Temperature Distribution in Two-Dimensional Electron Gases under a Strong Magnetic Field NAOMI HIRAYAMA, 1,7 AKIRA ENDO, 2 KAZUHIRO FUJITA, 2 YASUHIRO HASEGAWA, 3 NAOMICHI HATANO, 1 HIROAKI NAKAMURA, 4 RY  OEN SHIRASAKI, 5 and KENJI YONEMITSU 6 1.—Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan. 2.—Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan. 3.—Department of Environmental Science and Technology, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan. 4.—Funda- mental Physics Simulation Research Division, National Institute for Fusion Science, Oroshi-cho, Toki, Gifu 509-5292, Japan. 5.—Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan. 6.—Institute for Molecular Science, National Institutes of Natural Sciences, 38 Nishigo-Naka, Myodaiji, Okazaki 444-8585, Japan. 7.—e-mail: n-hira@iis.u-tokyo.ac.jp Two-dimensional electron gases having an electrochemical potential gradient under a magnetic field are numerically examined using the finite-difference method. The temperature, voltage, electric current, and heat flux are calcu- lated from transport equations describing thermoelectric and thermomagnetic effects, namely the Hall, Nernst, Ettingshausen, and Righi–Leduc effects. The results show that a magnetic field distorts equipotential lines and generates an uneven temperature distribution. In particular, a part of the system is found to become colder than the temperature of the heat baths. The cooling effect under a strong magnetic field is due primarily to the Ettingshausen and Hall effects. Key words: Thermoelectric power, thermomagnetic effect, Ettingshausen effect, two-dimensional electron gas, quantum Hall system, finite-difference method INTRODUCTION The thermoelectric and thermomagnetic phe- nomena 1–4 have been recognized as efficient tools for obtaining detailed information about electron behavior in mesoscopic systems. These phenomena can be more sensitive to the nature of electron gases than electric effects such as the electric conductivity and Hall effect. For instance, Behnia et al. 5 revealed that the Nernst effect exhibits clear quantum oscillation compared with the electric conductivity. Fujita et al. 6 observed the Nernst voltage of a two-dimensional electron gas (2DEG) using the direct Joule heating method, by which they could accurately extract the electron behavior without the influence of phonon drag, at low temperature (40 mK). They found that an unusual Nernst volt- age which is not theoretically expected appears under a strong magnetic field, B > 1.8 T. In a pre- vious study, 7 we simulated the distributions of the temperature T and the voltage / of a 2DEG. The results indicated that the magnetic field B distorts the / contours. A similar phenomenon at room temperature was reported in Ref. 8 . In addition, B produces an uneven distribution of T, where high- and low-temperature parts emerge. Surprisingly, the latter part has temperatures lower than the isothermal boundaries at fixed temperature. This result suggested that the experimental system 6 was heated irregularly under a magnetic field, and moreover that it might be partially cooled in spite of the uniform temperatures at isothermal boundaries. (Received July 3, 2010; accepted October 30, 2010; published online November 25, 2010) Journal of ELECTRONIC MATERIALS, Vol. 40, No. 5, 2011 DOI: 10.1007/s11664-010-1427-6 Ó 2010 TMS 529