Inelastic Interaction Corrections and Universal Relations for Full Counting Statistics

We analyze in detail the interaction correction to Full Counting Statistics (FCS) of electron transfer in a quantum contact originating from the electromagnetic environment surrounding the contact. The correction can be presented as a sum of two terms, corresponding to elastic/inelastic electron transfer. Here we primarily focus on the inelastic correction. For our analysis, it is important to understand more general -- universal -- relations imposed on FCS only by quantum mechanics and statistics with no regard for a concrete realization of a contact. So we derive and analyze these relations. We reveal that for FCS the universal relations can be presented in a form of detailed balance. We also present several useful formulas for the cumulants. To facilitate the experimental observation of the effect, we evaluate cumulants of FCS at finite voltage and temperature. Several analytical results obtained are supplemented by numerical calculations for the first three cumulants at various transmission eigenvalues.Comment: 10 pages, 3 figure

Scalar boundary value problems on junctions of thin rods and plates. I. Asymptotic analysis and error estimates

We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, i.e. the relative thickness, appears in the differential equation, too, while the asymptotic structures crucially depend on the contrastness ratio. Asymptotic error estimates are derived in anisotropic weighted Sobolev norms.Comment: 34 pages, 4 figure

Optical bio and chemical sensor in a one-dimensional photonic structure with bound states in the continuum

In this paper, we present the main results of the numerical calculation of the bound states in the continuum (BICs) application in the refractive index (RI) sensing. Weconsider a one-dimensional rectangular photonic structure at subwavelength regime and study the Fano resonance shift for off-Γ BIC. The results obtained will make it possible to create photonic structures for biosensing, for which a high-Q resonance is observed at nonzero incidence angles

Pressure-induced spin-state transition of iron in magnesiow\"ustite (Fe,Mg)O

We present a detailed theoretical study of the electronic, magnetic, and structural properties of magnesiow\"ustite Fe$_{1-x}$Mg$_x$O with $x$ in the range between 0$-$0.875 using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory (DFT+DMFT) method. In particular, we compute the electronic structure and phase stability of the rock-salt B1-structured (Fe,Mg)O at high pressures relevant for the Earth's lower mantle. We obtain that upon compression paramagnetic (Fe,Mg)O exhibits a spin-state transition of Fe$^{2+}$ ions from a high-spin to low-spin (HS-LS) state which is accompanied by a collapse of local magnetic moments. The HS-LS transition results in a substantial drop of the lattice volume by about 4$-$8 %, implying a complex interplay between electronic and lattice degrees of freedom. Our results reveal a strong sensitivity of the calculated transition pressure $P_{\rm tr.}$ upon addition of Mg. While for Fe-rich magnesiow\"ustite, Mg $x < 0.5$, $P_{\rm tr.}$ exhibits a rather weak variation at $\sim$80 GPa, for Fe-poor (Fe,Mg)O it drops, e.g., by about 35 % to 52 GPa for Mg $x=0.75$. This behavior is accompanied by a substantial change of the spin transition range from 50$-$140 GPa in FeO to 30$-$90 GPa for $x=0.75$. In addition, the calculated bulk modulus (in the HS state) is found to increase by $\sim$12 % from 142 GPa in FeO to 159 GPa in (Fe,Mg)O with Mg $x=0.875$. We find that the pressure-induced HS-LS transition has different consequences for the electronic properties of the Fe-rich and poor (Fe,Mg)O. For the Fe-rich (Fe,Mg)O, the transition is found to be accompanied by a Mott insulator to (semi-) metal phase transition. In contrast to that, for $x>0.25$, (Fe,Mg)O remains insulating up to the highest studied pressures, implying a Mott insulator to band insulator phase transition at the HS-LS transformation.Comment: 9 pages, 9 figure

Hierarchical Wigner Crystal at the Edge of Quantum Hall Bar

We show that quasiholes persist near the edge of incompressible Quantum Hall state forming a Wigner structure. The average density of quasiholes is fixed by electrostatics and decreases slowly with increasing distance from the edge. As we see from elementary reasoning, their specific arrangement can not be a regular Wigner lattice and shows a complex hierarchical structure of dislocations.Comment: LaTEX file. Ps figures upon reques

Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid

In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the 1D electron gas and 2D Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozieres-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the 1D case but finding no changes in the DOS of the 2D Hall fluid with short-range interaction. We also provide, for the first time, an exact solution of the Nozieres-De Dominicis equation for the 2D electron gas in the lowest Landau level.Comment: 6 pages, Revte

Coherent and incoherent pumping of electrons in double quantum dots

We propose a new mode of operation of an electron pump consisting of two weakly coupled quantum dots connected to reservoirs. An electron can be transferred within the device at zero bias voltage when it is subjected to electromagnetic radiation, thereby exciting the double dot. The excited state can decay by transferring charge from one lead and to the other lead in one direction. Depending on the energies of the intermediate states in the pumping cycle, which are controlled by the gate voltages, this transport is either incoherent via well-known sequential tunneling processes, or coherent via a inelastic co-tunneling process. The latter novel mode of operation is possible only when interdot Coulomb charging is important. The D.C. transport through the system can be controlled by the frequency of the applied radiation. We concentrate on the resonant case, when the frequency matches the energy difference for exciting an electron from one dot into the other. The resonant peaks in the pumping current should be experimentally observable. We have developed a density matrix approach which describes the dynamics of the system on timescales much larger than the period of the applied irradiation. In contrast to previous works we additionally consider the case of slow modulation of the irradiation amplitude. Harmonic modulation produces additional sidepeaks in the photoresponse, and pulsed modulation can be used to resolve the Rabi frequency in the time-averaged current.Comment: 5 pages, 6 figures. This is an extension of cond-mat/9707310 "A coherent double-quantum-dot electron pump" This version has been accepted for publication in Phys. Rev. B. Changes: Added references. Corrected typos. Changed content mainly the introduction. Regime of device operation is now specified more precisely. A stability diagram has been added as a figure has been adde

Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently presented by Abanov and Ivanov. A similar idea is used to derive a new expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long time limit. This provides a generalization of the Levitov-Lesovik formula for such systems.Comment: 17 pages, 6 figures, extended introduction, additional comment

On the shot-noise limit of a thermal current

The noise power spectral density of a thermal current between two macroscopic dielectric bodies held at different temperatures and connected only at a quantum point contact is calculated. Assuming the thermal energy is carried only by phonons, we model the quantum point contact as a mechanical link, having a harmonic spring potential. In the weak coupling, or weak-link limit, we find the thermal current analog of the well-known electronic shot-noise expression.Comment: 4 pages, 1 figur