If a 2D metal, also known as a quantum Hall system (QHS), is cooled down to not-too-low temperature, its electrical properties are strongly influenced by lattice vibrations (acoustic phonons). Surprisingly, even though phonons of all different energies below the thermal energy are present, electrons chose to respond to the most energetic phonons they can scatter off. In a magnetic field, electrons’ motion becomes quantized into equally spaced levels and scattering off such phonons is most effective when the phonon energy equals the integer multiple of the inter-level spacing. This leads to oscillations of electrical resistance with magnetic field. We have studied QHS driven by high electrical current in a wide range of temperatures. First, we have demonstrated the possibility to tune and enhance acoustic phonon resonances by dc current. Second, we have observed a prominent peak which emerges when electrons “break the sound barrier”, i.e. when their drift velocity passes through the speed of sound. Finally, unrelated to acoustic phonons, we have demonstrated that dc current can induce a novel state with zero- differential resistance which appears to be an analog of microwave-induced zero resistance states discovered in QHS a few years ago. Nonlinear Transport in Quantum Hall Systems (QHS) Michael A. Zudov, University of Minnesota, DMR Zhang, Zudov, Pfeiffer, West, Physical Review Letters 100, (2008) (a) Differential resistivity vs. dimension- less electric field at magnetic fields from 1 kG to 4 kG in 0.1 kG steps. Some traces (blue) show minima where one normally expects maxima (red). (b) Differential resistance in the magnetic field – dc current plane shows maxima (dark) where conditions for both enhanced phonon and impurity scattering are satisfied (double resonances). (c) At lower temperatures differential resistance might virtually vanish over the finite range of magnetic and electric fields, forming zero- differential resistance state (ZdRS). (a) (b) (c)

Nonlinear Transport in Quantum Hall Systems (QHS) Michael A. Zudov, University of Minnesota, DMR Education: Graduate students: H.-S. Chiang A. Hatke W. Zhang (graduating in 2008). Undergraduate students: Nicholas Eggert ( ) Emily Gras (2007 NSF REU program) Bryan Perfetti ( UROP Program) Students received training in cryogenic, vacuum, and microwave technologies, device nanofabrication, measurement techniques, data acquisition and analysis, programming, and web development. To date, students delivered twelve presentations about their research at conferences, seminars, and Open House events for incoming students. Societal Impact: Understanding electronic devices based on GaAs, one of the most technologically important semiconductors, contributes to advances in device fabrication, making possible applications ranging from fast transistors for cellular phones to lasers for compact disc players. Results were reported at the following conferences: HMF-18, Sao Pedro, Brazil (2008) NanoPeter-2008, St. Petersburg, Russia (2008) QPEQHS, MPIPKS, Dresden, Germany (2008) APS March Meeting, New Orleans (2008) Forschungszentrum, Karlsruhe, Germany (2007) EP2DS-17, Genova, Italy (2007) EPQHS-2, State College, Pennsylvania (2007) APS March Meeting, Denver, Colorado (2007) QHYST06, MPIPKS, Dresden, Germany (2006) More information is available at the group website: