L. W. Engel

Observation of quantum-Hall effect in gated epitaxial graphene grown on SiC (0001)

Epitaxial graphene films examined were formed on the Si-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. A high-k gate stack on the epitaxial graphene was realized by inserting a fully oxidized nanometer thin aluminum film as a seeding layer, followed by an atomic-layer deposition process. The electrical properties of epitaxial graphene films are retained after gate stack formation without significant degradation. At low temperatures, the quantum-Hall effect in Hall resistance is observed along with pronounced Shubnikov–de Haas oscillations in diagonal magnetoresistance of gated epitaxial graphene on SiC (0001).

Giant microwave photoresistance of two-dimensional electron gas

We measure microwave frequency (4–40 GHz) photoresistance at low magnetic field B, in high mobility two-dimensional electron gas samples, excited by signals applied to a transmission line fabricated on the sample surface. Oscillatory photoresistance vs B is observed. For excitation at the cyclotron resonance frequency, we find a giant relative photoresistance ΔR/R of up to 250%. The photoresistance is apparently proportional to the square root of applied power, and disappears as the temperature is increased.

Superconductivity-Related Insulating Behavior

We present the results of an experimental study of superconducting, disordered, thin films of amorphous indium oxide. These films can be driven from the superconducting phase to a reentrant insulating state by the application of a perpendicular magnetic field (B). We find that the high-B insulator exhibits activated transport with a characteristic temperature, TI. TI has a maximum value (TpI) that is close to the superconducting transition temperature (Tc) at B=0, suggesting a possible relation between the conduction mechanisms in the superconducting and insulating phases. Tp(I) and Tc display opposite dependences on the disorder strength.

Magnetoconductance oscillations in graphene antidot arrays

Epitaxial graphene films have been formed on the C-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. Nanoscale square antidot arrays have been fabricated on these graphene films. At low temperatures, magnetoconductance in these films exhibits pronounced Aharonov–Bohm oscillations with the period corresponding to magnetic flux quanta added to the area of a single antidot. At low fields, weak localization is observed and its visibility is enhanced by intervalley scattering on antidot edges. At high fields, we observe two distinctive minima in magnetoconductance, which can be attributed to commensurability oscillations between classical cyclotron orbits and antidot array. All mesoscopic features, surviving up to 70K, reveal the unique electronic properties of graphene.

Correlation lengths of the Wigner-crystal order in a two-dimensional electron system at high magnetic fields

The insulator terminating the fractional quantum Hall series at low Landau level filling nu is generally taken to be a pinned Wigner crystal (WC), and exhibits a microwave resonance that is interpreted as a WC pinning mode. For a high quality sample at several densities, n, we find maxima in resonance peak frequency, f(pk), vs magnetic field, B. L, the correlation length of WC order, is calculated from f(pk). For each n, L vs nu tends at low nu toward a line with positive intercept; the fit is accurate over as much as a factor of 5 range of nu. The linear behavior is interpreted as due to B compressing the electron wave functions, to alter the effective electron-impurity interaction.

Experimental evidence for a collective insulating state in two-dimensional superconductors

We present the results of an experimental study of the current-voltage characteristics in a strong magnetic field (B) of disordered, superconducting, thin films of amorphous indium oxide. As the B strength is increased superconductivity degrades, until a critical field (B(c)) where the system is forced into an insulating state. We show that the differential conductance measured in the insulating phase vanishes abruptly below a well-defined temperature, resulting in a clear threshold for conduction. Our results indicate that a new collective state emerges in two-dimensional superconductors at high B.

Melting of a 2D quantum electron solid in high magnetic field

The melting temperature Tm of a solid is generally determined by its solid–liquid transition on being heated at a fixed pressure, usually ambient pressure. It is also determined indirectly by the density n by means of the equation of state. This remains true even for solid helium1, in which quantum effects often lead to unusual properties2. Here, we present experimental evidence to show that for a two-dimensional (2D) solid formed by electrons in a semiconductor sample under a strong perpendicular magnetic field3 (B), Tm is not controlled by n, but effectively by the quantum correlation between the electrons through the Landau level filling factor ν=nh/eB (where h is the Planck constant and e is the electronic charge). Such melting behaviour, different from that of all other known solids (including a classical 2D electron solid at zero magnetic field4), suggests the quantum nature of the magnetic-field-induced electron solid. Moreover, Tm increases with the strength of the sample-dependent disorder that tends to pin the electron solid in place.

Microwave resonance of the bubble phases in 1/4 and 3/4 filled high Landau levels

We have measured the diagonal conductivity, sigma(xx), in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma(xx)] versus frequency when nu>4 and the partial filling of the highest Landau level, nu(*), is approximately 1/4 or 3/4 and temperatures <0.1 K. The resonance appears for a range of nu(*) from 0.20 to 0.38 and again from 0.64 to 0.80. The peak frequency f(pk) changes from approximately 500 to approximately 150 MHz as nu(*)=1/2 is approached. This range of f(pk) shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at about nu(*)=0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.

Microwave resonance of the 2D Wigner crystal around integer Landau fillings.

We have observed a resonance in the real part of the finite frequency diagonal conductivity using microwave absorption measurements in high quality 2D electron systems near integer fillings. The resonance exists in some neighborhood of filling factor around corresponding integers and is qualitatively similar to previously observed resonance of weakly pinned Wigner crystal in high B and very small filling factor regime. Data measured around both nu=1 and nu=2 are presented. We interpret the resonance as the signature of the Wigner crystal state around integer Landau levels.

Observation of pinning mode of stripe phases of 2D systems in high Landau levels.

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half-integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernible. The resonance is interpreted as a pinning mode of the stripe phase.