skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Landau levels for charged particles with anisotropic mass
The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem.  more » « less
Award ID(s):
2001980
PAR ID:
10560892
Author(s) / Creator(s):
Publisher / Repository:
AIP
Date Published:
Journal Name:
American Journal of Physics
Volume:
92
Issue:
8
ISSN:
0002-9505
Page Range / eLocation ID:
625 to 629
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. (, Symmetry)
    The loss of any symmetry in a system leads to quantum problems that are typically very difficult to solve. Such a situation arises for particles with anisotropic mass, like electrons in various semiconductor host materials, where it is known that they may have an anisotropic effective mass. In this work, we consider the quantum problem of a spinless charged particle with anisotropic mass in two dimensions and study the resulting energy and eigenstate spectrum in a uniform constant perpendicular magnetic field when a Landau gauge is adopted. The exact analytic solution to the problem is obtained for arbitrary values of the anisotropic mass using a mathematical technique that relies on the scaling of the original coordinates. The characteristic features of the energy spectrum and corresponding eigenstate wave functions are analyzed. The results of this study are expected to be of interest to quantum Hall effect theory. 
    more » « less
  2. ; ; ; ; (, The Journal of Chemical Physics)
    A simplified theoretical description of multiple-quantum excitation and mixing for nuclear magnetic resonance of half-integer quadrupolar nuclei is presented. The approach recasts the multiple-quantum nutation behavior in terms of reduced excitation and mixing curves through a scaling of the first-order offset frequency by the quadrupolar coupling constant. The two-dimensional correlation of the static first-order anisotropic line shape to the second-order anisotropic magic-angle-spinning (MAS) line shape is utilized to transform the three-dimensional integral over the three Euler angles into a single integral over the dimensionless first-order offset parameter. These transformations lead to a highly efficient algorithm for simulating the multiple-quantum (MQ)-MAS spectrum for arbitrary excitation and mixing radio frequency (RF) field strengths, pulse durations, and MAS rates within the static limit approximation, which is defined in terms of the rotation period, pulse duration, RF field strength, and quadrupolar coupling parameters. This algorithm enables a more accurate determination of the relative site populations and quadrupolar coupling parameters in a least-squares analysis of MQ-MAS spectra. Furthermore, this article examines practical considerations for eliminating experimental artifacts and employing affine transformations to improve least-squares analyses of MQ-MAS spectra. The optimum ratio of RF field strength to the quadrupolar coupling constant and the corresponding pulse durations that maximize sensitivity within experimental constraints are also examined. 
    more » « less
  3. ; ; ; (, Advanced Intelligent Systems)
    Planar magnetic microswimmers bear great potential for in vivo biomedical applications as they can be mass‐produced at minimal costs using standard photolithography techniques. Therefore, it is central to understand how to control their motion. This study examines the propulsion of planar V‐shaped microswimmers in an aqueous solution powered by a conically rotating magnetic field and compares the experimental results with theory. Propulsion is investigated upon altering the cone angle of the driving field. It is shown that a V‐shaped microswimmer magnetized along its symmetry axis exhibits unidirectional in‐sync propulsion with a constant (frequency‐independent) velocity in a limited band of actuation frequencies. It is also demonstrated that the motion of individual and multiple in‐plane magnetized planar microswimmers in a conically rotating field can be efficiently controlled. 
    more » « less
  4. ; ; ; ; ; ; ; ; ; ; et al (, Physical Review B)
    Kancharla, S (Ed.)
    We present the magnetic and structural properties of [Cu(pyrazine)0.5(glycine)]ClO4 under applied pressure. As previously reported, at ambient pressure this material consists of quasi-two-dimensional layers of weakly coupled antiferromagnetic dimers which undergo Bose-Einstein condensation of triplet excitations between two magnetic field-induced quantum critical points (QCPs). The molecular building blocks from which the compound is constructed give rise to exchange strengths that are considerably lower than those found in other S = 1/2 dimer materials, which allows us to determine the pressure evolution of the entire field-temperature magnetic phase diagram using radio-frequency magnetometry. We find that a distinct phase emerges above the upper field-induced transition at elevated pressures and also show that an additional QCP is induced at zero field at a critical pressure of pc = 15.7(5) kbar. Pressure-dependent single-crystal x-ray diffraction and density functional theory calculations indicate that this QCP arises primarily from a dimensional crossover driven by an increase in the interdimer interactions between the planes. While the effect of quantum fluctuations on the lower field-induced transition is enhanced with applied pressure, quantum Monte Carlo calculations suggest that this alone cannot explain an unconventional asymmetry that develops in the phase diagram. 
    more » « less
  5. ; ; (, Applied Physics Letters)
    Quantum defects are atomic defects in materials that provide resources to construct quantum information devices such as single-photon emitters and spin qubits. Recently, two-dimensional (2D) materials gained prominence as a host of quantum defects with many attractive features derived from their atomically thin and layered material formfactor. In this Perspective, we discuss first-principles computational methods and challenges to predict the spin and electronic properties of quantum defects in 2D materials. We focus on the open quantum system nature of the defects and their interaction with external parameters such as electric field, magnetic field, and lattice strain. We also discuss how such prediction and understanding can be used to guide experimental studies, ranging from defect identification to tuning of their spin and optical properties. This Perspective provides significant insights into the interplay between the defect, the host material, and the environment, which will be essential in the pursuit of ideal two-dimensional quantum defect platforms. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email