Conductance fluctuations and disorder induced $\nu =0$ quantum Hall plateau in topological insulator nanowires

Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and find, in contrast, that a zero Hall plateau emerges within a broad energy window close to the Dirac point. We numerically calculate the conductance and its distribution for a statistical ensemble of disordered nanowires, and use the conductance fluctuations to study the dependence of the insulating phase on system parameters, such as the nanowire length, disorder strength, and the magnetic field.

Figure 1

(i) A schema of a 3D strong topological insulator nanowire of cross section $(H,W)=$ (20 nm, 120 nm) and length $L$ with a magnetic field $B$ perpendicular to the nanowire axis. (ii) The energy spectrum of a clean such nanowire, exposed to a $B=4$ T magnetic field, as a function of the coaxial crystal momentum $k$. (iii) The probability density ${\left|\psi \right|}^2$ of the wave function in real space in the nanowire cross section. In all plots, the color scale goes from the red dark color for the maximum value to the yellow light color for the minimum. For a state at zero energy (c, f) the wave function is localized both at the top and at the bottom of the wire, while for higher momenta $k=(-0.4,-0.3,0.4,-0.3)$, corresponding to (a, b, d, e), it is localized at the edges revealing its chiral nature. The dashed line represents the theoretical values of the relativistic Landau levels.

Figure 2

The density of state $\rho$ as a function of the energy $E$ in a disordered, $660\mathrm{nm}$ long nanowire exposed to a 4 T magnetic field for three different disorder strengths $g$.

Figure 3

Average conductance $G$ at disorder strength $g$ as a function of the chemical potential $E_F$ for a 1100 nm long nanowire in a 4 T magnetic field. Inset: Length dependence of the conductance for fixed disorder strength $g=0.9$ at three different chemical potentials $E_F$. The dashed line represent an exponential fit with the decay length equal to the nanowire perimeter $P$.

Figure 4

Average conductance $G$ and the corresponding conductance variance $\delta G^2$ as a function of the chemical potential $E_F$ for nanowires of various lengths $L$ and disorder strengths $g$ in a 4 T magnetic field.

Figure 5

Dependence of the conductance variance peak center $x_c$ and width $\mathrm{\Gamma }$, obtained from a Gaussian fit, on the nanowire length $L$ and magnetic field $B$ for three different disorder strengths $g$.

Figure 6

The conductance variance peak center $x_c$ and width $\mathrm{\Gamma }$ as a function of the disorder strength $g$ for two different nanowire lengths $L$ and 4 T magnetic field. The dashed lines in the plots are $\sqrt{g}$ fits.

Figure 7

The conductance distribution at the variance peak point $x_c$ for various disordered nanowire statistical ensemble of a 4 T magnetic field but for different length $L$, disorder strength $g$, and energy $E$.

Figure 8

Conductance variance $\delta G^2$ for fixed disorder strength $g=1.0$ and fixed length $L=1000$ nm and a magnetic field $B=20$ T for various heights $H$ and widths $W$.