Universality of bias- and temperature-induced dephasing in ballistic electronic interferometers

Abstract

We performed a transport measurement in a ballistic Aharonov-Bohm ring and a Fabry-Pérot-type interferometer. In both cases we found that the interference signal is reversed at a certain bias voltage and that the visibility decays exponentially as a function of temperature, being in a strong analogy with recent reports on the electronic Mach-Zehnder interferometers. By analyzing the data including those in the previous works, the energy scales that characterize the dephasing are found to be dominantly dependent on the interferometer size, implying the presence of a universal behavior in ballistic interferometers in both linear and non-linear transport regimes.PACS numbers: 73.23. Ad, 71.10.Pm, 85.35.Ds, 03.65.Yz Electron interference has been the central issue in mesoscopic physics since 1980's, which has been promoting our understanding on the phase and coherence of electrons in solids [1]. Recently, an electronic MachZehnder interferometer (MZI) [2] is invoking considerable interest for its possibility to create electron entanglement by two-particle interference [3,4]. This MZI relies on the edge channel transport as it requires chirality of the electron beam, which is also an advantage as the coherence length of the edge electrons is expected to be long. Several experimental works on MZI [2,5,6,7], however, reported that the interference visibility, a measure of coherence, decreases exponentially as the temperature increases. Furthermore, the experimentalists found [5,7,8,9] the so-called "lobe structure", an unexpected phase reversal in the visibility at a certain bias voltage.Several theoretical attempts [10,11,12,13] have tried to explain the observed small energy scales that characterize the lobe structure as well as its drastic temperature dependence. The Coulomb interaction was proposed to be responsible for the observed energy scale proportional to the inverse of the size of MZI [11,12,13]. It is, however, still unclear whether or not the above observations are specific to MZI. Indeed, some theories [12,13] suggest that similar effects may occur in other ballistic interferometers. To investigate this possibility constitutes the central motivation of the present experimental work.Here we report the conductance measurements for an Aharonov-Bohm ring (ABR) around zero magnetic fields and for a Fabry-Pérot-type interferometer (FPI) in the integer quantum Hall (IQH) regime. In both cases, we observed the lobe-like structure and the exponential decay of the visibility with temperature, akin to those in MZI. By analyzing the present data as well as those obtained in previous works, the characteristic energy scales of the two effects are found to dominantly depend on the interferometer size. Figure 1a shows the atomic force microscope (AFM) image of the ABR fabricated by local oxidation using an AFM [14] on a GaAs/AlGaAs heterostructure twodimensional electron gas (2DEG) (the electron density 3.7 × 10 11 cm −2 and the mobility 2.7 × 10 5 cm 2 /Vs) [15]. Measurements were performed around zero magnetic field...

Temperature- and current-dependent dephasing in an Aharonov-Bohm ring

“…14,15 A number of experiments have measured the dephasing rate in ballistic quantum dots [16][17][18][19][20] and rings. [21][22][23][24] The dephasing rate is extracted from the temperature ͑T͒ dependence of the AB oscillation amplitude. For ballistic rings, it is found that the AB amplitude ⌬R AB decrease with T according to the relationship ⌬R AB ϰ exp͑− L / ͑T͒͒.…”

Quantum Coherence Engineering in the Integer Quantum Hall Regime

“…In particular, the Gaussian envelop of the visibility V / expðÀV 2 =2V 2 l Þ revealed in Ref. [11] and also observed in Fabry-Pérot interferometers [13] has not been accounted for. In Fig.…”

“…However, these electronic versions of optical experiments suffer from one major problem: an electron carries a charge with which it interacts with the surrounding world, leading to a finite quantum coherence length and a finite energy exchange length. Recently, both lengths have been measured in the IQH regime at a filling factor 2, definitively showing the role of the interaction between the inner and outer edge state [2,3,10].While the dependence of the coherence length with temperature has been clearly identified to result from the thermal charge noise in the neighboring edge state [3], it has not yet been possible to clearly identify the role of energy exchanges on the repeatedly observed but poorly understood Gaussian shape of the visibility as a function of the bias voltage [11][12][13]. It has been demonstrated recently that the energy exchange between the edge states, which form at a filling factor 2, can be frozen by opening a gap in the excitations of the inner edge state (IES).…”

“…While the dependence of the coherence length with temperature has been clearly identified to result from the thermal charge noise in the neighboring edge state [3], it has not yet been possible to clearly identify the role of energy exchanges on the repeatedly observed but poorly understood Gaussian shape of the visibility as a function of the bias voltage [11][12][13]. It has been demonstrated recently that the energy exchange between the edge states, which form at a filling factor 2, can be frozen by opening a gap in the excitations of the inner edge state (IES).…”

Scanning gate spectroscopy of transport across a quantum Hall nano-island

“…In open systems, i.e. when the conductance of the device σ is much larger than 2e 2 / h, electronic analogues of Mach-Zehnder [3][4][5] and Fabry-Pérot [6][7][8][9][10][11] interferometers have made it possible to study and control electron dephasing processes within ES and to estimate the electron phase coherence length [4,5,12]. In particular, McClure et al [7] used interference checkerboard patterns generated in a Fabry-Pérot geometry to determine the edge state velocity in the quantum Hall regime.…”