arXiv subjects

D. O. Oriekhov

Publications and source records attributed to D. O. Oriekhov.

29 records · Page 2Linked to original sources

arXiv2021

Gap generation and flat band catalysis in dice model with local interaction

The gap generation in the dice model with local four-fermion interaction is studied. Due to the presence of two valleys with degenerate electron states, there are two main types of gaps. The intra- and intervalley gap describes the electron and hole pairing in the same and different valleys, respectively. We found that while the generation of the intravalley gap takes place only in the supercritical regime, the intervalley gap is generated for an arbitrary small coupling. The physical reason for the absence of the critical coupling is the catalysis of the intervalley gap generation by the flat band in the electron spectrum of the dice model. The completely quenched kinetic energy in the flat band when integrated over momentum in the gap equation leads to extremely large intervalley gap proportional to the area of the Brillouin zone.

cond-mat.str-el↗

arXiv2021

Current distribution and group velocities for electronic states on $α-\mathcal{T}_3$ lattice ribbons in a magnetic field

We study the group velocities of electronic states and distributions of currents in $α-\mathcal{T}_3$ lattice ribbons under a uniform perpendicular magnetic field. Using the effective low-energy model we analyze all possible simple configurations of lattice termination with zigzag and armchair boundaries. We show that the edge current depends on the type of zigzag termination, and can be zero or finite near the edge. Also similar dependence is observed in the case of armchair termination and is related to the size of the ribbon. The nonzero current flowing along the edge can be used a signature of formation of propagating edge states. Also we show the qualitative difference in the distribution of the edge current between the case of $α=1$ (dice model) and other values of model parameter $α\neq 1$ for armchair-terminated ribbons.

cond-mat.str-el↗

arXiv2021

Voltage staircase in a current-biased quantum-dot Josephson junction

We calculate the current-voltage (I-V) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The phase $ϕ$ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase I-V characteristic. The number of voltage steps counts the number of Rabi oscillations per $2π$ increment of $ϕ$, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the "Majorana-induced DC Shapiro steps in topological Josephson junctions" of Phys. Rev. B 102, 140501(R) (2020) -- but now for a non-topological Andreev qubit.

cond-mat.mes-hall↗

arXiv2020

Shot noise distinguishes Majorana fermions from vortices injected in the edge mode of a chiral p-wave superconductor

The chiral edge modes of a topological superconductor support two types of excitations: fermionic quasiparticles known as Majorana fermions and $π$-phase domain walls known as edge vortices. Edge vortices are injected pairwise into counter-propagating edge modes by a flux bias or voltage bias applied to a Josephson junction. An unpaired edge mode carries zero electrical current on average, but there are time-dependent current fluctuations. We calculate the shot noise power produced by a sequence of edge vortices and find that it increases logarithmically with their spacing - even if the spacing is much larger than the core size so the vortices do not overlap. This nonlocality produces an anomalous V log V increase of the shot noise in a voltage-biased geometry, which serves as a distinguishing feature in comparison with the linear-in-V Majorana fermion shot noise.

cond-mat.supr-con↗

arXiv2020

Half-integer charge injection by a Josephson junction without excess noise

A Josephson junction in a topological superconductor can inject a charge e/2 into a normal-metal contact, carried by chiral Majorana edge modes. Here we address the question whether this half-integer charge is a sharp observable, without quantum fluctuations. Because the Majorana modes are gapless, they support charge fluctuations in equilibrium at zero temperature. But we find that the excess noise introduced out of equilibrium by the e/2 charge transfer vanishes. We discuss a strategy to reduce the equilibrium fluctuations, by means of a heavy-tailed time-dependent detection efficiency, to achieve a nearly noiseless half-integer charge transfer.

cond-mat.mes-hall↗

arXiv2020

RKKY interaction in a doped pseudospin-1 fermion system at finite temperature

We study the RKKY interaction of magnetic impurities in the $α-\mathcal{T}_3$ model which hosts pseudospin-1 fermions with two dispersive and one flat bands. By using the effective low-energy Hamiltonian we calculate the RKKY coupling for impurities placed on the same or different sublattices. We find that there are three types of interaction, which depend on the model parameter defining the relative strength of hoppings between sublattices, two of them can be reduced to graphene case while the third one is new and is due to the presence of a flat zero-energy band. We derive general analytical expressions for the RKKY interaction in terms of Mellin-Barnes type integrals and analyze different limiting cases. The cases of finite chemical potential and temperature, as well as asymptotic at large distances are considered. We show that the interaction between impurities located at different rim sites displays a very strong temperature dependence at small doping being a direct consequence of the flat band. The subtleties of the theorem for signs of the RKKY interaction at zero doping, as applied to the $\mathcal{T}_3$ lattice, related to the existence of a dispersionless flat band are discussed.

cond-mat.str-el↗

arXiv2020

Plasmon Resonances and Tachyon Ghost Modes in Highly Conducting Sheets

Plasmon-polariton modes in two-dimensional electron gases have a dual field-matter nature that endows them with unusual properties when electrical conductivity exceeds a certain threshold set by the speed of light. In this regime plasmons display an interesting relation with tachyons, the hypothetical faster-than-light particles. While not directly observable, tachyons directly impact properties of plasmon modes. Namely, in the ``tachyon'' regime, plasmon resonances remain sharp even when the carrier collision rate $γ$ exceeds plasmon resonance frequency. Resonances feature a recurrent behavior as $γ$ increases, first broadening and then narrowing and acquiring asymmetric non-Lorentzian lineshapes with power-law tails extending into the tachyon continuum $ω>ck$. This unusual behavior can be linked to the properties of tachyon poles located beneath $ω>ck$ branch cuts in the complex $ω$ plane: as $γ$ grows, tachyon poles approach the light cone and hybridize with plasmons. Narrow resonances persisting for $γ>ω$, along with the unusual density and temperature dependence of resonance frequencies, provide clear signatures of the tachyon regime.

cond-mat.mes-hall↗

arXiv2019

Electronic states of pseudospin-1 fermions in $α-\mathcal{T}_3$ lattice ribbons in a magnetic field

The electronic states on a finite width $α-\mathcal{T}_3$ ribbon in a magnetic field are studied in the framework of low-energy effective theory. Both zigzag and armchair types of boundary conditions are analyzed. The analytical solutions are compared with the results of numerical tight-binding calculations. It is found that the flat band of zero energy survives for all types of boundary conditions. The analytical estimates for the spectral gap in a weak magnetic field are discussed. For zigzag type boundary conditions the approximate expressions for the edge and bulk electron states in the strong magnetic field are found.

cond-mat.str-el↗

arXiv2018

Electron states for gapped pseudospin-1 fermions in the field of charged impurity

The electron states of gapped pseudospin-1 fermions of the $α-{\cal T}_3$ lattice in the Coulomb field of a charged impurity are studied. The free $α-{\cal T}_3$ model has three dispersive bands with two energy gaps between them depending on the parameter $Θ$ which controls the coupling of atoms of honeycomb lattice with atoms in the center of each hexagon, thus, interpolating between graphene $Θ=0$ and the dice model $Θ=π/4$. The middle band becomes flat one with zero energy in the dice model. The bound electron states are found in the two cases: the centrally symmetric potential well and a regularized Coulomb potential of the charged impurity. As the charge of impurity increases, bound state energy levels descend from the upper and central continua and dive at certain critical charges into the central and lower continuum, respectively. In the dice model, it is found that the flat band survives in the presence of a potential well, however, is absent in the case of the Coulomb potential. The analytical results are presented for the energy levels near continuum boundaries in the potential well. For the genuine Coulomb potential, we present the recursion relations that determine the coefficients of the series expansion of wave functions of bound states. It is shown that the condition for the termination of the series expansion gives two equations relating energy and charge values. Hence, analytical solutions can exist for a countably infinite set of values of impurity charge at fixed $Θ$.

cond-mat.str-el↗

arXiv2018

Electronic states of pseudospin-1 fermions in dice lattice ribbons

Boundary conditions for the two-dimensional fermions in ribbons of the hexagonal lattice are studied in the dice model whose energy spectrum in infinite system consists of three bands with one completely flat band of zero energy. Like in graphene the regular lattice terminations are of the armchair and zigzag types. However, there are four possible zigzag edge terminations in contrast to graphene where only one type of zigzag termination is possible. Determining the boundary conditions for these lattice terminations, the energy spectra of pseudospin-1 fermions in dice model ribbons with zigzag and armchair boundary conditions are found. It is shown that the energy levels for armchair ribbons display the same features as in graphene except the zero energy flat band inherent to the dice model. In addition, unlike graphene, there are no propagating edge states localized at zigzag boundary and there are specific zigzag terminations which give rise to bulk modes of a metallic type in dice model ribbons. We find that the existence of the flat zero-energy band in the dice model is very robust and is not affected by the zigzag and armchair boundaries.

cond-mat.str-el↗

arXiv2017

Coulomb center instability in bilayer graphene

In the low-energy two-band as well as four-band continuum models, we study the supercritical instability in gapped bilayer graphene in the field of a charged impurity. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge as the lowest-energy bound state dives into the lower continuum tends to zero as the gap $Δ$ vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for $Δ\to 0$. The different scalings of the kinetic energy of quasiparticles and the Coulomb interaction with respect to the distance to the charged impurity ensure that the wave function of the electron bound state does not shrink toward the impurity as its charge increases. This results in the absence of the fall-to-center phenomenon in bilayer graphene although the supercritical instability is realized.

cond-mat.str-el↗