Time domain capacitance spectroscopy of tunneling electrons in the two-dimensional electron gas

We have developed a technique capable of measuring the tunneling current into both localized and conducting states in a 2D electron system (2DES). The method yields I-V characteristics for tunneling with no distortions arising from low 2D in-plane conductivity. We have used the technique to determine the pseudogap energy spectrum for electron tunneling into and out of a 2D system and, further, we have demonstrated that such tunneling measurements reveal spin relaxation times within the 2DEG. Pseudogap: In a 2DEG in perpendicular magnetic field, a pseudogap develops in the tunneling density of states at the Fermi energy. We resolve a linear energy dependence of this pseudogap at low excitations. The slopes of this linear gap are strongly field dependent. No existing theory predicts the observed behavior. Spin relaxation: We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2DES. For most 2D Landau level filling factors, we find that electrons tunnel with a single, well-defined tunneling rate. However, for spin-polarized quantum Hall states (ν=1, 3 and 1/3) tunneling occurs at two distinct rates that differ by up to two orders of magnitude. The dependence of the two rates on temperature and tunnel barrier thickness suggests that slow in-plane spin relaxation creates a bottleneck for tunneling of electrons.     

NMR study of the dynamics of 3He impurities in the proposed supersolid state of solid 4He

The dynamics of (3)He atoms in solid (4)He have been investigated by measuring the NMR relaxation times T(1) and T(2) in the region where a significant nonclassical rotational inertia fraction has been reported. For (3)He concentrations x(3)=16 and 24 ppm, changes are observed for both the spin-lattice relaxation time T(1) and the spin-spin relaxation time T(2) at the temperatures corresponding to the onset of the nonclassical rotational inertia fraction and, at lower temperatures, to the (3)He-(4)He phase separation. The magnitudes of T(1) and T(2) at temperatures above the phase separation agree roughly with existing theory based on the tunneling of (3)He impurities in the elastic strain field due to isotopic mismatch. However, a distinct peak in T(1) and a less well-resolved feature in T(2) are observed near the reported nonclassical rotational inertia fraction onset temperature, in contrast to the temperature-independent relaxation times predicted by the tunneling theory.     

立方相Ag3PO4(111)面原子几何及弛豫结构的第一性原理计算

采用平面波超软赝势方法研究了立方相Ag3PO4(111)面的表面能和表面原子弛豫结构.首先对Ag3PO4(111)面的八种不同原子终止结构的体系总能量进行计算,结果表明B种表面模型被证实为最稳定的(111)面原子几何结构.针对该表面结构,探讨了表面能和原子弛豫与模型中原子层数和真空厚度的关系,当原子层数为24层,真空厚度为0.6 nm时,表面能收敛于1.41 J/m2(LDA-CAPZ)和1.39 J/m2(GGA-PBE).表面原子弛豫后,表面两个三配位的Ag原子均向里移动,超过0.06 nm,而表面次层的O原子则均向外移动约0.0042 nm,导致弛豫后暴露在最表面的是O原子,同时表面原子的核外电子向表面内部发生转移,结构趋于稳定.这些结果为进一步深入研究Ag3PO4表面的光催化活性起源提供理论支持.     

立方相Ag_3PO_4(111)面原子几何及弛豫结构的第一性原理计算

采用平面波超软赝势方法研究了立方相Ag_3PO_4(111)面的表面能和表面原子弛豫结构.首先对Ag_3PO_4(111)面的八种不同原子终止结构的体系总能量进行计算,结果表明B种表面模型被证实为最稳定的(111)面原子几何结构.针对该表面结构,探讨了表面能和原子弛豫与模型中原子层数和真空厚度的关系,当原子层数为24层,真空厚度为0.6 nm时,表面能收敛于1.41 J/m2(LDA-CAPZ)和1.39 J/m2(GGA-PBE).表面原子弛豫后,表面两个三配位的Ag原子均向里移动,超过0.06 nm,而表面次层的O原子则均向外移动约0.0042 nm,导致弛豫后暴露在最表面的是O原子,同时表面原子的核外电子向表面内部发生转移,结构趋于稳定.这些结果为进一步深入研究Ag_3PO_4表面的光催化活性起源提供理论支持.     

Dissipative quantum-creep studies in single-crystal La2CuO4+δ

Temperature-dependent magnetic relaxation was studied in a La₂CuO_4+δ crystal in the low-temperature range 2–10 K. The experimental data exhibited a non-vanishing magnetic relaxation in the low-temperature limit. These data could be well interpreted by a quantum-creep theory, suggesting the non-vanishing relaxation at low temperatures due to quantum tunneling of vortices. The effective Euclidean action determined as /|d ln M/d ln t| showed a quadratic temperature dependence. The quantitative analysis of the effective Euclidean action yields a classical activation energy, crossover temperature and zero-temperature quantum-tunneling rate.     

Spin relaxation mechanism of hopping transport in a 2D asymmetric quantum dot array

Spin relaxation is studied in the hopping conduction mode in 2D arrays of quantum dots (QDs) with structural asymmetry. It is shown that the absence of the “up-down” symmetry in a QD leads to the emergence of a new spin relaxation mechanism in tunneling in a 2D QD array. The difference in spin relaxation mechanisms for symmetric and asymmetric QDs is demonstrated on the basis of theoretical analysis of an elementary event (jump between two tunnel-coupled dots). It is shown that spin flip during tunneling between QDs is the main spin relaxation mechanism in the transport in dense arrays of QDs in Ge placed in weak (1–10 T) magnetic fields.     

Study of molecular reorientation and quantum rotational tunneling in tetramethylammonium selenate by 1H NMR

1H NMR spin-lattice relaxation time measurements have been carried out in [(CH3)4N]2SeO4 in the temperature range 389-6.6 K to understand the possible phase transitions, internal motions and quantum rotational tunneling. A broad T1 minimum observed around 280 K is attributed to the simultaneous motions of CH3 and (CH3)4N groups. Magnetization recovery is found to be stretched exponential below 72 K with varying stretched exponent. Low-temperature T1 behavior is interpreted in terms of methyl groups undergoing quantum rotational tunneling.     

Nonexponential proton relaxation for tunneling of NH+4 in the rotating frame

Proton spin-lattice relaxation times T₁ and T_1θ have been measured in NH₄IO₄ between 150 K and 50 K. The relaxation in the rotating frame was strongly nonexponential between 70 K and 53 K, which supports the tunneling assisted relaxation model of NH⁺₄ in the rotating frame. The tunneling frequency was determined to be $\text{Λ}{}_0\text{2Π}\text{=1.5 MHz}$.     

Spin transport and relaxation in graphene

We review our recent work on spin injection, transport and relaxation in graphene. The spin injection and transport in single layer graphene (SLG) were investigated using nonlocal magnetoresistance (MR) measurements. Spin injection was performed using either transparent contacts (Co/SLG) or tunneling contacts (Co/MgO/SLG). With tunneling contacts, the nonlocal MR was increased by a factor of ∼1000 and the spin injection/detection efficiency was greatly enhanced from ∼1% (transparent contacts) to ∼30%. Spin relaxation was investigated on graphene spin valves using nonlocal Hanle measurements. For transparent contacts, the spin lifetime was in the range of 50-100 ps. The effects of surface chemical doping showed that for spin lifetimes in the order of 100 ps, charged impurity scattering (Au) was not the dominant mechanism for spin relaxation. While using tunneling contacts to suppress the contact-induced spin relaxation, we observed the spin lifetimes as long as 771 ps at room temperature, 1.2 ns at 4 K in SLG, and 6.2 ns at 20 K in bilayer graphene (BLG). Furthermore, contrasting spin relaxation behaviors were observed in SLG and BLG. We found that Elliot-Yafet spin relaxation dominated in SLG at low temperatures whereas Dyakonov-Perel spin relaxation dominated in BLG at low temperatures. Gate tunable spin transport was studied using the SLG property of gate tunable conductivity and incorporating different types of contacts (transparent and tunneling contacts). Consistent with theoretical predictions, the nonlocal MR was proportional to the SLG conductivity for transparent contacts and varied inversely with the SLG conductivity for tunneling contacts. Finally, bipolar spin transport in SLG was studied and an electron-hole asymmetry was observed for SLG spin valves with transparent contacts, in which nonlocal MR was roughly independent of DC bias current for electrons, but varied significantly with DC bias current for holes. These results are very important for the use of graphene for spin-based logic and information storage applications.     

Long-distance super-exchange and quantum magnetic relaxation in a hybrid metal–organic framework

The hybrid metal–organic framework [(CH3)2NH2]Fe(HCOO)3with a perovskite-like structure exhibits a variety of unusual magnetic behaviors at low temperatures. While the long-distance super-exchange through the Fe-O–CH-O–Fe exchange path leads to a canted antiferromagnetic ordering at TN～ 19 K, a second transition of magnetic blocking develops at TB～ 9 K. The stair-shaped magnetization hysteresis loops below TBresemble the behaviors of resonant quantum tunneling of magnetization in single-molecular quantum magnets. Moreover, the magnetic relaxation also exhibits several features of resonant quantum relaxation, such as the exponential law with a single characteristic relaxation time, and the nonmonotonic dependence of relaxation rate on the applied magnetic field with a much faster relaxation around the resonant fields. The origin of quantum tunneling behaviors in the [(CH3)2NH2]Fe(HCOO)3metal–organic framework is discussed in terms of magnetic phase separation due to the modification of hydrogen bonding on the long-distance super-exchange interaction.     

Spin-lattice relaxation of deuterated methyl groups: Implications of the pauli principle

The high-field spin-lattice relaxation of deuterated methyl groups undergoing rotational tunneling is investigated theoretically. It is found that for systems showing a tunneling frequency comparable to accessible Larmor frequencies the relaxation to equilibrium of the Zeeman energy does not follow a simple exponential time dependence even in powdered samples due to a finite coupling to the relaxation of the tunneling system. This finding contrasts to the high-temperature behavior of reorienting methyl groups which undergo simple exponential relaxation. The nonexponentiality has its origin in the statistical coupling of the three deuteron spins due to the Pauli principle.     

Electrical pump-and-probe study of spin singlet-triplet relaxation in a quantum dot

Spin relaxation from a triplet excited state to a singlet ground state in a semiconductor quantum dot is studied by employing an electrical pump-and-probe method. Spin relaxation occurs via co-tunneling when the tunneling rate is relatively large, confirmed by a characteristic square dependence of the relaxation rate on the tunneling rate. When co-tunneling is suppressed by reducing the tunneling rate, the intrinsic spin relaxation is dominated by spin-orbit interaction. We discuss a selection rule of the spin-orbit interaction based on the observed double-exponential decay of the triplet state.     

Tunneling migrational polarization in dielectrics

The effect of tunneling accompanying volume-charge relaxation is analyzed. The Fokker-Planck equation, in which tunneling transitions are taken into account in the diffusion coefficient and the mobility in the quasiclassical approximation for rectangular potential barriers, is derived from the condition of transitions of the relaxation oscillators between neighboring states. The distribution of the volume charge was found by solving simultaneously the Fokker-Planck and Poisson equations by the small-parameter method with auxiliary contacts on the electrodes. The region of non-Debye dispersion was determined by taking into account the tunneling of relaxation oscillators. Formulas for calculating the complex dielectric constant were derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 71–75, November, 1990.     

An effective stochastic excitation strategy for finding elusive NMR signals from solids

The versatility of using a stochastic pulse sequence to elucidate peaks with a wide range of shifts, peak widths, and T(1) relaxation times is demonstrated. A stochastic sequence is combined with high speed magic angle spinning (MAS) to obtain the broad and largely shifted peak associated with (31)P in LiNiPO(4). A stochastic sequence is also used to obtain a spectrum of 85% H(3)PO(4), which has a much longer T(1) value. The signal-to-noise was comparable for spectra of 85% H(3)PO(4) obtained with either a stochastic sequence or an optimized Ernst angle experiment. Experimental parameters for the stochastic experiment are set depending only on the ringdown of the probe and not on any inherent qualities of the sample. A stochastic sequence, therefore, combined with MAS provides a useful strategy for finding peaks with unknown T(1) relaxation constants, peak widths, and shifts.     

Tunneling measurement of a single quantum spin

Measurement of the tunneling current of spin-polarized electrons via a molecule with a localized spin provides information on the orientation of that spin. We show that a strong tunneling current due to the shot noise suppresses the spin dynamics, such as the spin precession in an external magnetic field, and the relaxation due to the environment (quantum Zeno effect). A weak tunneling current preserves the spin precession with the oscillatory component of the current of the same order as the noise. We propose an experiment to observe the Zeno effect in a tunneling system and describe how the tunneling current may be used to read a qubit represented by a single spin 1/2.     

Simple theory of superparamagnetism and spin-tunneling in Mössbauer spectroscopy

The magnetic relaxation of isolated small (< 100 Å) monodomain magnetic particles is due to superparamagnetic relaxation (predominant at high temperatures) and eventually quantum tunneling of the magnetic moment (at low temperatures). The superparamagnetic relaxation process can be formally described by an (multiple phonon absorption and emission) Orbach process with an anisotropy Hamiltonian due to crystalline or form anisotropy \widehat_Ion = S² _z and a usual dynamical spin-Hamiltonian for the spin--phonon interaction. From this Mössbauer spectra can be calculated using ab-initio or stochastic methods. Phonon-assisted tunneling and its influence on Mössbauer spectra are discussed.     

Quantum-classical reentrant relaxation crossover in Dy2Ti2O7 spin ice

We have studied spin relaxation in the spin ice compound Dy2Ti2O7 through measurements of the ac magnetic susceptibility. While the characteristic spin-relaxation time (tau) is thermally activated at high temperatures, it becomes almost temperature independent below T(cross) approximately 13 K. This behavior, combined with nonmonotonic magnetic field dependence of tau, indicates that quantum tunneling dominates the relaxational process below that temperature. As the low-entropy spin ice state develops below T(ice) approximately 4 K, tau increases sharply with decreasing temperature, suggesting the emergence of a collective degree of freedom for which thermal relaxation processes again become important as the spins become strongly correlated.     

Transient optical absorption and luminescence in Li2B4O7 lithium tetraborate

This paper reports on a study of the transient optical absorption exhibited by Li₂B₄O₇ (LTB) in the visible and UV spectral regions. Using absorption optical spectroscopy with nanosecond time resolution, it is established that the transient optical absorption (TOA) in these crystals originates from optical transitions in hole centers and that the kinetics of the optical-density relaxation is controlled by interdefect tunneling recombination, which involves these hole centers and electronic Li⁰ centers representing neutral lithium atoms. At 290 K, the Li⁰ centers migrate in a thermally stimulated, one-dimensional manner, without carrier ejection into the conduction or valence band. The kinetics of the pulsed LTB cathodoluminescence is shown to be controlled by a relaxation process connected with tunneling electron transfer from a deep center to a small hole polaron migrating nearby, a process followed by the formation of a self-trapped exciton (STE) in an excited state. Radiative annihilation of the STE accounts for the characteristic σ-polarized LTB luminescence at 3.6 eV, whose kinetics is rate-limited by the tunneling electron transfer.     

Magnetotunneling relaxation of electrons in double quantum wells

Electron tunneling relaxation in double quantum wells subject to a transverse magnetic field is studied. The resonant peaks in the tunneling relaxation rate appear when the energy splitting Δ of the tunnel-coupled pair of the left- and right- well electron states is a multiple of the cyclotron energy ℏω_c and two series of the Landau levels coincide. The shape of such resonant oscillations of the relaxation rate is determined by the Landau levels' broadening (which is associated with the intrawell scattering in the case of small tunnel coupling), but it is not expressed through the electron density of states directly. The dependence of the tunneling relaxation rate on ℏω_c and Δ is calculated taking into account elastic scattering of the electrons by the inhomogeneities of the structure in the limit when the scattering potential is slowly changing on the magnetic length scale.     

Interaction of two-level tunneling system with phonons

Properties of two-level tunneling system which interacts with lattice vibrations are discussed in the framework of the polaron theory and the phase space approach. The decrease of the dynamic distortion of the lattice with increasing ratio η of the rigid-lattice tunneling matrix element to the small polaron binding energy is calculated in the intermediate coupling regime 0 < η < 2. A relatively sharp transition from the distorted to the undistorted state of the lattice takes place when η crosses the value 2. The expressions for the renormalized tunneling matrix element and for the longitudinal relaxation time T₁ are derived. A two-level tunneling model in which the double-well potential is asymmetric is also investigated.