Density of states and de Haas-van Alphen effect in two-dimensional electron systems

Ultrafast Electron Microscopy of Nanoscale Charge Dynamics in Semiconductors

The ultrafast dynamics of charge carriers in solids plays a pivotal role in emerging optoelectronics, photonics, energy harvesting, and quantum technology applications. However, the investigation and direct visualization of such nonequilibrium phenomena remains as a long-standing challenge, owing to the nanometer-femtosecond spatiotemporal scales at which the charge carriers evolve. Here, we propose and demonstrate an interaction mechanism enabling nanoscale imaging of the femtosecond dynamics of charge carriers in solids. This imaging modality, which we name charge dynamics electron microscopy (CDEM), exploits the strong interaction of free-electron pulses with terahertz (THz) near fields produced by the moving charges in an ultrafast scanning transmission electron microscope. The measured free-electron energy at different spatiotemporal coordinates allows us to directly retrieve the THz near-field amplitude and phase, from which we reconstruct movies of the generated charges by comparison to microscopic theory. The CDEM technique thus allows us to investigate previously inaccessible spatiotemporal regimes of charge dynamics in solids, providing insight into the photo-Dember effect and showing oscillations of photogenerated electron-hole distributions inside a semiconductor. Our work facilitates the exploration of a wide range of previously inaccessible charge-transport phenomena in condensed matter using ultrafast electron microscopy.

Mechanical Detection of the De Haas-van Alphen Effect in Graphene

In our work, we study the dynamics of a graphene Corbino disk supported by a gold mechanical resonator in the presence of a magnetic field. We demonstrate here that our graphene/gold mechanical structure exhibits a nontrivial resonance frequency dependence on the applied magnetic field, showing how this feature is indicative of the de Haas-van Alphen effect in the graphene Corbino disk. Relying on the mechanical resonances of the Au structure, our detection scheme is essentially independent of the material considered and can be applied for dHvA measurements on any conducting 2D material. In particular, the scheme is expected to be an important tool in studies of centrosymmetric transition metal dichalcogenide (TMD) crystals, shedding new light on hidden magnetization and interaction effects.

Two-dimensional Fermi surfaces in Kondo insulator SmB6

In the Kondo insulator samarium hexaboride (SmB6), strong correlation and band hybridization lead to an insulating gap and a diverging resistance at low temperature. The resistance divergence ends at about 3 kelvin, a behavior that may arise from surface conductance. We used torque magnetometry to resolve the Fermi surface topology in this material. The observed oscillation patterns reveal two Fermi surfaces on the (100) surface plane and one Fermi surface on the (101) surface plane. The measured Fermi surface cross sections scale as the inverse cosine function of the magnetic field tilt angles, which demonstrates the two-dimensional nature of the conducting electronic states of SmB6.

Gap structure of the Hofstadter system of interacting Dirac fermions in graphene

The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum are investigated. For two flux quanta per unit cell of the periodic potential, interactions open a gap in each Landau level with the smallest gap in the n=1 Landau level. For more flux quanta through the unit cell, where the noninteracting energy spectra have many gaps in each Landau level, interactions enhance the low-energy gaps and strongly suppress the high-energy gaps and almost close a high-energy gap for n=1. The signature of the interaction effects in the Hofstadter system can be probed through magnetization, which is governed by the mixing of the Landau levels and is enhanced by the Coulomb interaction.

Direct measurement of the Fermi energy in graphene using a double-layer heterostructure

We describe a technique which allows a direct measurement of the relative Fermi energy in an electron system by employing a double-layer heterostructure. We illustrate this method by using a graphene double layer to probe the Fermi energy as a function of carrier density in monolayer graphene, at zero and in high magnetic fields. This technique allows us to determine the Fermi velocity, Landau level spacing, and Landau level broadening. We find that the N=0 Landau level broadening is larger by comparison to the broadening of upper and lower Landau levels.

What lurks below the last plateau: experimental studies of the 0.7 × 2e(2)/h conductance anomaly in one-dimensional systems

The integer quantised conductance of one-dimensional electron systems is a well-understood effect of quantum confinement. A number of fractionally quantised plateaus are also commonly observed. They are attributed to many-body effects, but their precise origin is still a matter of debate, having attracted considerable interest over the past 15 years. This review reports on experimental studies of fractionally quantised plateaus in semiconductor quantum point contacts and quantum wires, focusing on the 0.7 × 2e(2)/h conductance anomaly, its analogues at higher conductances and the zero-bias peak observed in the dc source-drain bias for conductances less than 2e(2)/h.

Magnetometry of low-dimensional electron and hole systems

The high-magnetic-field, low-temperature magnetic properties of low-dimensional 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.

Principal thermodynamic properties of quasi-two-dimensional carriers under in-plane magnetic field

An external magnetic field, H, applied parallel to a quasi-two-dimensional carrier system modifies quantitatively and qualitatively the density of states. We examine how this affects primary thermodynamic properties, namely, the entropy, S, the internal and free energy, U and F, the magnetization, M, and the magnetic susceptibility, χ(m), using a self-consistent numerical approach. Although M is mainly in the opposite direction to H, the system is not linear. Hence, surprisingly, [Formula: see text] swings between negative and positive values, i.e. a diamagnetic to paramagnetic transition of entirely orbital origin is predicted. This phenomenon is important compared to the ideal de Haas-van Alphen effect, i.e. the corresponding phenomenon under perpendicular magnetic field. By augmenting temperature, the diamagnetic to paramagnetic transition fades away. The overall behaviour of entropy is also foreseen and consistently interpreted. While the entropy contribution to the free energy is very small at low temperatures, entropy shows a clear dependence on the external magnetic field.

Oscillatory persistent currents in self-assembled quantum rings

We report the direct measurement of the persistent current carried by a single electron by means of magnetization experiments on self-assembled InAs/GaAs quantum rings. We measured the first Aharonov-Bohm oscillation at a field of 14 T, in perfect agreement with our model based on the structural properties determined by cross-sectional scanning tunneling microscopy measurements. The observed oscillation magnitude of the magnetic moment per electron is remarkably large for the topology of our nanostructures, which are singly connected and exhibit a pronounced shape asymmetry.

Magnetization of a strongly interacting two-dimensional electron system in perpendicular magnetic fields

We measure the thermodynamic magnetization of a low-disordered, strongly correlated two-dimensional electron system in silicon in perpendicular magnetic fields. A new, parameter-free method is used to directly determine the spectrum characteristics (Landé g factor and the cyclotron mass) when the Fermi level lies outside the spectral gaps and the interlevel interactions between quasiparticles are avoided. Intralevel interactions are found to strongly modify the magnetization, without affecting the determined g* and m*.

Quantum interference effects in the magnetopiezoresistance of InAs/AlGaSb quasi-one-dimensional electron systems

We measured the low temperature magnetopiezoresistance of a quasi-one-dimensional electron system by fabricating an InAs/AlGaSb micromechanical cantilever. The magnetopiezoresistance curve showed aperiodic but reproducible oscillation, which was similar to the differential magnetoresistance curve obtained for the same device. A detailed comparison with model calculations strongly suggests that the quantum interference effects that cause the conductance fluctuations in the magnetoresistance are responsible for the peculiar behavior of the magnetopiezoresistance.

Quantum magneto-oscillations in a supramolecular Mn(II)-[3 x 3] grid

The magnetic grid molecule Mn(II)-[3 x 3] has been studied by high-field torque magnetometry at 3He temperatures. At fields above 5 T, the torque versus field curves exhibit an unprecedented oscillatory behavior. A model is proposed which describes these magneto-oscillations well.

Magnetization measurements of magnetic two-dimensional electron gases

We directly measure the magnetization of both the conduction electrons and Mn2+ ions in (Zn,Cd,Mn)Se two-dimensional electron gases (2DEGs) by integrating them into ultrasensitive micromechanical magnetometers. The interplay between spin and orbital energy in these magnetic 2DEGs causes Landau level degeneracies at the Fermi energy. These Landau level crossings result in novel features in the de Haas-van Alphen oscillations, which are quantitatively reproduced by a simple model.