arXiv subjects

K. A. Matveev

Publications and source records attributed to K. A. Matveev.

At least 73 records · Page 4Linked to original sources

arXiv2005

Exchange Coupling in a One-Dimensional Wigner Crystal

We consider a long quantum wire at low electron densities. In this strong interaction regime a Wigner crystal may form, in which electrons comprise an antiferromagnetic Heisenberg spin chain. The coupling constant J is exponentially small, as it originates from tunneling of two neighboring electrons through the segregating potential barrier. We study this exponential dependence, properly accounting for the many-body effects and the finite width of the wire.

cond-mat.mes-hall↗

arXiv2004

Stochastic current switching in bistable resonant tunneling systems

Current-voltage characteristics of resonant-tunneling structures often exhibit intrinsic bistabilities. In the bistable region of the I-V curve one of the two current states is metastable. The system switches from the metastable state to the stable one at a random moment in time. The mean switching time τdepends exponentially on the bias measured from the boundary of the bistable region V_{th}. We find full expressions for τ(including prefactors) as functions of bias, sample geometry, and in-plane conductivity. Our results take universal form upon appropriate renormalization of the threshold voltage V_{th}. We also show that in large samples the switching initiates inside, at the edge, or at a corner of the sample depending on the parameters of the system.

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arXiv2004

Conductance of a quantum wire at low electron density

We study the transport of electrons through a long quantum wire connecting two bulk leads. As the electron density in the wire is lowered, the Coulomb interactions lead to short-range crystalline ordering of electrons. In this Wigner crystal state the spins of electrons form an antiferromagnetic Heisenberg spin chain with exponentially small exchange coupling J. Inhomogeneity of the electron density due to the coupling of the wire to the leads results in violation of spin-charge separation in the device. As a result the spins affect the conductance of the wire. At zero temperature the low-energy spin excitations propagate freely through the wire, and its conductance remains 2e^2/h. Since the energy of the elementary excitations in the spin chain (spinons) cannot exceed πJ/2, the conductance of the wire acquires an exponentially small negative correction δG \propto - exp(-πJ/2T) at low temperatures T< >J, most of the spin excitations in the leads are reflected by the wire, and the conductance levels off at a new universal value e^2/h.

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arXiv2003

Conductance of a quantum wire in the Wigner crystal regime

We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T << J this effect is small, and the conductance of the wire remains close to 2e^2/h. At T >> J the spin effect reduces the conductance to e^2/h.

cond-mat.mes-hall↗

arXiv2002

Electron-phonon scattering in quantum point contacts

We study the negative correction to the quantized value $2e^2/h$ of the conductance of a quantum point contact due to the backscattering of electrons by acoustic phonons. The correction shows activated temperature dependence and also gives rise to a zero-bias anomaly in conductance. Our results are in qualitative agreement with recent experiments studying the 0.7 feature in the conductance of quantum point contacts.

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arXiv2002

Lifetime of metastable states in resonant tunneling structures

We investigate the transport of electrons through a double-barrier resonant-tunneling structure in the regime where the current-voltage characteristics exhibit bistability. In this regime one of the states is metastable, and the system eventually switches from it to the stable state. We show that the mean switching time grows exponentially as the voltage across the device is tuned from the its boundary value into the bistable region. In samples of small area we find that the logarithm of the lifetime is proportional to the voltage (measured from its boundary value) to the 3/2 power, while in larger samples the logarithm of the lifetime is linearly proportional to the voltage.

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arXiv2002

Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrodinger equation with twisted boundary conditions.

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arXiv2002

Thermopower of a single electron transistor in the regime of strong inelastic cotunneling

We study Coulomb blockade oscillations of thermoelectric coefficients of a single electron transistor based on a quantum dot strongly coupled to one of the leads by a quantum point contact. At temperatures below the charging energy E_C the transport of electrons is dominated by strong inelastic cotunneling. In this regime we find analytic expressions for the thermopower as a function of temperature T and the reflection amplitude $r$ in the contact. In the case when the electron spins are polarized by a strong external magnetic field, the thermopower shows sinusoidal oscillations as a function of the gate voltage with the amplitude of the order of $e^{-1}|r|\frac{T}{E_C}$. We obtain qualitatively different results in the absence of the magnetic field. At temperatures between $E_C$ and $E_C|r|^2$ the thermopower oscillations are sinusoidal with the amplitude of order $e^{-1}|r|^2 \ln \frac{E_C}{T}$. On the other hand, at $T\ll E_C|r|^2$ we find non-sinusoidal oscillations of the thermopower with the amplitude $\sim e^{-1} |r| \sqrt{T/E_C} \ln(E_C/T)$.

cond-mat.mes-hall↗

arXiv2001

Cotunneling thermopower of single electron transistors

We study the thermopower of a quantum dot weakly coupled to two reservoirs by tunnel junctions. At low temperatures the transport through the dot is suppressed by charging effects (Coulomb blockade). As a result the thermopower shows an oscillatory dependence on the gate voltage. We study this dependence in the limit of low temperatures where the transport through the dot is dominated by the processes of inelastic cotunneling. We also obtain a crossover formula for intermediate temperatures which connects our cotunneling results to the known sawtooth behavior in the sequential tunneling regime. As the temperature is lowered, the amplitude of thermopower oscillations increases, and their shape changes qualitatively.

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arXiv2001

Occupation of a resonant level coupled to a chiral Luttinger liquid

We consider a resonant level coupled to a chiral Luttinger liquid which can be realized, e.g., at a fractional quantum Hall edge. We study the dependence of the occupation probability n of the level on its energy εfor various values of the Luttinger-liquid parameter g. At g<1/2 a weakly coupled level shows a sharp jump in n(ε) at the Fermi level. As the coupling is increased, the magnitude of the jump decreases until \sqrt{2g}, and then the discontinuity in n(ε) disappears. We show that n(ε) can be expressed in terms of the magnetization of a Kondo impurity as a function of magnetic field.

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arXiv2000

Smearing of Coulomb Blockade by Resonant Tunneling

We study the Coulomb blockade in a grain coupled to a lead via a resonant impurity level. We show that the strong energy dependence of the transmission coefficient through the impurity level can have a dramatic effect on the quantization of the grain charge. In particular, if the resonance is sufficiently narrow, the Coulomb staircase shows very sharp steps even if the transmission through the impurity at the Fermi energy is perfect. This is in contrast to the naive expectation that perfect transmission should completely smear charging effects.

cond-mat.mes-hall↗

arXiv2000

Coulomb Blockade Oscillations in the Thermopower of Open Quantum Dots

We consider Coulomb blockade oscillations of thermoelectric coefficients of a single electron transistor based on a quantum dot strongly coupled to one of the leads. Analytic expression for the thermopower as a function of temperature $T$ and the reflection amplitude $r$ in the quantum point contact is obtained. Two regimes can be identified: $T \ll E_C|r|^2$ and $T \gg E_C |r|^2$, where $E_C$ is the charging energy of the dot. The former regime is characterized by weak logarithmic dependence of the thermopower on the reflection coefficient, in the latter the thermopower is linear in the reflection coefficient $|r|^2$ but depends on temperature only logarithmically.

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arXiv2000

The g-factors of discrete levels in nanoparticles

Spin-orbit scattering suppresses Zeeman splitting of individual energy levels in small metal particles. This suppression becomes significant when the spin-orbit scattering rate τ_{so}^{-1} is comparable with the quantum level spacing δ. The g-factor exhibits mesoscopic fluctuations; at small δτ_{so} it is distributed according to the Maxwell distribution. At δτ_{so}\to 0 the average g-factor levels off at a small value g\sim(l/L)^{1/2} given by the ratio of the electron mean free path l to the particle size L. On the contrary, in 2D quantum dots the g-factor is strongly enhanced by spin-orbit coupling.

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arXiv1998

Strong tunneling and charge quantization in S-I-N Coulomb blockade structures

We study the charge of a small normal island connected by a tunnel junction to a superconducting lead. Unlike the N-I-N case, the steps of the Coulomb staircase remain sharp even if the conductance of the tunneling barrier exceeds e^2/h. One can observe the transition from sharp steps to the smeared ones by applying magnetic field to destroy the superconductivity.

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arXiv1997

Shifts of Random Energy Levels by a Local Perturbation

We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of unitary ensemble we also find the two-point correlation function of initial and final densities of states.

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arXiv1997

Parity Effect in Ground State Energies of Ultrasmall Superconducting Grains

We study the superconductivity in small grains in the regime when the quantum level spacing $δ\varepsilon$ is comparable to the gap $Δ$. As $δ\varepsilon$ is increased, the system crosses over from superconducting to normal state. This crossover is studied by calculating the dependence of the ground state energy of a grain on the parity of the number of electrons. The states with odd numbers of particles carry an additional energy $Δ_P$, which shows non-monotonic dependence on $δ\varepsilon$. Our predictions can be tested experimentally by studying the parity-induced alternation of Coulomb blockade peak spacings in grains of different sizes.

cond-mat.mes-hall↗

arXiv1995

Coulomb Blockade of Tunneling Through a Double Quantum Dot

We study the Coulomb blockade of tunneling through a double quantum dot. The temperature dependence of the linear conductance is strongly affected by the inter-dot tunneling. As the tunneling grows, a crossover from temperature-independent peak conductance to a power-law suppression of conductance at low temperatures is predicted. This suppression is a manifestation of the Anderson orthogonality catastrophe associated with the charge re-distribution between the dots, which accompanies the tunneling of an electron into a dot. We find analytically the shapes of the Coulomb blockade peaks in conductance as a function of gate voltage.

cond-mat↗

arXiv1995

Theory of strong inelastic co-tunneling

We develop a theory of the conductance of a quantum dot connected to two leads by single-mode quantum point contacts. If the contacts are in the regime of perfect transmission, the conductance shows no Coulomb blockade oscillations as a function of the gate voltage. In the presence of small reflection in both contacts, the conductance develops small Coulomb blockade oscillations. As the temperature of the system is lowered, the amplitude of the oscillations grows, and eventually sharp periodic peaks in conductance are formed. Away from the centers of the peaks the conductance vanishes at low temperatures as $T^2$, in agreement with the theory of inelastic co-tunneling developed for the weak-tunneling case. Conductance near the center of a peak can be studied using an analogy with the multichannel Kondo problem. In the case of symmetric barriers, the peak conductance at $T\to 0$ is of the order of $e^2/\hbar$. In the asymmetric case, the peak conductance vanishes linearly in temperature.

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