Josephson effect in ballistic graphene
Josephson effect in ballistic graphene
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DOI：
10.1103/physrevb.74.041401
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发表时间：
2006-05
影响因子：
3.7
通讯作者：
M. Titov;C. Beenakker
中科院分区：
文献类型：
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作者：
M. Titov;C. Beenakker
我们在无杂质超导\char21{}普通金属\char21{}超导结中求解 Dirac\char21{}Bogoliubov\char21{}de Gennes 方程，以确定可以流过具有重掺杂超导电极的未掺杂石墨烯带的最大超电流 ${I}_{c}$。结果 ${I}_{c}\ensuremath{\simeq}(W∕L)e{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$ 由超导间隙 ${\ensuremath{\Delta}}_{0}$ 和结的纵横比（长度 $L$ 相对于宽度 $W$ 和超导相干长度而言较小）确定。远离零掺杂的狄拉克点，我们恢复通常的弹道结果 ${I}_{c}\ensuremath{\simeq}(W∕{\ensuremath{\lambda}}_{F})e{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$，其中费米波长 ${\ensuremath{\lambda}}_{F}$ 接管$L$。临界电流和正常状态电阻的乘积 ${I}_{c}{R}_{\mathrm{N}}\ensuremath{\simeq}{\ensuremath{\Delta}}_{0}∕e$ 在接近狄拉克点时保持其通用值（最多为数值前置因子）。
We solve the Dirac\char21{}Bogoliubov\char21{}de Gennes equation in an impurity-free superconductor\char21{}normal-metal\char21{}superconductor junction, to determine the maximal supercurrent ${I}_{c}$ that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result ${I}_{c}\ensuremath{\simeq}(W∕L)e{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$ is determined by the superconducting gap ${\ensuremath{\Delta}}_{0}$ and by the aspect ratio of the junction (length $L$ small relative to the width $W$ and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result ${I}_{c}\ensuremath{\simeq}(W∕{\ensuremath{\lambda}}_{F})e{\ensuremath{\Delta}}_{0}∕\ensuremath{\hbar}$, in which the Fermi wavelength ${\ensuremath{\lambda}}_{F}$ takes over from $L$. The product ${I}_{c}{R}_{\mathrm{N}}\ensuremath{\simeq}{\ensuremath{\Delta}}_{0}∕e$ of the critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.