Interface-mediated pairing in field effect devices

We consider the pairing induced in a strictly two-dimensional electron gas (2DEG) by a proximate insulating film with polarizable localized excitations. Within a model of interacting 2D electrons and localized two-level systems, we calculate the critical temperature $T_c$ as a function of applied voltage and for different materials properties. Assuming that a sufficient carrier density can be induced in a field-gated device, we argue that superconductivity may be observable in such systems. $T_c$ is found to be a nonmonotonic function of both electric field and the excitation energy of the two-level systems.

Figure 1

Our model of a field effect transistor is represented by two layers ($L1$ and $L2$). $L1$: dielectric layer with local dipoles of dipole moment $e{d}_{sp}$, presented by two-level systems; $L2$: metallic DS channel with a 2D electron gas.

Figure 2

Left panel: Effective pair interaction $V_{\mathrm{eff}}∕4t$ vs normalized electric field energy $E_{sp}∕4t$ for various excitation energies ${\Delta }_{sp}$ of the local two-level systems in layer $L1$. The dielectric constant $ϵ=100$ controls the increase of charge density in the metallic layer $L2$ with electric field [see Eqs. (38, 39)], whereby we chose a bandwidth $4t=400\mathrm{meV}$, a dipole length $d_{sp}=2\mathrm{\AA }$ (for charge transfer excitations), and a lattice constant $a=4\mathrm{\AA }$. The coupling of the dipoles to the conduction electrons is fixed at $V_{sp}∕4t=1.89$ which corresponds to a spatial distance $r∕a=1.5$ [see Eq. (40)]. Right panel: variational parameter $\gamma$ vs normalized electric field $E_{sp}∕4t$, where $\gamma$ is found from the minimization of the free energy [right-hand side of Eq. (26)].

Figure 3

Left panel: Effective hopping $t_{\mathrm{eff}}∕t$ vs normalized electric field energy $E_{sp}∕4t$ at the transition temperature $T_c$; all paramaters are identical to those of Fig. 2. Right panel: bosonic occupation number $n_b$ (the relative number of inverted two-level systems per site) vs normalized electric field energy $E_{sp}∕4t$ at the transistion temperature $T_c$.

Figure 4

The derivative of the chemical potential with respect to particle density $\partial \mu ∕\partial n$ versus particle density $n$ at the respective $T_c$, calculated in Sec. 2. All paramaters are identical to those of Fig. 2. For a positive value of the derivative, the normal and superconducting states are globally stable in the vicinity of the transition.

Figure 5

Ionic displacement in atomic clusters: induced pairing interaction $V_{\mathrm{eff}}∕4t$ versus electric field energy $E_{sp}∕4t$ for $ϵ=10$, $d_{sp}=0.1\mathrm{\AA }$, and $r∕a=1$ (which corresponds to $V_{sp}∕4t=0.2125$). Left and lower right panels show different scales. Upper right panel: Pairing interaction versus dielectric constant $ϵ$ for charge density $n=0.5$.

Figure 6

Charge transfer excitations: transition temperature $T_c∕4t$ versus excitation energy ${\Delta }_{sp}∕4t$. The three curves present $T_c$ for small and intermediate band filling. The dielectric constant is $ϵ=100$, which implies $c=1.87$ for the considered set of parameters [see Eq. (41)]. The coupling of the dipoles to the conduction electrons is fixed to $V_{sp}∕4t=1.89$ which corresponds to a spatial distance $r∕a=1.5$ [see Eq. (40)].

Figure 7

Charge transfer excitations: transition temperature $T_c∕4t$ versus electric field energy $E_{sp}∕4t$ and band filling $n$, lower axis and upper axis, respectively. The three curves present different dielectrics which are characterized by different excitation energies only, other parameters are fixed for comparison. The dielectric constant $ϵ$ is 100 and $V_{sp}∕4t=1.89(r∕a=1.5)$.

Figure 8

Charge transfer excitations: transition temperature $T_c∕4t$ versus excitation energy ${\Delta }_{sp}∕4t$. The three curves present different dielectrics $(ϵ=10,50,100)$. The band filling is fixed at $n=0.1$, and the interaction $V_{sp}∕4t=1.89$ corresponds to $r∕a=1.5$.

Figure 9

Charge transfer excitations $(d_{sp}=2\mathrm{\AA },$ ${\Delta }_{sp}∕4t=2.5,$ $ϵ=100)$: transition temperature $T_c∕4t$ versus electric field energy $E_{sp}∕4t$, parametrized by $r∕a$. The corresponding $V_{sp}$ is in the intermediate coupling range: $V_{sp}∕4t=4.25$ (corresponds to $r∕a=1$), $V_{sp}∕4t=2.72(r∕a=1.25)$, $V_{sp}∕4t=1.89(r∕a=1.5)$, $V_{sp}∕4t=1.39(r∕a=1.75)$.

Figure 10

Charge transfer excitations: transition temperature $T_c∕4t$ versus electric field energy $E_{sp}∕4t$ and band filling $n$, lower axis, and upper axis, respectively. A local electronic interaction $U$ (within layer $L2$) is included in a weak coupling evaluation. The dielectric constant $ϵ$ is 100 and $V_{sp}∕4t=1.89$ $(r∕a=1.5)$.

Figure 11

Atomic excitations ($d_{sp}=1\mathrm{\AA }$, ${\Delta }_{sp}=10\mathrm{eV}$, $ϵ=100$): transition temperature $T_c∕4t$ versus electric field energy $E_{sp}∕4t$, parametrized by $r∕a$: $V_{sp}∕4t=2.125$ (corresponds to $r∕a=1$), $V_{sp}∕4t=1.36$ $(r∕a=1.25)$, $V_{sp}∕4t=0.94$ $(r∕a=1.5)$.