Direct Spectroscopic Observation of Electrons in Image-Potential States Outside Liquid Helium

Low Temperature Physics

Monarkha

2008

Resonance variations of the in-plane conductivity of surface electrons (SEs) over liquid 3 He induced by microwave (MW) radiation of a fixed frequency are experimentally and theoretically studied for low temperature scattering regimes (T < 0.5 K). The system was tuned to resonance by varying the amplitude of the vertical electric field which shifts the positions of SE Rydberg levels. The line-shape change and reversing of the sign of the effect are found to be opposite to that reported previously for weak vertical electric fields. A theoretical analysis of conductivity of the SE system heated due to decay of electrons excited to the second Rydberg level by the MW explains well the line-shape variations observed. It shows also that shifting the MW resonance into the range of weak vertical fields leads to important qualitative changes in the line-shape of SE conductivity which are in agreement with observations reported previously.

Section: Introductionmentioning

confidence: 99%

“…for liquid 3 He). In an approximation V 0 ® ¥, SE energy levels are spaced similarly to Rydberg levels of a Hydrogen atom: D D l R l = -/ 2 , where l = 12 , ,..., and D R is the corresponding Rydberg energy which are about 7.6 K for liquid 4 He and about 4.2 K for liquid 3 He. The effective Bohr radius of SE Rydberg states a m…”

Section: Introductionmentioning

confidence: 99%

Photoresonance and conductivity of surface electrons on liquid He3

Low Temperature Physics

Monarkha

2008

“…In the asymmetric potential formed by the repulsive surface barrier, the attractive image force and the field E ⊥ , the quantized energies ǫ n (n = 1, 2, ...) of the electron motion normal to the surface define the inter-subband transition frequencies ω n ′ n = (ǫ n ′ − ǫ n )/h. The inter-subband n = 1 → 2 transition is excited using resonant microwave radiation of the angular frequency ω by tuning ω 21 with the field E ⊥ through the linear Stark shift [6].The low-frequency (3 kHz) in-plane magnetoconductivity σ xx [19] is measured in magnetic fields of B < 1 T applied perpendicular to the liquid surface. For these measurements, we employed the capacitivecoupling technique [20] using a Corbino disk that constituted one of the circular plates.…”

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confidence: 99%

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confidence: 99%

Novel Radiation-Induced Magnetoresistance Oscillations in a Nondegenerate Two-Dimensional Electron System on Liquid Helium

2009

Phys. Rev. Lett.

We report the observation of novel magnetoresistance oscillations induced by the resonant intersubband absorption in nondegenerate 2D electrons bound to the surface of liquid 3 He. The oscillations are periodic in B −1 and originate from the scattering-mediated transitions of the excited electrons into the Landau levels of the first subband. The structure of the oscillations is affected by the collision broadening of the Landau levels and by many-electron effects.PACS numbers: 03.67.Lx, 73.25.+i, 78.70.Gq The dynamical response of a two-dimensional electron system (2DES) is strongly affected by the magnetic field applied perpendicular to the 2D plane. In particular, the Landau quantization of the electron energy for the inplane motion alters the transport properties of such systems and often results in oscillations of the electron magnetoresistivity. In degenerate 2DESs in semiconductors, the most well known example of such oscillations is the Shubnikov-de Haas oscillations arising from the sequential passing of Landau levels (LLs) through the Fermi level. Other examples include magnetointersubband oscillations in GaAs quantum wells [1] and microwaveinduced resistance oscillations (MIRO) in GaAs/AlGaAs heterostructures [2,3]. A novel type of resistance oscillation induced by resonant inter-subband absorption in nondegenerate 2DES is the subject of this Letter.Low-density classical 2D electrons formed on the surface of liquid helium are the complement of quantum 2DESs in semiconductors [4,5]. The difference in energy between subbands is small and inter-subband transitions can be excited with resonant millimeter-wave radiation [6]. At high temperatures, the electron in-plane transport is determined by the short-range quasi-elastic scattering from helium vapor atoms, which is similar to the scattering due to disorder in semiconductors. At low temperatures (below 0.3 K for 3 He), the scattering only occurs from surface capillary waves (ripplons). Unique correlation properties of 2DES are observed through the Wigner crystallization [7], quantum tunneling phenomena [8] and inter-subband absorption [9].At high temperatures, the magnetotransport of 2DES on helium is well described by an independent-electron theory based on the self-consistent Born approximation (SCBA) [10]. Below 1 K, the many-electron fluctuating electric field originating from the Coulomb interaction affects the electron scattering in both classically strong and quantizing magnetic fields. This was shown by Dykman et al., who presented a theory for both ripplon [11] and vapor atom scattering [12]. Many-electron effects have also been observed in quantum cyclotron resonance [13].Interest in this system also stems from the proposals for quantum computing using electrons on helium [14,15]. These proposals rely on the robust control of electronic quantum states using resonant microwaves. For such applications, microwave-induced inter-subband absorption has been recently studied for electrons on both liquid 4 He and liquid 3 He [16]. It was shown that ...

“…The microwave (MW) resonance absorption experiment [1] had given the first direct observation of image-potential-induced Rydberg levels outside liquid helium. For weak holding fields E^, positions of surface levels were shown to be well described by the simple formula D D l R l = -/ 2 , where l = 1 2 , , ... , and D R is the corresponding Rydberg energy which is about 7.6 K for liquid 4 He.…”

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confidence: 99%

Microwave absorption saturation and decay heating of surface electrons on liquid helium

Monarkha

Low Temperature Physics

2007

The microwave (MW) resonance absorption and decay heating of surface electrons (SEs) on liquid 4 He are theoretically studied for the vapor atom scattering regime. The decay heating is shown to be an essential occurrence of a MW resonance experiment appearing even at low excitation rates. It strongly affects the occupancies of surface levels and the broadening of resonance lines long before the absorption suturation condition is reached. Contrary to the model of cold SEs usually used for description of the MW resonance, the new theory leads to MW absorption saturation when only a very small fraction of electrons (less than 10%) is left on the ground and the first excited levels. The microwave (MW) resonance absorption experiment [1] had given the first direct observation of image-potential-induced Rydberg levels outside liquid helium. For weak holding fields E^, positions of surface levels were shown to be well described by the simple for-/ 2 , where l = 1 2 , , ... , and D R is the corresponding Rydberg energy which is about 7.6 K for liquid 4 He. Because the dielectric constant of liquid helium e is close to unity (e -1 0 057; . ), the effective Bohr radius of these Rydberg levels,, is large (about 76 C). Therefore, surface electrons (SEs) can move freely along the interface, forming a remarkable two-dimensional (2D) electron liquid, useful for studying many-body effects in a highly correlated 2D electron gas (for a review see [2]).The recent interest in the MW resonance is evoked by experimental development of the idea of using SEs as electronic qubits (see [3] and references there in). These qubits would be controlled by the MW field whose frequency w is close to w 0 2 1tem is tuned to resonance by varying E^). Since the electron potential is anharmonic, it is assumed that coupling to outer levels (l > 2) is negligible, and a simple two-level model is an excellent approximation. As an important achievement in this field, observation of MW absorption saturation of Rydberg states of SEs was reported [3]. The electron decay from the excited surface level to the ground level due to scattering by vapor atoms and ripplons is a negative factor for SE qubits. MW absorption saturation appears when the stimulated absorption (emission) rate r is larger than the decay rate of the first excited level n t 2 1 1 ® º / . The dimensionless parameter rt could be considered as a measure of electron excitation by MW. In the simple model of cold SEs [3], for low excitation rt << 1, the fractional occupancy of the first excited level n 2 is much smaller than that of the ground level n 1 . In this case, power absorbed by electrons from the filed P A increases linear with r, or with the in-put power P in .