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Adiabatic pumping driven by moving kink and quantum standard ampere in buckled graphene nanoribbon

Suszalski Dominik, Rycerz Adam
21 Jul 2020 cond-mat.mes-hall arxiv.org/abs/2007.11145

A quantum pump in buckled graphene ribbon with armchair edges is discussed numerically. By solving the Su-Schrieffer-Heeger model and performing the computer simulation of quantum transport we find that a kink adiabatically moving along the metallic ribbon results in highly-efficient pumping, with a charge per kink transition close to the maximal value determined by the Fermi velocity in graphene. Remarkably, insulating nanoribbon show the quantized value of a charge per kink ($2e$) in relatively wide range of the system parameters, providing a candidate for the quantum standard ampere. We attribute it to the presence of a localized electronic state, moving together with a kink, whose energy lies within the ribbon energy gap.

Graphene disk in a solenoid magnetic potential: Aharonov-Bohm effect without a two-slit-like setup

Rycerz Adam, Suszalski Dominik
06 Apr 2020 cond-mat.mes-hall arxiv.org/abs/2004.03018

The Aharonov-Bohm effect allows one to demonstrate the physical meaningfulness of magnetic vector potential by passing the current in zero magnetic field regions. In the standard (a {\em two-slit-like}) setup a conducting ring is pierced by magnetic flux and the quantum interference for an electron passing simultaneously the two ring arms is observed. Here we show, by analyzing the transport via evanescent waves, that the ballistic Corbino disk in graphene subjected to a solenoid magnetic potential may exhibit the conductance oscillations of the Aharonov-Bohm kind although the current flows through a single conducting element only.

Adiabatic quantum pumping in buckled graphene nanoribbon driven by a kink

Suszalski Dominik, Rycerz Adam
19 Feb 2020 cond-mat.mes-hall arxiv.org/abs/2002.08507

We propose a new type of quantum pump in buckled graphene nanoribbon, adiabatically driven by a kink moving along the ribbon. From a practical point of view, pumps with moving scatterers present advantages as compared to gate-driven pumps, like enhanced charge transfer per cycle per channel. The kink geometry is simplified by truncating the spatial arrangement of carbon atoms with the classical $\phi^4$ model solution, including a width renormalization following from the Su-Schrieffer-Heeger model for carbon nanostructures. We demonstrate numerically, as a proof of concept, that for moderate deformations a stationary kink at the ribbon center may block the current driven by the external voltage bias. In the absence of a bias, a moving kink leads to highly-effective pump effect, with a charge per unit cycle dependent on the gate voltage.

Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian

Suszalski Dominik, Rut Grzegorz, Rycerz Adam
06 Dec 2019 cond-mat.mes-hall arxiv.org/abs/1912.03235

We study the ballistic conductivity of bilayer graphene in the presence of symmetry-breaking terms in effective Hamiltonian for low-energy excitations, such as the trigonal-warping term ($\gamma_3$), the electron-hole symmetry breaking interlayer hopping ($\gamma_4$), and the staggered potential ($\delta_{AB}$). Earlier, it was shown that for $\gamma_3\neq{}0$, in the absence of remaining symmetry-breaking terms (i.e., $\gamma_4=\delta_{AB}=0$), the conductivity ($\sigma$) approaches the value of $3\sigma_0$ for the system size $L\rightarrow{}\infty$ (with $\sigma_0=8e^2/(\pi{}h)$ being the result in the absence of trigonal warping, $\gamma_3=0$). We demonstrate that $\gamma_4\neq{}0$ leads to the divergent conductivity if $\gamma_3\neq{}0$, or to the vanishing conductivity if $\gamma_3=0$. For realistic values of the tight-binding model parameters, $\gamma_3=0.3\,$eV, $\gamma_4=0.15\,$eV (and $\delta_{AB}=0$), the conductivity values are in the range of $\sigma/\sigma_0\approx{}4-5$ for $100\,$nm$\ <L<1\,\mu$m, in agreement with existing experimental results. The staggered potential ($\delta_{AB}\neq{}0$) suppresses zero-temperature transport, leading to $\sigma\rightarrow{}0$ for $L\rightarrow{}\infty$. Although $\sigma=\sigma(L)$ is no longer universal, the Fano factor approaches the pseudodiffusive value ($F\rightarrow{}1/3$ for $L\rightarrow{}\infty$) in any case with non-vanishing $\sigma$ (otherwise, $F\rightarrow{}1$) signaling the transport is ruled by evanescent waves. Temperature effects are briefly discussed in terms of a phenomenological model for staggered potential $\delta_{AB}=\delta_{AB}(T)$ showing that, for $0<T\leqslant{}T_c\approx{}12\,$K and $\delta_{AB}(0)=1.5\,$meV, $\sigma(L)$ is noticeably affected by $T$ for $L\gtrsim{}100\,$nm.

Mesoscopic valley filter in graphene Corbino disk containing a p-n junction

Suszalski Dominik, Rut Grzegorz, Rycerz Adam
04 Jul 2019 cond-mat.mes-hall arxiv.org/abs/1907.02599

The Corbino geometry allows one to investigate the propagation of electric current along a p-n interface in ballistic graphene in the absence of edge states appearing for the familiar Hall-bar geometry. Using the transfer matrix in the angular-momentum space we find that for sufficiently strong magnetic fields the current propagates only in one direction, determined by the magnetic field direction and the interface orientation, and the two valleys, K and K', are equally occupied. Spatially-anisotropic effective mass may suppress one of the valley currents, selected by the external electric field, transforming the system into a mesoscopic version of the valley filter. The filtering mechanism can be fully understood within the effective Dirac theory, without referring to atomic-scale effects which are significant in proposals operating on localized edge states.

Thermoelectric properties of gapped bilayer graphene

Suszalski Dominik, Rut Grzegorz, Rycerz Adam
04 Oct 2018 cond-mat.mes-hall arxiv.org/abs/1810.02280

Unlike in conventional semiconductors, both the chemical potential and the band gap in bilayer graphene (BLG) can be tuned via application of external electric field. Among numerous device implications, this property also designates BLG as a candidate for high-performance thermoelectric material. In this theoretical study we have calculated the Seebeck coefficients for abrupt interface separating weakly- and heavily-doped areas in BLG, and for a more realistic rectangular sample of mesoscopic size, contacted by two electrodes. For a given band gap ($\Delta$) and temperature ($T$) the maximal Seebeck coefficient is close to the Goldsmid-Sharp value $|S|{\rm max}^{\rm GS}=\Delta/(2eT)$, the deviations can be approximated by the asymptotic expression $|S|{\rm max}^{\rm GS}-|S|_{\rm max}=(k_B/e)\times\left[\frac{1}{2}\ln{u}+\ln{}2-\frac{1}{2}+{\cal O}(u^{-1})\right]$, with the electron charge $-e$, the Boltzmann constant $k_B$, and $u = \Delta/(2k_BT)\gg{}1$. Surprisingly, the effects of trigonal warping term in the BLG low-energy Hamiltonian are clearly visible at few-Kelvin temperatures, for all accessible values of $\Delta\leqslant{}300\,$meV. We also show that thermoelectric figure of merit is noticeably enhanced ($ZT>3$) when a rigid substrate suppresses out-of-plane vibrations, reducing the contribution from $ZA$ phonons to the thermal conductivity.

Lifshitz transition and thermoelectric properties of bilayer graphene

Suszalski Dominik, Rut Grzegorz, Rycerz Adam
15 Dec 2017 cond-mat.mes-hall arxiv.org/abs/1712.05857

This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length $L>10\,\mu{}$m at sub-Kelvin temperatures, that both the Seebeck coefficient and the Lorentz number show anomalies (the additional maximum and minimum, respectively) when the electrochemical potential is close to the Lifshitz energy, which can be attributed to the presence of the van Hove singularity in a bulk density of states. At higher temperatures the anomalies vanish, but measurable quantities characterizing remaining maximum of the Seebeck coefficient still unveil the presence of massless Dirac fermions and make it possible to determine the trigonal warping strength. Behavior of the thermoelectric figure of merit ($ZT$) is also discussed.

Pairwise entanglement and the Mott transition for correlated electrons in nanochains

Rycerz Adam
03 Nov 2016 cond-mat.str-el arxiv.org/abs/1611.01134

Pairwise entanglement, calculated separately for charge and spin degrees of freedom, is proposed as a ground-state signature of the Mott transition in correlated nanoscopic systems. Utilizing the exact diagonalization - ab initio method (EDABI), for chains containing $N\leqslant{}16$ hydrogenic-like atoms (at the half filling), we find that the vanishing of the nearest-neighbor charge concurrence indicates the crossover from a partly-localized quantum liquid to the Mott insulator. Spin concurrence remains nonzero at the insulating phase, showing that the decopling of spin and charge degrees of freedom may manifest itself by wavefunctions entangled in spin, but separable in charge coordinates. At the quarter filling, the analysis for $N\leqslant{}20$ shows that spin concurrence vanishes immediately when the charge-energy gap obtained from the scaling with $1/N\rightarrow{}0$ vanishes, constituting a finite-system version of the Mott transition. Analytic derivations of the formulas expressing either charge or spin concurrence in terms of ground-state correlation functions are also provided.

Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakes

Rycerz Adam
13 Apr 2016 cond-mat.mes-hall arxiv.org/abs/1604.03783

Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic field, accompanied by approximate twofold valley degeneracy of each energy level [Phys. Rev. B 85, 245424 (2012)]. Atomic-scale disorder induce the scattering of charge carriers between the valleys and restores the spectral fluctuations of GOE. A simplified description of such a nonstandard GUE-GOE transition, employing the mixed ensemble of 4x4 real symmetric matrices was also proposed. Here we complement our previous study by analyzing numerically the spectral fluctuations of large matrices belonging the same mixed ensemble. Resulting scaling laws relate the ensemble parameter to physical size and the number of atomic-scale defects in graphene flake. A phase diagram, indicating the regions in which the signatures of GUE may by observable in the size-doping parameter plane, is presented.

Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer-graphene Corbino disks

Rut Grzegorz, Rycerz Adam
15 Nov 2015 cond-mat.mes-hall arxiv.org/abs/1511.04705

Using the transfer matrix in the angular-momentum space we investigate the impact of trigonal warping on magnetotransport and scaling properties of a ballistic bilayer graphene in the Corbino geometry. Although the conductivity at the charge-neutrality point and zero magnetic field exhibits a one-parameter scaling, the shot-noise characteristics, quantified by the Fano factor $\mathcal{F}$ and the third charge-transfer cumulant $\mathcal{R}$, remain pseudodiffusive. This shows that the pseudodiffusive transport regime in bilayer graphene is not related to the universal value of the conductivity but can be identified by higher charge-transfer cumulants. For Corbino disks with larger radii ratios the conductivity is suppressed by the trigonal warping, mainly because the symmetry reduction amplifies backscattering for normal modes corresponding to angular-momentum eigenvalues $\pm{}2\hbar$. Weak magnetic fields enhance the conductivity, reaching the maximal value near the crossover field $B_L=\frac{4}{3}\sqrt{3}\,({\hbar}/{e})\,t't_\perp!\left[{t_0^2a(R_{\rm o}-R_{\rm i})}\right]^{-1}$, where $t_0$ ($t_\perp$) is the nearest-neighbor intra- (inter-)layer hopping integral, $t'$ is the skew-interlayer hopping integral, and $R_{\rm o}$ ($R_{\rm i}$) is the outer (inner) disk radius. For magnetic fields $B\gtrsim{}B_L$ we observe quasiperiodic conductance oscillations characterized by the decreasing mean value $\langle\sigma\rangle-\sigma_0\propto{}B_L/B$, where $\sigma_0=(8/\pi)\,e^2/h$. The conductivity, as well as higher charge-transfer cumulants, show beating patterns with an envelope period proportional to $\sqrt{B/B_L}$. This constitutes a qualitative difference between the high-field ($B\gg{}B_L$) magnetotransport in the $t'=0$ case (earlier discussed in Ref. [1]) and in the $t'\neq{}0$ case, providing a finite-system analog of the Lifshitz transition.