Engineering topics

Raikh, M. E.

Publications and source records attributed to Raikh, M. E..

8 records

DOE OSTI2022

Damping of the Franz–Keldysh oscillations in the presence of disorder

Franz–Keldysh oscillations of the optical absorption in the presence of short-range disorder are studied theoretically. The magnitude of the effect depends on the relation between the mean-free path in a zero field and the distance between the turning points in electric field. As is adopted in the literature, turning points are the points where the net energy is equal to potential energy. Damping of the Franz–Keldysh oscillations by the disorder develops at high absorption frequency. Effect of damping is amplified by the fact that, that electron and hole are most sensitive to the disorder near the turning points. This is because, near the turning points, velocities of electron and hole turn to zero.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Landau-Zener transition between two levels coupled to continuum

We report for a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, i, to survive the transition and to remain in the first level, depends exponentially on the square of the tunnel matrix element between the two levels. This result remains valid when the second level, f, is broadened due to e.g. coupling to continuum (Akulin and Schleich (1992) [26]). If the level, i, is also coupled to continuum, albeit much weaker than the level f, a particle, upon surviving the transition, will eventually escape. However, for shorter times, the probability to find the particle in the level i after crossing f is enhanced due to the coupling to continuum. This, as shown in the present paper, is the result of a second-order process, which is an additional coupling between the levels. The underlying mechanism of this additional coupling is virtual tunneling from i into continuum followed by tunneling back into f.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Long-living excited states of a 2D diamagnetic exciton

Hydrogenic excited states of a 2D exciton are degenerate. In the presence of a weak magnetic field, the -states with a zero momentum of the center of mass get coupled to the -states with finite momentum of the center of mass. This field-induced coupling leads to a strong modification of the dispersion branches of the exciton spectrum. Namely, the lower branch acquires a shape of a “mexican hat” with a minimum at a finite momentum. At certain magnetic field, exciton branches exhibit a linear crossing, similarly to the spectrum of a 2D electron in the presence of spin–orbit coupling. While spin is not involved, degenerate and states play the role of the spin projections. Lifting of degeneracy due to diamagnetic shifts and deviation of electron–hole attraction from purely Coulomb suppresses the linear crossing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Interaction effects in graphene in a weak magnetic field

A weak perpendicular magnetic field, B, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. Here we explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that the electron-electron interaction lifetime acquires an anomalous B dependence. Also, the ballistic zero-bias anomaly, δv(ω), where ω is the energy measured from the Fermi level, emerges at a weak B and has the form δv(B) ~ B 2 /ω 2 . Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous. We discuss experimental manifestations of the effects predicted. The microscopic origin of the B-field sensitivity is an extra phase acquired by the electron wave function resulting from the chirality-induced pseudospin precession.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Renormalization of the 3D exciton spectrum by the disorder

Effect of short-range disorder on the excited states of the exciton is studied. Disorder causes an obvious effect of broadening. Microscopically, an exciton, as an entity, is scattered by the large-scale disorder fluctuations. Much less trivial is that short-scale fluctuations, with a period of the order of the Bohr radius, cause a well-defined down-shift of the exciton levels. We demonstrate that this shift exceeds the broadening parametrically and study the dependence of this shift on the orbital number. Difference of the shifts for neighboring levels leads to effective renormalization of the Bohr energy. Most remarkable effect is the disorder-induced splitting of S and P exciton levels. The splitting originates from the fact that disorder lifts the accidental degeneracy of the hydrogen-like levels. We draw an analogy between this splitting and the Lamb shift in quantum electrodynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Size quantization of an exciton: A toy model of the “dead layer”

In this paper, size-quantization levels of an exciton in large nanocrystals is studied theoretically. For the nanocrystal size, L , much bigger than the Bohr radius, a B , the level positions do not depend on a B . The correction to the levels in a small parameter a B / L depends on the reflection phase of the exciton from the boundary. Calculation of this phase constitutes a three-body problem: electron, hole, and the boundary. This calculation can be performed analytically in the limit when the hole is much heavier than the electron. Physically, a slow motion of the hole towards the boundary takes place in the effective potential created by the fast motion of the electron orbiting the hole and touching the boundary. As a result, the hole is reflected before reaching the boundary. The distance of the closest approach of the hole to the boundary (the dead layer) exceeds a B parametrically .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Persistent Friedel oscillations in graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a two-dimensional (2D) graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $\textit{r}$ much larger than the de Broglie wavelength, it decays as 1/$r^3$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is dominant in a parametrically large spatial interval $p^{–1}_0 ≲ r ≲ k_Fl^2$, where $\textit{l}$ is the magnetic length, $k_F$ is Fermi momentum, and $p^{–1}_0 = (k_Fl)^{4/3} /k_F$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. Further, the obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Scattering of electron from a disk in 2D electron gas: Full cross section, transport cross section, and the interaction correction

It is known that the presence of the Fermi sea modifies the scattering of an electron from a point-like impurity. This is due to the Friedel oscillations of the electron density around the impurity. These oscillations create an additional scattering potential for incident electrons. The closer the energy of the incident electron to the Fermi level, the stronger the additional scattering. Here, we study this effect for the case when the impurity is not point-like but rather a hard disk, with a radius much bigger than the de Broglie wavelength. We start with a careful examination of the full and transport cross sections from an extended target. Both cross sections approach their limiting values upon increasing the wave vector of the incident electron. We establish that the transport cross section saturates much faster than the full cross section. With regard to the interaction correction, we establish that it vanishes for the full cross section, while for the transport cross section, it is enhanced compared to the case of a point-like scatterer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗