Observation of largeh/2eoscillations in semiconductor antidot lattices

Abstract

We report the observation of large-amplitude oscillations in the magnetoresistance of a twodimensional electron gas in a GaAs-Al Gaz As heterostructure with an artificially imposed antidot lattice potential. The period of the oscillations is about k/2e as a function of the magnetic 6ux threading through the unit cell of the antidot lattice. The oscillations are definitely visible in the antidot array with a hexagonal lattice configuration, the amplitude reaching 20'Po of the sample resistance, but almost invisible with a square lattice configuration. We believe that the hexagonal lattice potential is suitable for electrons to return to their starting points and to contribute to coherent backscattering. We also show the oscillations cannot be described by the theory for the diffusive regime established by Al'tshuler, Aronov, and Spivak.The resistance of a conductor in the shape of a hollow cylinder oscillates as a function of the magnetic Bux threading through the hollow with a period of b, /2e. This was predicted by Al'tshuler, Aronov, and Spivak (AAS) for the diffusive regime where the mean free path of the electrons is much smaller than the sample size. The conductance amplitude of the oscillations is of the order of e /6 and depends on the phase coherence length over which an electron maintains its phase coherence. The oscillations are caused by coherent backscattering of an electron, where a pair of backscattered partial waves with time-reversal symmetry interfere with each other. This prediction has been proved experimentally by using cylindrical metal films and other geometric structures such as networks.Those experiments were done using polycrystalline metal where electrons move diffusively due to impurity scattering. The amplitudes of the oscillations reported so far have been very small, i.e. , less than 0.1% of the sample resistance.Negative magnetoresistance, which has been observed in the diffusive regime, is also caused by the coherent backscattering of electrons. A recent experiment demonstrated that the negative magnetoresistance emerges even in ballistic microstructures. This can be explained by the semiclassical theory of quantum billiards, where chaotic electron trajectories contribute to the interference. From this theory one may expect that h/2e oscillations should also occur in the magnetoresistance of ballistic microstructures in the shape of a cylinder or network. However, there have been very few experiments showing the existence of the 6/2e oscillations in the ballistic regime.Recently, a two-dimensional electron gas (2DEG) in a GaAs-Al Gai As heterostructure with an artificially imposed two-dimensional array of potential peaks has attracted much attention. In the antidot lattice, the periodic potential is so strong that it forms a two-dimensional array of small depletion regions in the 2DEG plane. When the period of the antidots is smaller than the mean &ee path of electrons, a sequence of peaks appears in the magnetoresistance.The origin of the peaks has been explained with a classical ...

Spin-orbit interaction determined by antilocalization in an InSb quantum well

“…45 A hypothetical origin for the oscillatory magnetoresistance lies in Altshuler-Aronov-Spivak oscillations 46 occurring for electron trajectories encompassing such mesoscopic defects, as also observed in lithographic antidot lattices. 47 In the present case the irregular defect size and spacing preclude welldeveloped oscillations while still allowing for magnetoresistance effects associated with orbits of defined enclosed magnetic flux. AL phenomena do not encompass such oscillatory structure, and hence the structure is ignored for the remainder of the present work.…”

Commensurability effects in hexagonal antidot lattices with large antidot diameters

“…3. Around B = 0, the well-known AltshulerAronov-Spivak oscillations with a period of δB = 8mT are observed (not shown) [13], which evolve into quasiperiodic Aharonov-Bohm type oscillations with a period of δB = 16mT for B > 60mT. The Aharonov-Bohm period corresponds to a characteristic area of A = h/eδB = …”

“…More recently, signatures of the famous fractal energy spectrum of such potentials, also known as the Hofstadter butterfly, have been observed [8,9]. A large fraction of these studies was performed on square [1,2,3,6,8,9,10] or rectangular [11] lattices, while only a few experiments on hexagonal lattices have been published [12,13,14,15]. For the majority of the effects, the lattice type is, in principle, irrelevant.…”

Magnetoresistance of antidot lattices with grain boundaries

“…In hexagonal lattices, a transition from Altshuler-Aronov-Spivak oscillations at small magnetic fields to Aharonov-Bohm oscillations at larger fields has been observed. 9,10,11 Moreover, the longstanding prediction of the Hofstadter butterfly, 12 the fractal energy spectrum of a periodic potential in strong magnetic fields, has been experimentally confirmed in weak periodic superlattices. 13,14,15 Antidots have furthermore been used to demonstrate the quasi-particle character of composite fermions in a very intuitive way.…”