arXiv subjects

M. E. Raikh

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

At least 19 recordsLinked to original sources

arXiv2023

High-temperature magneto-inter-chirality oscillations in 2D systems with strong spin-orbit coupling

Conventional magneto-oscillations of conductivity in three dimensions are washed out as the temperature exceeds the spacing between the Landau levels. This is due to smearing of the Fermi distribution. In two dimensions, in the presence of two or more size-quantization sub-bands, there is an additional type of magneto-oscillations, usually referred to as magneto-inter-sub-band oscillations, which do not decay exponentially with temperature. The period of these oscillations is determined by the condition that the energy separation between the sub-bands contains an integer number of Landau levels. Under this condition, which does not contain the Fermi distribution, the inter-sub-band scattering rate is maximal. Here we show that, with only one sub-band, high-temperature oscillations are still possible. They develop when the electron spectrum is split due to the spin-orbit coupling. For these additional oscillations, the coupling enters both, the period and the decay rate.

cond-mat.mes-hall↗

arXiv2023

Lifshitz model in the presence of spin-orbit coupling

Wave function of a localized state created by a short-range impurity in two dimensions falls off with distance, r, from the impurity as r^{-1/2}exp(-r/a), where "a" is the localization radius. With randomly positioned identical impurities with low concentration, n<<a^{-2}, the level smears into a band due to the overlap of the impurity wave functions. This is the essence of the Lifshitz model. We demonstrate that, upon incorporation of the spin-orbit coupling, the impurity wave functions acquire oscillating factors which, subsequently, modify their overlap. As a result of such modification, the density of states develops singularities at certain energies.

cond-mat.dis-nn↗

arXiv2023

Combined effect of mutually frequency-detuned strong and weak drives on a two-level system: Envelope of the Rabi oscillations

Near-resonant ac-drive acting on a two-level system induces the Rabi oscillations of the level occupations. It is shown that additional weak drive properly frequency-detuned from the primary drive causes a resonant response. This response manifests itself in the emergence of the envelope of the oscillations. At resonance, the inverse period of the envelope is proportional to the amplitude of the weak drive. The resonant condition reads: difference of frequencies between the two drives is equal to the ac-splitting of quasilevels in the field of the strong drive. Technically, the resonance can be inferred from the analogy between the equations for the time-evolution of the spin amplitude and the Mathieu equation, which describes e.g. the parametric resonance.

cond-mat.mes-hall↗

arXiv2023

Effect of the resonant ac-drive on the spin-dependent recombination of polaron pairs: Relation to organic magnetoresistance

The origin of magnetoresistance is bipolar organic materials is the influence of magnetic field on the dynamics of recombination within localized electron-hole pairs. Recombination from the $S$ spin-state of the pair in preceded by the beatings between the states $S$ and $T_0$. Period of the beating is set by the the random hyperfine field. For the case when recombination time from $S$ is shorter than the period, we demonstrate that a {\em weak} resonant ac drive, which couples $T_0$ to $T_+$ and $T_{-}$ affects dramatically the recombination dynamics and, thus, the current A distinctive characteristics of the effect is that the current versus the drive amplitude exhibits a {\em maximum}.

cond-mat.dis-nn↗

arXiv2022

Landau-Zener transition with energy-dependent decay rate of the excited state

A remarkable feature of the Landau-Zener transition is insensitivity of the survival probability to the decay rate, of the excited state. Namely, the probability for a particle, which is initially in the ground state, to remain in the same state is insensitive to decay, which is due to e.g. coupling to continuum [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)]. This insensitivity was demonstrated for the case when the density of states in the continuum is energy-independent. We study the opposite limit when the density of states in the continuum is a step-like function of energy. As a result of this step-like behavior of the density of states, the decay rate of a driven excited level experiences a jump as a function of time at certain moment t_0. We take advantage of the fact that the analytical solution at t t_0 is known. We show that the decay enters the survival probability when t_0 is comparable to the transition time.

cond-mat.mes-hall↗

arXiv2022

Landau-Zener transition between two quantum dots coupled by resonant tunneling

We consider the transition of electron between two quantum dots in which the discrete levels are swept past each other with a constant velocity. If a direct tunneling between the dot levels was allowed, an electron will be transferred between the dots when the levels cross. This transfer is described in terms of the conventional Landau-Zener theory. We assume that direct tunneling between the dots is forbidden. Rather, the transfer is due to the resonant tunneling via a discrete impurity level separating the dots. Then the description of the electron transfer reduces to a threestate (two dots plus impurity) Landau-Zener transition. Transition probability depends on the relative positions of the resonant level and the energy at which the levels cross. It also depends on the left-right asymmetry of tunneling between the impurity and the left(right) dots. We calculate the transition probability in different limits of the horizontal (in space) and vertical (in energy) impurity level positions.

cond-mat.mes-hall↗

arXiv2022

Landau-Zener transition between two levels coupled to continuum

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, {\em 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, {\em f}, is broadened due to e.g. coupling to continuum [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. If the level, {\em i}, is also coupled to continuum, albeit much weaker than the level {\em f}, a particle, upon surviving the transition, will eventually escape. However, for shorter times, the probability to find the particle in the level {\em i} after crossing {\em f} is {\em 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 {\em additional coupling between the levels}. The underlying mechanism of this additional coupling is virtual tunneling from {\em i} into continuum followed by tunneling back into {\em f}.

cond-mat.mes-hall↗

arXiv2022

Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, to survive the transition and to remain in the first level, does not depend on whether or not the second level is broadened [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. In other words, the seminal Landau-Zener result applies regardless of the broadening of the second level. The same question for the multistate Landau-Zener transition is addressed in the present paper. While for integrable multistate models, where the transition does not involve interference of the virtual paths, it can be argued that the independence of the broadening persists, we focus on non-integrable models involving interference. For a simple four-state model, which allows an analytical treatment, we demonstrate that the decay of the excited states affects the survival probability provided that {\em the widths of the final states are different}.

cond-mat.mes-hall↗

arXiv2021

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. 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, $δν(ω)$, where $ω$ is the energy measured from the Fermi level, emerges at a weak $B$ and has the form $δν(B)\sim B^2/ω^2$. 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.

cond-mat.mes-hall↗

arXiv2021

Three-electron bunches in occupation of a 5-site Coulomb cluster

Attraction of like charges in a localized system implies that, upon increasing the Fermi energy, the occupation of the system changes as, n\rightarrow (n+2), while the occupation, (n+1), is skipped. In this way, the attraction translates into the bunching of electrons. For a localized system of N=4 sites, attraction of electrons manifests itself in skipping of n=2 occupation. The origin of the attraction is rearrangement of the occupations of the surrounding sites which plays the role of a polaronic effect. We consider an N=5-site cluster and demonstrate that, with screened Coulomb repulsion, three-electron bunching becomes possible, i.e. the change of occupation n=1\rightarrow n=4 with n=2 and n=3 occupations skipped.

cond-mat.mes-hall↗

arXiv2021

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. 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.

cond-mat.dis-nn↗

arXiv2021

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 $S$-states with a zero momentum of the center of mass get coupled to the $P$-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 $S$ and $P$ 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.

cond-mat.mes-hall↗

arXiv2021

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. The draw an analogy between this splitting and the Lamb shift in quantum electrodynamics.

cond-mat.dis-nn↗

arXiv2021

Persistent Friedel oscillations in Graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a 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 $r$ 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 {\em dominant} in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, $k_F$ is Fermi momentum and $p_0^{-1}=(k_Fl)^{4/3}/k_F$. 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. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.

cond-mat.mes-hall↗

arXiv2020

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

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.

cond-mat.mes-hall↗

arXiv2020

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. 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.

cond-mat.mes-hall↗

arXiv2020

Slow oscillating dynamics of a two-level system subject to a fast telegraph noise: beyond the NIBA approximation

We study the dynamics of a two-site model in which the tunneling amplitude between the sites is not constant but rather a high-frequency noise. Obviously, the population imbalance in this model decays exponentially with time. Remarkably, the decay is modified dramatically when the level asymmetry fluctuates in-phase with fluctuations of the tunneling amplitude. For particular type of these in-phase fluctuations, namely, the telegraph noise, we find the exact solution for the average population dynamics. It appears that the population imbalance between the sites starting from 1 at time $t=0$ approaches a constant value in the limit $t\rightarrow \infty$. At finite bias, the imbalance goes to zero at $t\rightarrow \infty$, while the dynamics of the decay governed by noise acquires an oscillatory character.

cond-mat.dis-nn↗

arXiv2019

Two-photon absorption in a two-level system enabled by noise

We address the textbook problem of dynamics of a spin placed in a dc magnetic field and subjected to an ac drive. If the drive is polarized in the plane perpendicular to the dc field, the drive photons are resonantly absorbed when the spacing between the Zeeman levels is close to the photon energy. This is the only resonance when the drive is circularly polarized. For linearly polarized drive, additional resonances corresponding to absorption of three, five, and multiple odd numbers of photons is possible. Interaction with the environment causes the broadening of the absorption lines. We demonstrate that the interaction with environment enables the forbidden two-photon absorption. We adopt a model of the environment in the form of random telegraph noise produced by a single fluctuator. As a result of the synchronous time fluctuations of different components of the random field, the shape of the two-photon absorption line is non-Lorentzian and depends dramatically on the drive amplitude. This shape is a monotonic curve at strong drive, while, at weak drive, it develops a two-peak structure reminiscent of an induced transparency on resonance.

quant-ph↗