Local Density of States of a Three-Dimensional Conductor in the Extreme Quantum Limit

Abstract

The electronic structure of the narrow gap semiconductor InAs is investigated by scanning tunneling spectroscopy and magnetotransport measurements in the extreme quantum limit. The well-known oscillations of the Hall coefficient are reproduced and the last, most pronounced oscillation is shown to be correlated with the appearance of corrugations in the local density of states. While the increasing part of the Hall constant corresponds to the existence of isolated patterns indicating magnetic field induced localization, the decreasing part correlates with the development of a network which most likely consists of one-dimensional channels. We conclude that the decrease of the Hall constant in the extreme quantum limit is caused by a transition from a purely three-dimensional to a partly one-dimensional transport regime.

Magneto-oscillations of the Hall coefficient in n-type GaSb at the extreme quantum limit

“…(ii) The r xy ðBÞ Hall resistivity exhibits small deviations from linearity, with a knee-like structure more pronounced at the lowest temperatures and practically absent at T , 15 K. This behavior results in oscillations of the Hall coefficient R H around the R cl classical value obtained from the low fields slope of the linear r xy ðBÞ dependence. (iii) The amplitude of the R H oscillation is anomalously large near the EQL with the maximum at a field B M which is slightly larger than B EQL : The above results are qualitatively similar to those found in narrow gap semiconductors such as InSb, InAs and HgCdTe [15,18,19,[22][23][24] although in the most of the latter cases the condition r xy . r xx is generally satisfied at high magnetic fields and only in a few cases r xy just approaches r xx ; as in the present one.…”

“…As suggested by Zeitler et al [19] two Hall dips should then be observed, a first one before the MI transition of the spin-down electron system and a second one, more pronounced, at an even higher field before the MI transition of the spin-up electrons. Haude et al [24] were able to put the whole question on a sound experimental basis. By combining magnetotransport measurements at the EQL and scanning tunneling spectroscopy they correlated the last R H oscillation in InAs with the appearance of spatial corrugations (ascribed to localized states) in the observed local DOS of the lowest ðn ¼ 0Þ LL.…”

Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields

“…2(g) and indeed exhibits a width distribution around l B 10:5 nm. The corrugation strength in the dI=dV images is 75% 5% [20], a value which is larger than for the same 2DES at B 0 T (60% 5%) [7], much larger than for a similar 3DES at B 0 T (3% 0:5%) [21] and also larger than for the 3DES in the extreme quantum limit (30%-65%) [22]. Thus, we observe rather strong LDOS corrugations indicating strongly fluctuating wave functions.…”

Scanning Tunneling Spectroscopy

“…More interestingly, the transformation of the wave functions in a magnetic field could be observed in real space. While 0D and 1D systems did not show pronounced changes due to the relatively large confinement, a distinct change has been observed for 2D [29] and 3D [30]. In both cases, serpentine structures exhibiting strong corrugation appear as shown in Fig.…”