temperature spectrum. Using the proposed model, the experimental results obtained for narrow-gap semiconductors are analyzed. The theoretical results are compared with experimental results.

scholarly journals Ground state and stability of the fractional plateau phase in metallic Shastry–Sutherland system TmB4

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matúš Orendáč ◽  
Slavomír Gabáni ◽  
Pavol Farkašovský ◽  
Emil Gažo ◽  
Jozef Kačmarčík ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Ground State ◽  
Constant Magnetic Field ◽  
Paramagnetic Phase ◽  
The Other ◽  
Zero Field ◽  
Plateau Phase ◽  
Low Field ◽  
Zero Field Cooling

AbstractWe present a study of the ground state and stability of the fractional plateau phase (FPP) with M/Msat = 1/8 in the metallic Shastry–Sutherland system TmB4. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/Msat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 Msat.

MICROWAVE ABSORPTION STUDIES ON HIGH-Tc SUPERCONDUCTORS AND RELATED MATERIALS II: Electron Spin Resonance of DPPH Coated on Y1Ba2Cu3Oy as A Probe of Magnetic Field Variations

1991 ◽  
Vol 05 (11) ◽  
pp. 779-787
Author(s):  
K. SUGAWARA ◽  
D.J. BAAR ◽  
Y. SHIOHARA ◽  
S. TANAKA
Keyword(s):  
Magnetic Field ◽  
Temporal Variations ◽  
Zero Field ◽  
High Tc ◽  
Spin Resonance ◽  
Absorption Studies ◽  
Powder Particles ◽  
Increasing Temperature ◽  
Linewidth Broadening ◽  
Magnetic Field Variations

The ESR linewidth (∆H pp ) of DPPH coated on the surface of powder specimens of Y 1 Ba 2 Cu 3 O y has been studied under various magnetic field and temperature conditions. ∆H pp increases substantially with decreasing temperature in the field cooled case, whereas almost no linewidth broadening was found in the zero field cooled case. ∆H pp was found to be sensitive to the applied magnetic field. This effect was very pronounced at temperatures lower than 40 K, but decreased strongly with increasing temperature. The broadening of the resonance lineshape has been attributed to spatial and temporal variations of the fluxon distribution in the powder particles.

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