Magnetometry of low-dimensional electron and hole systems

Abstract

Abstract. The high magnetic field, low-temperature magnetic properties of lowdimensional electron and hole systems reveal a wealth of fundamental information. Quantum oscillations of the thermodynamic equilibrium magnetization yield the total density of states, a central quantity in understanding the quantum Hall effect in 2D systems. The magnetization arising from non-equilibrium circulating currents reveals details, not accessible with traditional measurements, of the vanishingly small longitudinal resistance in the quantum Hall regime. We review how the technique of magnetometry has been applied to these systems, the most important discoveries that have been made, and their theoretical significance.

Chemical potential oscillations from nodal Fermi surface pocket in the underdoped high-temperature superconductor YBa2Cu3O6+x

“…Large oscillations in µ tend to occur in layered metals owing to the absence of a large reservoir of phase-incoherent states to pin µ at an essentially constant value [21][22][23] . Instead of the Landau levels passing through a constant chemical potential-as described in the simplest Lifshitz-Kosevich theory 17 -µ itself oscillates.…”

“…The second harmonic is extracted by fitting and subtracting from the data an unconstrained sum of four low frequencies (F < 700T), similar to those earlier reported in references 6,7,9,10, and a slowly varying aperiodic background (fit procedure shown in Methods). From the analysis of the measured second harmonic oscillations, we present the surprising finding that the harmonic content in underdoped YBa 2 Cu 3 O 6 + x (x = 0.56) arises from oscillations of the chemical potential, which are enhanced compared to normal metals by the quasi-two-dimensional topology of the Fermi surface 17,[21][22][23][24] . Oscillatory features corresponding to multiple frequencies in 1/B previously reported 3,6,7,9 are observed: (F α = 535(5) T, F γ1 = 440(10) T, F γ2 = 610(20) T) down to 22 T, and F β = 1,550(50) T at the lowest temperatures 1 K (to be presented elsewhere); yet, we conclude, from the magnitude and phase of the second harmonic with respect to the fundamental oscillations, that the Fermi surface consists chiefly of a single carrier pocket, the multiple frequency components arising from effects of finite c-axis dispersion, bilayer splitting, and magnetic breakdown.…”

Frequency anomaly in the Rashba-effect induced magnetization oscillations of a high-mobility two-dimensional electron system

“…8 Experimental data M(B) in transverse magnetic fields to verify the theories have not yet been available due to the challenging magnetometry. 9,10 In this paper we report on beating patterns in M(B) measured at low temperature in nearly perpendicular and tilted magnetic fields on a 2DES in an asymmetric InGaAs/InP quantum well exhibiting SOI. In addition, we have taken data ρ xx vs B on the same heterostructure under the same tilt angles.…”

Temperature derivative of the chemical potential and its magneto-oscillations in a two-dimensional system

“…), and, hence, allow comprehensive magnetooscillation studies. Quantum oscillations in 2D systems are most often studied in resistivity (Shubnikov-de Haas effect) [1], and magnetization (de Haas-Van Alphen) [2]. However, other physical quantities in 2D systems, such as thermo-EMF [3], heat capacity [4], chemical potential [5,6], compressibility [7], also oscillate with magnetic field.…”

“…The Lorentzian lineshape of the Landau levels is in the agreement with magnetization measurements of Potts et al [28] on the moderate mobility GaAs-based sample. Generally, the shape of DOS in 2D systems is still debated, with a history of research reviewed, e.g., by Usher et al [2]. Different approaches are used to determine DOS with many contradictory results obtained.…”