arXiv subjects

M. E. Raikh

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

At least 73 records · Page 4Linked to original sources

arXiv2012

Analytical description of spin-Rabi oscillation controlled electronic transitions rates between weakly coupled pairs of paramagnetic states with S=1/2

We report on an analytical description of spin-dependent electronic transition rates which are controlled by a radiation induced spin-Rabi oscillation of weakly spin-exchange and spin-dipolar coupled paramagnetic states (S=1/2). The oscillation components (the Fourier content) of the net transition rates within spin-pair ensembles are derived for randomly distributed spin resonances with account of a possible correlation between the two distributions that correspond to the two individual pair partners. The results presented here show that when electrically or optically detected Rabi spectroscopy is conducted under an increasing driving field B_ 1, the Rabi spectrum evolves from a single resonance peak at s=Ω_R, where Ω_R=γB_1 is the Rabi frequency (γis the gyromagnetic ratio), to three peaks at s= Ω_R, s=2Ω_R, and at low s<< Ω_R. The crossover between the two regimes takes place when Ω_R exceeds the expectation value δ_0 of the difference of the Zeeman energies within the pairs, which corresponds to the broadening of the magnetic resonance lines in the presence of disorder caused by hyperfine field or distributions of Lande g-factors. We capture this crossover by analytically calculating the shapes of all three peaks at arbitrary relation between Ω_R and δ_0. When the peaks are well-developed their widths are Δs ~ δ_0^2/Ω_R.

cond-mat.mtrl-sci↗

arXiv2011

Rabi-vibronic resonance with large number of vibrational quanta

We study theoretically the Rabi oscillations of a resonantly driven two-level system linearly coupled to a harmonic oscillator (vibrational mode) with frequency, ω_0. We show that for weak coupling, ω_p \ll ω_0, where ω_p is the polaronic shift, Rabi oscillations are strongly modified in the vicinity of the Rabi-vibronic resonance Ω_R = ω_0, where Ω_R is the Rabi frequency. The width of the resonance is (Ω_R-ω_0) \sim ω_p^{2/3} ω_0^{1/3} \gg ω_p. Within this domain of Ω_R the actual frequency of the Rabi oscillations exhibits a bistable behavior as a function of Ω_R. Importantly, within the resonant domain, the oscillator is highly excited, which allows to treat it classically.

cond-mat.mes-hall↗

arXiv2011

Phase diagram of weak-magnetic-field quantum Hall transition quantified from classical percolation

We consider magnetotransport in high-mobility 2D electron gas in a non-quantizing magnetic field. We employ a weakly chiral network model to test numerically the prediction of the scaling theory that the transition from an Anderson to a quantum Hall insulator takes place when the Drude value of the non-diagonal conductivity is equal to 1/2. The weaker is the magnetic field the harder it is to locate a delocalization transition using quantum simulations. The main idea of the present study is that the position of the transition does not change when a strong local inhomogeneity is introduced. Since the strong inhomogeneity suppresses interference, transport reduces to classical percolation. We show that the corresponding percolation problem is bond percolation over two sublattices coupled to each other by random bonds. Simulation of this percolation allows to access the domain of very weak magnetic fields. Simulation results confirm the criterion σ_{xy}=1/2 for values σ_{xx}\sim 10, where they agree with earlier quantum simulation results. However for larger σ_{xx} we find that the transition boundary is described by σ_{xy} σ_{xx}^k with k= 0.5, i.e., the transition takes place at higher magnetic fields. The strong inhomogeneity limit of magnetotransport in the presence of a random magnetic field, pertinent to composite fermions, corresponds to a different percolation problem. In this limit we find for the delocalization transition boundary σ_{xy} σ_{xx}^{0.6}.

cond-mat.dis-nn↗

arXiv2011

Nonlocal correlations of the local density of states in disordered quantum Hall systems

Motivated by recent high-resolution scanning tunneling microscopy (STM) experiments in the quantum Hall regime both on massive two-dimensional electron gas and on graphene, we consider theoretically the disorder averaged nonlocal correlations of the local density of states (LDoS) for electrons moving in a smooth disordered potential in the presence of a high magnetic field. The intersection of two quantum cyclotron rings around the two different positions of the STM tip, correlated by the local disorder, provides peaks in the spatial dispersion of the LDoS-LDoS correlations when the intertip distance matches the sum of the two quantum Larmor radii. The energy dependence displays also complex behavior: for the local LDoS-LDoS average (i.e., at coinciding tip positions), sharp positive correlations are obtained for tip voltages near Landau level, and weak anticorrelations otherwise.

cond-mat.mes-hall↗

arXiv2010

Localization properties of random-mass Dirac fermions from real-space renormalization group

Localization properties of random-mass Dirac fermions for a realization of mass disorder, commonly referred to as Cho-Fisher model, is studied on the D-class chiral network. We show that a simple RG description captures accurately three phases: thermal metal and two insulators with quantized Hall conductances, as well as transitions between them (including critical exponents). We find that, with no randomness in phases on the links, transmission via the RG block exhibits a sizable portion of perfect resonances. Delocalization occurs by proliferation of these resonances to larger scales. Evolution of the thermal conductance distribution towards metallic fixed point is synchronized with evolution of signs of transmission coefficients, so that delocalization is accompanied with sign percolation

cond-mat.mes-hall↗

arXiv2010

Disorder-induced magnetooscillations in bilayer graphene at high bias

Energy spectrum of biased bilayer graphene near the bottom has a "Mexican-hat"-like shape. For the Fermi level within the Mexican hat we predict that, apart from conventional magnetooscillations which vanish with temperature, there are additional magnetooscillations which are weakly sensitive to temperature. These oscillations are also insensitive to a long-range disorder. Their period in magnetic field scales with bias, V, as V^2. The origin of these oscillations is the disorder-induced scattering between electron-like and hole-like Fermi-surfaces, specific for Mexican hat.

cond-mat.mes-hall↗

arXiv2010

Fermi-edge singularity in the vicinity of the resonant scattering condition

Fermi-edge absorption theory predicting the spectrum, A(ω)\propto ω^{-2δ_0/π+δ^2_0/π^2}, relies on the assumption that scattering phase, δ_0, is frequency-independent. Dependence of δ_0 on ωbecomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, due to finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate this time delay into the theory, solve the Dyson equation with a modified kernel and find that, near the resonance, A(ω) behaves as ω^{-3/4} |\ln ω|. Resonant scattering off the core hole takes place in 1D and 2D in the presence of an empty subband above the Fermi level; then attraction to hole splits off a resonant level from the bottom of the empty subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.

cond-mat.mes-hall↗

arXiv2010

Weakly chiral networks and 2D delocalized states in a weak magnetic field

We study the localization properties of two-dimensional electrons in a weak perpendicular magnetic field. For this purpose we construct weakly chiral network models on the square and triangular lattices, by separating in space the regions with phase action of magnetic field, where it affects interference in course of disorder scattering, and the regions with orbital action of magnetic field, where it bends electron trajectories. In our models, the disorder mixes counter-propagating channels on the links, while scattering at the nodes describes the bending of electron trajectories. By introducing a strong spread in the scattering strengths on the links, we eliminate the interference and reduce the electron propagation over a network to a percolation problem. In this limit we establish the form of the disorder vs. magnetic field phase diagram, which is in agreement with levitation scenario: energy separating the Anderson and quantum Hall insulating phases floats up to infinity upon decreasing magnetic field. From numerical study we conclude that the positions of the weak-field quantum Hall transitions on the phase diagram are very close to our percolation results. We checked that, in accord with the Pruisken's theory, presence or absence of time reversal symmetry has no effect on the line of delocalization transitions.

cond-mat.mes-hall↗

arXiv2010

Spontaneously Localized Photonic Modes Due to Disorder in the Dielectric Constant

We present the first experimental evidence for the existence of strongly localized photonic modes due to random two dimensional fluctuations in the dielectric constant. In one direction, the modes are trapped by ordered Bragg reflecting mirrors of a planar, one wavelength long, microcavity. In the cavity plane, they are localized by disorder, which is due to randomness in the position, composition and sizes of quantum dots located in the anti-node of the cavity. We extend the theory of disorder induced strong localization of electron states to optical modes and obtain quantitative agreement with the main experimental observations.

cond-mat.mes-hall↗

arXiv2009

The photon absorption edge in superconductors and gapped 1D systems

Opening of a gap in the low-energy excitations spectrum affects the power-law singularity in the photon absorption spectrum $A(Ω)$. In the normal state, the singularity, $A(Ω)\propto [D/(Ω-Ω_{\rm th})]^α$, is characterized by an interaction-dependent exponent $α$. On the contrary, in the supeconducting state the divergence, $A(Ω)\propto (D/Δ)^α(Ω-\tildeΩ_{\rm th})^{-1/2}$, is interaction-independent, while threshold is shifted, $\tildeΩ_{\rm th}=Ω_{\rm th}+Δ$; the ``normal-metal'' form of $A(Ω)$ resumes at $(Ω-\tildeΩ_{\rm th})\gtrsim Δ\exp(1/α)$. If the core hole is magnetic, it creates in-gap states; these states transform drastically the absorption edge. In addition, processes of scattering off the magnetic core hole involving spin-flip give rise to inelastic absorption with one or several {\it real} excited pairs in the final state, yielding a structure of peaks in $A(Ω)$ at multiples of $2Δ$ above the threshold frequency. The above conclusions apply to a broad class of systems, e.g., Mott insulators, where a gap opens at the Fermi level due to the interactions.

cond-mat.mes-hall↗

arXiv2009

A simple microscopic description of quantum Hall transition without Landau levels

By restricting the motion of high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum-mechanically, the interplay of backscattering, and of the bending action of a weak magnetic field. Backscattering limits the mobility, while bending initiates quantization of the Hall conductivity. We demonstrate that, in restricted geometry, electron motion reduces to two Chalker-Coddington networks, with opposite directions of propagation along the links, which are weakly coupled by disorder. Interplay of backscattering and bending results in the quantum Hall transition in a non-quantizing magnetic field, which decreases with increasing mobility. This is in accord with scenario of floating up delocalized states.

cond-mat.mes-hall↗

arXiv2009

Quantum site percolation on triangular lattice and the integer quantum Hall effect

Generic classical electron motion in a strong perpendicular magnetic field and random potential reduces to the bond percolation on a square lattice. Here we point out that for certain smooth 2D potentials with 120 degrees rotational symmetry this problem reduces to the site percolation on a triangular lattice. We use this observation to develop an approximate analytical description of the integer quantum Hall transition. For this purpose we devise a quantum generalization of the real-space renormalization group (RG) treatment of the site percolation on the triangular lattice. In quantum case, the RG transformation describes the evolution of the distribution of the $3\times 3$ scattering matrix at the sites. We find the fixed point of this distribution and use it to determine the critical exponent, $ν$, for which we find the value $ν\approx 2.3-2.76$. The RG step involves only a single Hikami box, and thus can serve as a minimal RG description of the quantum Hall transition.

cond-mat.mes-hall↗

arXiv2009

Scattering of plasmons at the intersection of two metallic nanotubes: Implications for tunnelling

We study theoretically the plasmon scattering at the intersection of two metallic carbon nanotubes. We demonstrate that for a small angle of crossing, $θ\ll 1$, the transmission coefficient is an oscillatory function of $λ/θ$, where $λ$ is the interaction parameter of the Luttinger liquid in an individual nanotube. We calculate the tunnel density of states, $ν(ω,x)$, as a function of energy, $ω$, and distance, $x$, from the intersection. In contrast to a single nanotube, we find that, in the geometry of crossed nanotubes, conventional "rapid" oscillations in $ν(ω,x)$ due to the plasmon scattering acquire an aperiodic "slow-breathing" envelope which has $λ/θ$ nodes.

cond-mat.mes-hall↗

arXiv2008

Disorder-induced tail states in a gapped bilayer graphene

The instanton approach to the in-gap fluctuation states is applied to the spectrum of biased bilayer graphene. It is shown that the density of states falls off with energy measured from the band-edge as $ν(ε)\propto \exp(-|ε/ε_t|^{3/2})$, where the characteristic tail energy, $ε_t$, scales with the concentration of impurities, $n_i$, as $n_i^{2/3}$. While the bare energy spectrum is characterized by two energies: the bias-induced gap, $V$, and interlayer tunneling, $t_{\perp}$, the tail, $ε_t$, contains a {\it single} combination $V^{1/3}t_{\perp}^{2/3}$. We show that the above expression for $ν(ε)$ in the tail actually applies all the way down to the mid-gap.

cond-mat.mes-hall↗

arXiv2008

2D skew scattering in the vicinity and away from resonant scattering condition

We studied the energy dependence of the 2D skew scattering from strong potential, for which the Born approximation is not applicable. Since the skew scattering cross section is zero both at low and at high energies, it exhibits a maximum as a function of energy of incident electron. We found analytically the shape of the maximum for an exactly solvable model of circular-barrier potential. Within a rescaling factor, this shape is universal for strong potentials. If the repulsive potential has an attractive core, the discrete levels of the core become quasilocal due to degeneracy with continuum. For energy of incident electron close to the quasilocal state with zero angular momentum, the enhancement of the net cross section is accompanied by resonant enhancement of the skew scattering. By contrast, near the resonance with quasilocal states having momenta $\pm 1$, the skew scattering cross section is an odd function of energy deviation from the resonance, and passes through zero, i.e., it exhibits a sign reversal. In the latter case, in the presence of the Fermi sea, the Kondo resonance manifests itself in strong temperature dependence of the skew scattering.

cond-mat.mes-hall↗

arXiv2008

Interaction effects in 2D electron gas in a random magnetic field: Implications for composite fermions and quantum critical point

We consider a clean two-dimensional interacting electron gas subject to a random perpendicular magnetic field, h({\bf r}). The field is nonquantizing, in the sense, that {\cal N}_h-a typical flux into the area λ_{\text{\tiny F}}^2 in the units of the flux quantum (λ_{\text{\tiny F}} is the de Broglie wavelength) is small, {\cal N}_h\ll 1. If the spacial scale, ξ, of change of h({\bf r}) is much larger than λ_{\text{\tiny F}}, the electrons move along semiclassical trajectories. We demonstrate that a weak field-induced curving of the trajectories affects the interaction-induced electron lifetime in a singular fashion: it gives rise to the correction to the lifetime with a very sharp energy dependence. The correction persists within the interval ω\sim ω_0= E_{\text{\tiny F}}{\cal N}_h^{2/3} much smaller than the Fermi energy, E_{\text{\tiny F}}. It emerges in the third order in the interaction strength; the underlying physics is that a small phase volume \sim (ω/E_{\text{\tiny F}})^{1/2} for scattering processes, involving {\em two} electron-hole pairs, is suppressed by curving. Even more surprising effect that we find is that {\em disorder-averaged} interaction correction to the density of states, δν(ω), exhibits {\em oscillatory} behavior, periodic in \bigl(ω/ω_0\bigr)^{3/2}. In our calculations of interaction corrections random field is incorporated via the phases of the Green functions in the coordinate space. We discuss the relevance of the new low-energy scale for realizations of a smooth random field in composite fermions and in disordered phase of spin-fermion model of ferromagnetic quantum criticality.

cond-mat.mes-hall↗

arXiv2008

Crossover from weak localization to Shubnikov-de Haas oscillations in a high mobility 2D electron gas

We study the magnetoresistance, δρ_{xx}(B)/ρ_0, of a high-mobility 2D electron gas in the domain of magnetic fields, B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where δρ_{xx}(B)/ρ_0 is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the {\em second order} in the interaction parameter, $λ$, a {\em linear} B-dependence, δρ_{xx}(B)/ρ_0\sim λ^2ω_c/E_F with {\em temperature-independent} slope emerges in this domain of B (here ω_c and E_F are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is {\em unrelated} to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B-dependence of the {\em phase} of the impurity-induced Friedel oscillations.

cond-mat.mes-hall↗

arXiv2008

Magneto-oscillations due to electron-electron interactions in the ac conductivity of a 2D electron gas

Electron-electron interactions give rise to the correction, δσ^{int}(ω), to the ac magnetoconductivity, σ(ω), of a clean 2D electron gas that is periodic in ω_c^{-1}, where ω_c is the cyclotron frequency. Unlike conventional harmonics of the cyclotron resonance, which are periodic with ω, this correction is periodic with ω^{3/2}. Oscillations in δσ^{int}(ω) develop at low magnetic fields, ω_c\llω, when the conventional harmonics are suppressed by the disorder. Their origin is a {\em double} backscattering of an electron from the impurity-induced Friedel oscillations. During the time \simω^{-1} between the two backscattering events the electron travels only a {\em small portion} of the Larmour circle.

cond-mat.mes-hall↗