arXiv subjects

V. V. Mkhitaryan

Publications and source records attributed to V. V. Mkhitaryan.

33 records · Page 2Linked to original sources

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↗

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

Next-nearest-neighbor spin-spin and chiral-spin correlation functions in generalized XXX chain

We develop a simple technique for calculation of next to nearest neighbor spin-spin and chiral-spin correlation functions in inhomogeneous XXX model. Exact expression of the chiral-spin order parameter as a function of the model parameter, $ω$, is analytically found. Using the same method we also calculate the next to nearest neighbor spin-spin correlation function. In the limit $ω-> 0$ it reproduces the known result for the vacuum expectation value of the next to nearest neighbor spins in the standard Heisenberg spin chain. The technique is simple and can be extended for calculation of next to next to nearest neighbor correlation functions as well as for calculation of correlation functions in XXZ model.

cond-mat.str-el↗

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

Supergap anomalies in cotunneling between N-S and between S-S leads via a small quantum dot

Cotunneling current through a resonant level coupled to either normal and superconducting or to two superconducting leads is studied for the domain of bias voltages, V, exceeding the superconducting gap, 2Δ. Due to the on-site repulsion in the resonant level, cotunneling of an electron is accompanied by creation of a quasiparticle in a superconducting lead. Energy conservation imposes a threshold for this inelastic transport channel: V_c=3Δfor N-S case and \tilde{V}_c=4Δfor the S-S case. We demonstrate that the behavior of current near the respective thresholds is nonanalytic, namely, δI^{in}(V)\propto (V-V_c)^{3/2}Θ(V-V_c) and δI^{in}(V) \propto (V-\tilde{V}_c)Θ(V-\tilde{V}_c). Stronger anomaly for the S-S leads is the consequence of the enhanced density of states at the edges of the gap. In addition, the enhanced density of states makes the threshold anomalies for two-electron cotunneling processes in the Coulomb-blockaded regions more pronounced than for the N-N leads.

cond-mat.mes-hall↗

arXiv2006

Mean-field theory for Heisenberg zigzag ladder: Ground state energy and spontaneous symmetry breaking

The spin-1/2 zig-zag Heisenberg ladder (J_1 - J_2 model) is considered. A new representation for the model is found and a saddle point approximation over the spin-liquid order parameter < \vec σ_{n-1}(\vec σ_{n}\times \vec σ_{n+1}) > is performed. Corresponding effective action is derived and analytically analyzed. We observe the presence of phase transitions at values J_2/J_1=0.231 and J_2/J_1=1/2.

cond-mat.str-el↗

arXiv2003

Thermodynamic Bethe Ansatz for the Spin-1/2 Staggered XXZ- Model

We develop the technique of Thermodynamic Bethe Ansatz to investigate the ground state and the spectrum in the thermodynamic limit of the staggered $XXZ$ models proposed recently as an example of integrable ladder model. This model appeared due to staggered inhomogeneity of the anisotropy parameter $Δ$ and the staggered shift of the spectral parameter. We give the structure of ground states and lowest lying excitations in two different phases which occur at zero temperature.

hep-th↗

arXiv1999

Perturbation theory in radial quantization approach and the expectation values of exponential fields in sine-Gordon model

A perturbation theory for Massive Thirring Model (MTM) in radial quantization approach is developed. Investigation of the twisted sector in this theory allows us to calculate the vacuum expectation values of exponential fields $ exp iaphi (0) $ of the sine-Gordon theory in first order over Massive Thirring Models coupling constant. It appears that the apparent difficulty in radial quantization of massive theories, namely the explicite ''time'' dependence of the Hamiltonian, may be successfully overcome. The result we have obtained agrees with the exact formula conjectured by Lukyanov and Zamolodchikov and coincides with the analogous calculations recently carried out in dual angular quantization approach by one of the authors.

hep-th↗