Hiroshi Akera

Electronic Processes at the Breakdown of the Quantum Hall Effect.

Microscopic processes giving the energy gain and loss of a two-dimensional electron system in long-range potential fluctuations are studied theoretically at the breakdown of the quantum Hall effect...

Hydrodynamic Equations in Quantum Hall Systems at Large Currents

Hydrodynamic equations (HDEQs) are derived which describe spatio-temporal evolutions of the electron temperature and the chemical potential of two-dimensional systems in strong magnetic fields in states with large diagonal resistivity appearing at the breakdown of the quantum Hall effect. The derivation is based on microscopic electronic processes consisting of drift motions in a slowly-fluctuating potential and scattering processes due to electron-electron and electron-phonon interactions. In contrast with the usual HDEQs, one of the derived HDEQs has a term with an energy flux perpendicular to the electric field due to the drift motions in the magnetic field. As an illustration, the current distribution is calculated using the derived HDEQs.

Spatial distributions of electron temperature in quantum hall systems with compressible and incompressible strips

Spatial distributions of the electron temperature perpendicular to the applied current are obtained in quantum Hall systems with compressible and incompressible strips at low lattice temperatures by solving equations of electron number conservation and energy conservation as well as Poissons equation self-consistently. In the linear-response regime, variations of the electron temperature concentrate in the incompressible strips as the lattice temperature decreases. The electron temperature indicates an anti-symmetric distribution: it becomes lower than the lattice temperature in the side of a sample with a higher electrochemical potential, and higher in the opposite side. Around the breakdown of the quantum Hall effects, the electron temperature becomes much higher than the lattice temperature as the applied current increases. Reflecting the anti-symmetric distribution in the linear-response regime, the rise of the electron temperature is suppressed in the higher potential side with increasing current. I...

Thermohydrodynamics in Quantum Hall Systems

A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron tem...

Self-Consistent Calculation of the Charging Energy in a Quantum Dot Coupled to Leads.

A self-consistent calculation scheme in the Coulomb-blockade regime is formulated to obtain the charging energy required in adding a single electron to a quantum dot which is electrostatically coupled to leads and a gate electrode. This method is applied to the quantum-dot transistor fabricated recently from a double-barrier heterostructure, showing that the electrostatic coupling to leads significantly influences the charging energy of the dot in such devices when the leads are close to the dot and the electron density is high in the leads.

Hydrodynamic Equation for the Breakdown of the Quantum Hall Effect in a Uniform Current.

The hydrodynamic equation for the spatial and temporal evolutions of the electron temperature T e in the breakdown of the quantum Hall effect at even-integer filling factors in a uniform current density j x is derived from the Boltzmann-type equation, which takes into account electron-electron and electron-phonon scattering processes. The derived equation has a drift term, which is proportional to j x and the first spatial derivative of T e . When applied to the spatial evolution of T e in a sample with an abrupt change of the width along the current direction, the equation gives a distinct dependence on the current direction as well as a critical relaxation, in agreement with results of recent experiments.

Extrinsic spin Nernst effect in two-dimensional electron systems

The spin accumulation due to the spin current induced by the perpendicular temperature gradient (the spin Nernst effect) is studied in a two-dimensional electron system (2DES) with spin-orbit interaction by employing the Boltzmann equation. The considered 2DES is confined within a symmetric quantum well with delta doping at the center of the well. A symmetry consideration leads to the spin-orbit interaction which is diagonal in the spin component perpendicular to the 2DES. As origins of the spin current, the skew scattering and the side jump are considered at each impurity on the center plane of the well. It is shown that, for repulsive impurity potentials, the spin-Nernst coefficient changes its sign at the impurity density where contributions from the skew scattering and the side jump cancel each other out. This is in contrast to the spin Hall effect in which the sign change of the coefficient occurs for attractive impurity potentials.

Electron Temperature Distribution and Hot Spots in Quantum Hall Systems

The spatial variations of the electron temperature in the vicinity of metallic current contacts in a quantum Hall system are calculated based on thermohydrodynamics with an energy gain. It is shown that, at large currents, hot spots with high electron temperatures appear at diagonally opposite corners of a sample. At small currents, however, the electron temperature at one of the corners is lower than the lattice temperature, while that at the other corner is higher than the lattice temperature. As a function of the chemical potential, the electron temperature at each corner shows quantum oscillations.

Spatial Distributions of Electron Temperature in Quantum Hall Systems with Slowly-Varying Confining Potentials

Spatial distributions of the electron temperature perpendicular to the applied current in quantum Hall systems with slowly-varying confining potentials are calculated in the linear-response regime by employing hydrodynamic equations for number conservation and energy conservation. The electron temperature exhibits spatial pattern, reflecting the confining potential, along the Hall field induced by the current. The local electron temperature shows oscillations as a function of the filling factor. Such spatially dependent electron temperature causes a certain change in distributions of the current density and the current-induced potential even in the linear-response regime.

Aharonov-Bohm Effect in Quantum Dots

The Aharonov-Bohm oscillations of the conductance through two quantum dots in parallel is studied theoretically in the limit of large one-electron level separations in each dot. An electron tunnels through a single energy level in each dot, which is closest to the chemical potential (µ) of the emitter and collector electrodes. It is assumed that the level in the first dot is well above µ, while that in the second dot is close to µ. The conductance is calculated by solving the equations of motion for the Green function at temperatures higher than the level broadening due to tunneling. It is shown that the ratio of an oscillating component to a nonoscillating component of the conductance in this case is not changed by the interaction at the second dot.