Importance of complex band structure and resonant states for tunneling

The paper aims at understanding the tunneling process in epitaxial magnetic tunnel junctions. Firstly, we stress the importance of the complex band structure of the insulator for the tunneling of the metal electrons. For large insulator thicknesses the tunneling current is carried by very few states, i.e., those states in the gap of the semiconductor having the smallest imaginary component of the k-vector. In the case of GaAs, ZnSe and MgO these are Δ₁-states at the -point. Secondly, we discuss the role of resonant interface states for tunneling. Based on simple model calculations and ab initio results we demonstrate that for symmetrical barriers the minority conductance can be dominated in an intermediate thickness range by few ‘hot spots’ in the surface Brillouin zone, arising from resonant interface states. In these hot spots full transmission can still be obtained, when all other states are already strongly attenuated, so that the usual exponential decay can be considerably delayed.     

Resonant tunneling,eigenvalue and energy band calculation for potential and periodic potential structures

Recursion formulae for the reflection and the transmission probability amplitudes and the eigenvalue equation for multistep potential structures are derived. Using the recursion relations, a dispersion equation for periodic potential structures is presented. Some numerical results for the transmission probability of a double barrier structure with scattering centers, the lifetime of the quasi-bound state in a single quantum well with an applied field, and the miniband of a periodic potential structure are presented.     

一维时间周期势的量子隧穿

研究了一维时间周期势的量子隧穿,建立了周期势的两种物理模型,并分别在不同情况下对其进行理论研究和推导,证明了一维周期势下的量子隧穿可统一由一种模型处理.     

正弦平方势与带电粒子沟道效应的能带结构

在量子力学的框架内描述了带电粒子与晶体相互作用，利用正弦平方势把沟道粒子的Schr?dinger方程化为Mathieu方程，根据Bloch定理讨论了系统能量分布，并用摄动法求解了方程的低阶不稳定区及其禁带宽度，系统自动呈现出了能带结构，再现了粒子束同晶体相互作用的周期性特征.而这一点正是其他相互作用势不曾有的. 关键词： 沟道效应 能带结构 正弦平方势 摄动法     

Quantum size effects and band structure in InSb

Quantum Size Effects (Q.S.E.) in InSb films have been detected by different experimental procedures.The work function dependence on thickness obtained from photoelectric emission threshold measurements is compared with prior results obtained with the retarding potential method. With both methods, the measured work function values are comparable. They are less than the corresponding bulk values, conforming to current theoretical predictions.The interband energy gap has been determined from photoelectric absorption band edge data: its value differs with respect to the bulk one, by the location of the first allowed energy subband in the conduction band due to the presence of Q.S.E.Some evidence is given for absence of a band structure dependence on Q.S.E.     

Energy gap in tunneling spectroscopy: Effect of the chemical potential shift

We study the effect of a shift of the chemical potential level on the tunneling conductance spectra. In the systems with gapped energy spectra, significant chemical-potential dependent distortions of the differential tunneling conductance curves, dI/dV, arise in the gap region. An expression is derived for the correction of dI/dV, which in a number of cases is found to be large. The sign of the correction depends on the chemical potential level position with respect to the gap. The correction of associated with the dI/dV chemical potential shift has a nearly linear dependence on the tip-sample separation z and vanishes at z → 0.     

Energy band structure of cadmium fluoride

The electronic band structure of cadmium fluoride is calculated by a combined tight binding and pseudopotential method. The band structure is found to be rather similar in shape with that of CaF₂. In particular it is shown that the occupied cationic d⁺ bands do not perturb significantly the upper valence band predominantly composed of the F^-p-orbital. This explains the great similarity of the low energy part of the reflection spectra of CaF₂ and CdF₂.     

Complex band structure and tunneling through ferromagnet /Insulator /Ferromagnet junctions

We investigate the importance of metal-induced gap states for the tunneling of metal electrons through epitaxial insulator films. By introducing an imaginary part kappa to the wave vector in order to describe the decay of the wave function in the insulator, we obtain the complex band structure in the gap region. The spectrum of the decay parameters kappa is calculated for the semiconductors Si, Ge, GaAs, and ZnSe. In most cases, for large enough film thicknesses the tunneling is dominated by states of normal incidence on the interface. Possible exceptions are considered. Based on our conclusions, we discuss the spin-dependent tunneling in Fe/semiconductor/Fe (001) junctions.     

Quantum tunneling: A general study in multi-dimensional potential barriers with and without dissipative coupling

Quantum tunneling is formulated in terms of the time evolution of a localized state and thus shown to be dependent upon the eigenspectrum of the system Hamiltonian. A number of exactly solvable models with local and non-local double-well potentials are discussed, and it is shown how, for local potentials, other solvable models can be generated by using Gelfand-Levitan and Darboux transformations. Tunneling in multi-dimensional potential barriers is investigated under semi-classical approximation by developing the method of asymptotic expansion of the wave function for large quantum numbers and the WKB approximation for separable systems. General expressions for the imaginary-time tunneling trajectory are obtained in both methods and specific applications are discussed. Approximation schemes for non-separable systems are also presented. A general study of dissipative multi-dimensional tunneling is carried out by using the Gisin equation, the Schrödinger-Langevin equation and the complex potential model. It is shown that, in general, different models of dissipation are not equivalent in the tunneling context. Using these models one can show (a) the existence of critical damping beyond which no tunneling can occur, (b) that tunneling trajectories are dependent on the damping constant and (c) that dissipation may stabilize the excited state rather than the ground state. Finally the tunneling time delay in one-dimensional systems for undamped and for dissipative systems is formulated in terms of the phase shift, and this has been used to show that the effect of damping on the time delay is ignorable.     

Quantum tunneling and information entropy in a double square well potential: The ammonia molecule

We study the implications of quantum tunneling on information entropy measures (Shannon and Fisher), disequilibrium and LMC complexity in a Double Square Well Potential (DSWP), using the ammonia molecule as a test bed. We also apply a similar analysis to the Infinite Square Well Potential (ISWP) in order to compare the corresponding results with a system where tunneling is absent. In particular, we show that contrary to the Heisenberg uncertainty product, information-theoretic tools provide a more sensitive analysis and manage to differentiate DSWP from ISWP case, formulating an empirical criterion whether the tunneling effect is present or not.     

Variational calculation of the sine-Gordon effective potential

The Gaussian effective potential of the sine-Gordon model is calculated in 1+1 and 2+1 dimensions. Issues like renormalization, vacuum energy and stability of the vacuum are discussed in detail.     

Quantum tunneling and negative eigenvalues

In the path-integral approach to the decay of a metastable state by quantum tunneling, the tunneling process is dominated by a solution to the imaginary-time equations of motion, called the bounce. In all known cases, the second variational derivative of the euclidean action at the bounce has one and only one negative eigenvalue. This note explains this phenomenon by showing it is an inevitable feature of the bounce for a wide class of systems. This class includes a set of particles interacting through potentials obeying some mild technical restrictions, and also theories of interacting scalar and gauge fields. There may exist solutions in other ways like bounces and which have more than one negative eigenvalue, but, even if they do exist, they have nothing to do with tunneling.     

Quantum tunneling and trace anomaly

We compute the corrections, using the tunneling formalism based on a quantum WKB approach, to the Hawking temperature and Bekenstein–Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawking's original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.     

Quantum tunneling and back reaction

We give a correction to the tunneling probability by taking into account the back reaction effect to the metric of the black hole spacetime. We then show how this gives rise to the modifications in the semiclassical black hole entropy and Hawking temperature. Finally, we reproduce the familiar logarithmic correction to the Bekenstein–Hawking area law.     

Energy band structure of CdSnAs2 and CdGeAs2

The energy band structure of CdSnA₂ and CdGeAs₂2 is calculated by the empirical-pseudopotential method, taking account of spin-orbital interaction. The calculated parameters – E_g = 0.25, _cr = 0.05, _s.o = 0.44 for CdSnAs₂ and E_g = 0.55, _cr = 0.20, and _s.o = 0.33 for CdGeAs₂ (all in eV) — are in good agreement with experiment. The conclusion drawn in a series of experimental works that there are additional minima close to the bottom of the CdSnAs₂ conduction band is not confirmed in the calculation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 78–82, December, 1981.     

A relation between structure and pair potential for liquid metals

We emphasize the importance of considering the relationship between the structure of a liquid and the interatomic potential directly from the point of view of wave vector space (k space). Although the Ornstein-Zernike equation was not originally derived from this point of view, this equation when transformed into the k-space representation has direct physical content, when coupled with a normal mode representation according to the approaches of Pines and Bohm (1952), and Percus and Yevick (1958). These normal modes are defined isothermally, and the relation to the dynamical modes of the liquid is discussed. The use of a simple k-space relationship between the transform of the Ornstein-Zernike direct correlation function and the transform, V_k , of the interatomic potential is explored. This leads to a correspondingly simple relationship between the structure factor and the interatomic potential. It is equivalent to a generalized Debye-Hückel equation and is expected to be valid only under special circumstances; namely, where the potential is long range in a particular sense and the small k behaviour of V_k is dependent mainly upon this long-range behaviour and relatively insensitive to details of the potential at short distances. It is noted that these conditions appear to be met reasonably well for the liquid alkali metals. The comparison of theory and experiment is somewhat uncertain because of incomplete experimental data on the structure factor as well as unresolved theoretical issues.