Bound state with negative binding energy induced by coherent transport in a two-dimensional quantum wire

In a two-dimensional quantum wire in a perpendicular magnetic field with a smooth embedded repulsive scattering potential we find in the multimode conductance resonances caused by bound states with negative binding energy. These resonances are the counterexamples to well-known dips in the conductance and evanescent states caused by quasibound states of attractive scattering centers in the wire.

Figure 1

(Color online) (a) The conductance in units of $G_0=2e^2∕h$ of a broad wire with one embedded narrow potential well at the center $x=0$, as function of $X=E∕\left(\hslash {\Omega }_w\right)+1∕2$. (b) The probability density of the scattering state corresponding to an incident state with $X=1.996$ and $n=1$. $E_0=\hslash {\Omega }_0=1\mathrm{meV},V_0=-8\mathrm{meV},\beta ={10}^{-2}{\mathrm{nm}}^{-2}$, and for GaAs $a_0=9.79\mathrm{nm}$. $a_w=29.34\mathrm{nm}$ at $B=0.5\mathrm{T}$, and $a_w=14.68\mathrm{nm}$ at $B=3.0\mathrm{T}$.

Figure 2

(Color online) The conductance in units of $G_0=2e^2∕h$ of a broad wire with one embedded narrow potential hill at the center $x=0$, as function of $X=E∕\left(\hslash {\Omega }_w\right)+1∕2$ (a), and the same repeated for a narrow range of $X,E_0=\hslash {\Omega }_0=1\mathrm{meV},V_0=+8\mathrm{meV},\beta ={10}^{-2}{\mathrm{nm}}^{-2}$.

Figure 3

(Color online) Corresponding to special values of $X$ in Fig. 2 the probability density of the scattering state corresponding to an incident state with $X=1.242$, $n=1$, and $B=2\mathrm{T}$ (a), $X=2.054$, $n=2$, and $B=3\mathrm{T}$ (b), and $X=2.242$, $n=2$, and $B=3\mathrm{T}$ (c). $E_0=\hslash {\Omega }_0=1\mathrm{meV},V_0=+8\mathrm{meV},\beta ={10}^{-2}{\mathrm{nm}}^{-2}$.

Figure 4

(Color online) The probability density of the scattering state corresponding to an incident state with $X=2.29$, $n=2$, and $B=2\mathrm{T}$ corresponding to a broad resonance in Fig. 2a, $E_0=\hslash {\Omega }_0=1\mathrm{meV},V_0=+8\mathrm{meV},\beta ={10}^{-2}{\mathrm{nm}}^{-2}$.