Two-dimensional fermionic Hong-Ou-Mandel interference with massless Dirac fermions

We propose a two-dimensional Hong-Ou-Mandel (HOM) type interference experiment for massless Dirac fermions in graphene and 3D topological insulators. Since massless Dirac fermions exhibit linear dispersion, similar to photons in vacuum, they can be used to obtain the HOM interference intensity pattern as a function of the delay time between two massless Dirac fermions. We show that while the Coulomb interaction leads to a significant change in the angle dependence of the tunneling of two identical massless Dirac fermions incident from opposite sides of a potential barrier, it does not affect the HOM interference pattern. We apply our formalism to develop a massless Dirac fermion beam splitter (BS) for controlling the transmission and reflection coefficients. We calculate the resulting time-resolved correlation function for two identical massless Dirac fermions scattering off the BS.

Figure 1

HOM experiment with massless Dirac fermion BS.

Figure 2

Transmission probability $T$ as a function of incident angle $\varphi$. The electron concentration $n$ outside the barrier is chosen as $0.5\times {10}^{12}$ $\text{cm}{}^{-2}$. This corresponds to a Fermi energy and wavelength of incident electrons of $E_F\approx 80$ meV and $\lambda \approx 50$ nm, respectively. The barrier height $V_0=200$ meV. The red curve is the solution for $\Delta =0$ and the blue curve is the solution for $\Delta =-0.63$. Black (dashed) semicircle is drawn at 50% transmission probability.

Figure 3

Interference peak for normalized number of coincidences ${\tilde{N}}_c\left(\delta \tau \right)$ against time delay $\delta \tau$. The red curve is for $R=T=1/2$ and for ${\Gamma }_1={\Gamma }_2=\Gamma$, and the black curve is for $R=1/5,T=4/5$ and for ${\Gamma }_1={\Gamma }_2=2\Gamma /3$. The blue curve is for $T=2/3,R=1/3$ and ${\Gamma }_1=2\Gamma /3,{\Gamma }_2=7\Gamma /3$, where $\Gamma =3\times {10}^{-12}{\text{s}}^{-1}$.