We describe the implementation of a scanning Hall probe microscope of outstanding magnetic field sensitivity (∼0.1 G) and unprecedented spatial resolution (∼0.35 μm) to detect surface magnetic fields at close proximity to a sample. Our microscope combines the advantages of a submicron Hall probe fabricated on a GaAs/Al0.3Ga0.7As heterostructure chip and the scanning tunneling microscopy technique for precise positioning. We demonstrate its usefulness by imaging individual vortices in high Tc La1.85Sr0.15CuO4 films and superconducting networks, and magnetic bubble domains.
We have fabricated high-mobility, one-dimensional wires in GaAs-AlGaAs heterostructures and measured the resistance as a function of magnetic field and temperature. Because of the size of the devices and the high mobility, only a few channels carry the current at 35 mK with minimal scattering. Fluctuations in the resistance as a function of magnetic field due to quantum interference are observed for 0 &~, r & 300, where co, is the cyclotron frequency and r is the scattering time, superimposed upon Shubnikov-de Haas oscillations and the Hall eA'ect.PACS numbers: 72. 15.Gd, 72.90.+y, 73.60.Aq It is now technologically feasible to fabricate devices in GaAs-A1GaAs heterostructures which are comparable in width to the electron wavelength, and yet possess high mobility. ' Such devices provide a unique opportunity to investigate the role of quantum interference (QI) and the quantized Hall efrect in transport, because phase coherence is maintained on the length scale of a device, and because the role of current-carrying edge states is exaggerated. The following describes our measurements of the temperature dependence of the magnetoresistance of wires fabricated in modulation-doped GaAs-AlGaAs which vary in length from 700 nm to 4.7 pm, and are estimated to be 220-75 nm wide. The carrier density determined from the Hall eAect is n = (2.0-2.6) x 10'' cm corresponding to a Fermi wavelength of =(2'/n) '~= 50-56 nm, while the mobility p at 4 K is larger than 3.3X10 cm /V s, so that the elastic mean free path L, =hp/ekF is greater than 1.6 pm. Thus, the width of the sample is comparable to an electron wavelength, while the distance between voltage probes is less than L,. Because of quantization in the transverse direction, the current is carried by only a few ( & 8) channels (or transverse subbands) at the Fermi energy with minimal scattering. Consequently, we have measured the electrical resistance associated with a few channels in an electron-wave guide.Fluctuations in the resistance are observed as a function of 0 for 0~co, z.~3 00, where m, is the cyclotron frequency and r is the scattering time, concomitantly with Shubnikov-de-Haas oscillations and the quantum Hall eA'ect. The fluctuations are correlated and the amplitude is so large at 35 mK that negative dynamic resistance is observed. The fluctuations change to a lower frequency of oscillation and smaller amplitude in the extreme magnetic quantum limit where only the N =0 Landau level is filled. We tentatively propose that the fluctuations in the resistance of the wire are due to the Aharonov-Bohm eAect, and that the change in the typical frequency is indicative of change with magnetic field in the width of the distribution of electron trajectories across the waveguide. Recent experiments have demonstrated QI in magnetotransport of disordered metals, and of silicon inversion layers, but have been exclusively concerned with the quasi one-dimensional (QI D) regime L, «L, W & L&, where L is the sample length, W is the width, and L& is the phase coherence length, for ...
We study two kinds of quantum interference effects in transport -the Aharonov-Bohm effect and the weak-localization effect -in quasi-one-dimensional wires and rings to address issues concerning the phase-coherence length, spin-orbit scattering, and the Aux cancellation mechanism which is predicted to be present when the elastic mean free path exceeds the sample width. Our devices are fabricated on GaAs/Al"Gal "As and pseudomorphic Ga"Inl As/Al" In, As heterostructure materials and the experiments carried out at 0.4 -20 K temperatures. In the GaAs/Al"Ga~, As devices which exhibit no significant spin-orbit scattering, we were able to extract a phase-coherence length I& from the amplitude of the Aharonov-Bohm magnetoresistance oscillations in different sized rings. We find it to be in agreement with l& deduced from the weak-localization data in parallel wires when the one-dimensional weaklocalization theory including thegux cancellation mechttnism is used to fit the data. We therefore unambiguously establish that the same l& governs the behavior of the two quantum interference phenomena of Aharonov-Bohm oscillations and weak localization, and that the Aux cancellation is in force. In the pseudomorphic Ga"In, "As/Al"In, "As heterostructure devices which exhibit strong spin-orbit interaction effects, l& exceeds the spin-orbit-scattering length at low temperatures.The amplitude of Aharonov-Bohm oscillations can only be explained by introducing reduction factors due to spin-orbit scattering.
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