arXiv subjects

M. Moško

Publications and source records attributed to M. Moško.

3 recordsLinked to original sources

arXiv2017

Note on the Coulomb blockade of a weak tunnel junction with Nyquist noise: Conductance formula for a broad temperature range

We revisit the Coulomb blockade of the tunnel junction with conductance much smaller than $e^2/\hbar$. We study the junction with capacitance $C$, embedded in an Ohmic electromagnetic environment modelled by a series resistance $R$ which produces the Nyquist noise. In the semiclassical limit the Nyquist noise charges the junction by a random charge with a Gaussian distribution. Assuming the Gaussian distribution, we derive analytically the temperature-dependent junction conductance $G(T)$ valid for temperatures $k_BT \gtrsim (R_K/2πR)E_c$ and resistances $R \gtrsim R_K$, where $R_K = h/e^2$ and $E_c=e^2/2C \ \text{is}$ the single-electron charging energy. Our analytical result shows the leading dependence $G(T) \propto e^{-E_c/4k_BT}$, so far believed to exist only if $(R_K/πR)E_c \ll k_BT \ll E_c$ and $R \gg R_K$. The validity of our result for $k_BT \gtrsim (R_K/2πR)E_c$ and $R \gtrsim R_K$ is confirmed by a good agreement with the numerical studies which do not assume the semiclassical limit, and by a reasonable agreement with experimental data for $R$ as low as $R_K$. Our result also reproduces various asymptotic formulae derived in the past. The factor of $1/4$ in the activation energy $E_c/4$ is due to the semiclassical Nyquist noise.

cond-mat.mes-hall↗

arXiv2011

Bloch-Wannier theory of persistent current in a ring made of the band insulator: Exact result for one-dimensional lattice and estimates for realistic lattices

In this work, persistent currents in rings made of band insulators are analyzed theoretically. We first formulate a recipe which determines the Bloch states of a one-dimensional (1D) ring from the Bloch states of an infinite 1D crystal created by the periodic repetition of the ring. Using the recipe, we derive an expression for the persistent current in a 1D ring made of an insulator with an arbitrary valence band E(k). To find an exact result for a specific insulator, we consider a 1D ring represented by a periodic lattice of N identical sites with a single value of the on-site energy. If the Bloch states in the ring are expanded over a complete set of N on-site Wannier functions, the discrete on-site energy splits into the energy band. At full filling, the band emulates the valence band of the band insulator and the ring is insulating. It carries a persistent current equal to the product of N and the derivative of the on-site energy with respect to the magnetic flux. This current is not zero if one takes into account that the on-site Wannier function and consequently the on-site energy of each ring site depend on magnetic flux. To derive the current analytically, we expand all N Wannier functions of the ring over the infinite basis of Wannier functions of the constituting infinite 1D crystal and eventually determine the crystal Wannier functions by a method of localized atomic orbitals. Finally, we estimate the persistent current at full filling in rings made of real band insulators (GaAs, Ge, InAs). The current decays with the ring length exponentially due to the exponential decay of the Wannier functions. In spite of that, it can be of measurable size.

cond-mat.mes-hall↗

arXiv2009

Persistent current of Luttinger liquid in one-dimensional ring with weak link: Continuous model studied by configuration interaction and quantum Monte Carlo

We study the persistent current of correlated spinless electrons in a continuous one-dimensional ring with a single weak link. We include correlations by solving the many-body Schrodinger equation for several tens of electrons interacting via the short-ranged pair interaction V(x - x'). We solve this many-body problem by advanced configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. Our CI and DMC results show, that the persistent current (I) as a function of the ring length (L) exhibits for large L the power law typical of the Luttinger liquid, $I \propto L^{-1-α}$, where the power $α$ depends only on the electron-electron (e-e) interaction. For strong e-e interaction the previous theories predicted for $α$ the formula $α= {(1 + 2 α_{RG})}^{1/2} - 1$, where $α_{RG} = [V(0)-V(2k_F)]/2π\hbar v_F$ is the renormalisation-group result for weakly interacting electrons, with V(q) being the Fourier transform of V(x-x'). Our numerical data show that this theoretical result holds in the continuous model only if the range of V(x - x') is small (roughly $d \lesssim 1/2k_F$, more precisely $4d^2k_F^2 << 1$). For strong e-e interaction ($α_{RG} > 0.25$) our CI data show the power law $I \propto L^{-1-α}$ already for rings with only ten electrons, i.e., ten electrons are already enough to behave like the Luttinger liquid. The DMC data for $α_{RG} > 0.25$ are damaged by the so-called fixed-phase approximation. Finally, we also treat the e-e interaction in the Hartree-Fock approximation. We find the exponentially decaying I(L) instead of the power law, however, the slope of log(I(L)) still depends solely on the parameter $α_{RG}$ as long as the range of V(x - x') approaches zero.

cond-mat.mes-hall↗