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 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 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 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.

scholarly journals EDGE ASYMPTOTICS OF PLANAR ELECTRON DENSITIES

1994 ◽  
Vol 08 (11n12) ◽  
pp. 1625-1638 ◽  
Author(s):  
GERALD V. DUNNE
Keyword(s):  
Asymptotic Expansion ◽  
Magnetic Flux ◽  
Landau Level ◽  
Particle Number ◽  
Landau Levels ◽  
Electron Densities ◽  
Boundary Location ◽  
Boundary Characteristics ◽  
Planar Electron

The N→∞ limit of the edges of finite planar electron densities is discussed for higher Landau levels. For full filling, the particle number is correlated with the magnetic flux, and hence with the boundary location, making the N→∞ limit more subtle at the edges than in the bulk. In the nth Landau level, the density exhibits n distinct steps at the edge, in both circular and rectangular samples. The boundary characteristics for individual Landau levels, and for successively filled Landau levels, are computed in an asymptotic expansion.

Disorientation of Cs(62P1/2) atoms, induced in collisions with noble gases

1976 ◽  
Vol 54 (7) ◽  
pp. 748-752 ◽  
Author(s):  
B. Niewitecka ◽  
L. Krause
Keyword(s):  
Cross Sections ◽  
Noble Gas ◽  
Zero Magnetic Field ◽  
Zero Field ◽  
Buffer Gas ◽  
Resonance Fluorescence ◽  
Circularly Polarized ◽  
Low Field ◽  
Good Agreement ◽  
Gas Pressures

The disorientation of 62P1/2 cesium atoms, induced in collisions with noble gas atoms in their ground states, was systematically investigated by monitoring the depolarization of cesium resonance fluorescence in relation to noble gas pressures. The Cs atoms, contained together with a buffer gas in a fluorescence cell and located in zero magnetic field, were excited and oriented by irradiation with circularly polarized 8943 Å resonance radiation, and the resonance fluorescence, emitted in an approximately backward direction, was analyzed with respect to circular polarization. The experiments yielded the following disorientation cross sections which have been corrected for the effects of nuclear spin: Cs–He: 4.9 ± 0.7 Å2; Cs–Ne: 2.1 ± 0.3 Å2; Cs–Ar: 5.6 ± 0.8 Å2; Cs–Kr: 5.8 ± 0.9 Å2; Cs–Xe: 6.3 ± 0.9 Å2. The results are in good agreement with most of the available zero-field and low-field data.

scholarly journals Numerical test of disk trial wave function for a half-filled Landau level

2000 ◽  
Vol 62 (12) ◽  
pp. 8171-8179 ◽  
Author(s):  
S.-R. Eric Yang ◽  
Min-Chul Cha ◽  
Jung Hoon Han
Keyword(s):  
Wave Function ◽  
Landau Level ◽  
Numerical Test ◽  
Trial Wave Function

scholarly journals Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Tao ◽  
Peng Wang ◽  
Haitang Yang
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Statistical Physics ◽  
Turning Point ◽  
Minimal Length ◽  
Jacobi Method ◽  
Homogeneous Field ◽  
Quantization Rule ◽  
Connection Formula ◽  
Forbidden Region

In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up toOβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

scholarly journals Flat Band and Hole-induced Ferromagnetism in a Novel Carbon Monolayer

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Jing-Yang You ◽  
Bo Gu ◽  
Gang Su
Keyword(s):  
Density Functional ◽  
Doping Concentration ◽  
Carbon Materials ◽  
Density Functional Theory Calculations ◽  
Hole Doping ◽  
Flat Band ◽  
Ferromagnetic Transition ◽  
Functional Theory ◽  
Flat Bands ◽  
Half Metal

AbstractIn recent experiments, superconductivity and correlated insulating states were observed in twisted bilayer graphene (TBG) with small magic angles, which highlights the importance of the flat bands near Fermi energy. However, the moiré pattern of TBG consists of more than ten thousand carbon atoms that is not easy to handle with conventional methods. By density functional theory calculations, we obtain a flat band at EF in a novel carbon monolayer coined as cyclicgraphdiyne with the unit cell of eighteen atoms. By doping holes into cyclicgraphdiyne to make the flat band partially occupied, we find that cyclicgraphdiyne with 1/8, 1/4, 3/8 and 1/2 hole doping concentration shows ferromagnetism (half-metal) while the case without doping is nonmagnetic, indicating a hole-induced nonmagnetic-ferromagnetic transition. The calculated conductivity of cyclicgraphdiyne with 1/8, 1/4 and 3/8 hole doping concentration is much higher than that without doping or with 1/2 hole doping. These results make cyclicgraphdiyne really attractive. By studying several carbon monolayers, we find that a perfect flat band may occur in the lattices with both separated or corner-connected triangular motifs with only including nearest-neighboring hopping of electrons, and the dispersion of flat band can be tuned by next-nearest-neighboring hopping. Our results shed insightful light on the formation of flat band in TBG. The present study also poses an alternative way to manipulate magnetism through doping flat band in carbon materials.

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