According to Bohr's complementarity principle 1 , a particle possesses wave-like properties only when the different paths the particle may take are indistinguishable. In a canonical example of a two-path interferometer with a which-path detector, observation of interference and obtaining which-path information are mutually exclusive 2,3 . Such duality has been demonstrated in optics with a pair of correlated photons 4 and in solid-state devices with phasecoherent electrons 5 . In the latter case, which-path information was provided by a charge detector embedded near one path of a two-path electron interferometer 5 .Note that suppression of interference can always be understood either as obtaining path information or as unavoidable back action by the detector 3 . The present study reports on dephasing of an Aharonov-Bohm (AB) ring interferometer 6 via a coupled charge detector adjacent to the ring. In contrast to the two-path interferometer, charge detection in the ring does not always provide path information. Indeed, we found that the interference was suppressed only when path information could be acquired, even if only in principle. This demonstrates that dephasing does not always take place by coupling the 'environment' to the interfering particle: path information of the particle must be available too. Moreover, this is valid regardlessof the strength of environment-interferometer coupling, which refutes the general notion of the effect of strong interaction with the environment 7 . In other words, it verifies that an acquisition of which-path information is more fundamental than the back-action in understanding quantum mechanical complementarity. Recently, a series of electronic 'which-path' experiments have been performed in mesoscopic solid-state devices. 5 The devices, fabricated in the plane of a highmobility two-dimensional electron gas (2DEG), were based on a double-path interferometer, consisting of an open Aharonov-Bohm (AB) ring, with a source and a drain of electrons weakly coupled to the open ring 5 . In one path of the interferometer a coherent quantum dot (QD) was embedded 5-6,8 , being electrostatically coupled to a quantum-point-contact (QPC) charge detector (in the immediate proximity to the QD).An electron trapped in the QD modified the conductance of the nearby QPC and thus allowed charge detection by the QPC 5,[9][10][11] . Being an open geometry, with multiple grounded drains (bases) along the paths of the electron, assured that only two paths interfered while the backscattered electrons were drained out by the grounded bases.Thus, the detection of a charge inside the QD (by the QPC) provided path information,

A new consistent approach to forming the 0.7 structure by using a quantum dot rather than a quantum point contact is demonstrated. With this new scheme, it was possible to tune on and off the 0.7 structure. The new 0.7 structure continuously evolved into a normal integer conductance plateau by varying the tuning condition. Unlike the conventional 0.7 plateau, the new 0.7 structure was observed even at low electron temperatures down to 100 mK, with unprecedented flatness.From our results, it is concluded that electron interference as well as the electron interaction effect should be taken into consideration to explain the 0.7 structure.

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One of the points at issue with closed-loop-type interferometers is beating in the Aharonov-Bohm (AB) oscillations. Recent observations suggest the possibility that the beating results from the Berry-phase pickup by the conducting electrons in materials with the strong spin-orbit interaction (SOI). In this study, we also observed beats in the AB oscillations in a gate-defined closed-loop interferometer fabricated on a GaAs/AlGaAs two-dimensional electron-gas heterostructure. Since this heterostructure has very small SOI, the picture of the Berry-phase pickup is ruled out. The observation of beats in this study, with the controllability of forming a single transverse subband mode in both arms of our gate-defined interferometer, also rules out the often-claimed multiple transverse subband effect. It is observed that nodes of the beats with an h/2e period exhibit a parabolic distribution for varying the side gate. These results are shown to be well interpreted, without resorting to the SOI effect, by the existence of two-dimensional multiple longitudinal modes in a single transverse subband. The Fourier spectrum of measured conductance, despite showing multiple h/e peaks with the magnetic-field dependence that are very similar to that from strong-SOI materials, can also be interpreted as the two-dimensional multiple-longitudinal-modes effect