Towards high-temperature coherence-enhanced transport in heterostructures of a few atomic layers

The possibility to exploit quantum coherence to strongly enhance the efficiency of charge transport in solid state devices working at ambient conditions would pave the way to disruptive technological applications. In this work, we tackle the problem of the quantum transport of photogenerated electronic excitations subject to dephasing and on-site Coulomb interactions. We show that the transport to a continuum of states representing metallic collectors can be optimized by exploiting the “superradiance” phenomena. We demonstrate that this is a coherent effect which is robust against dephasing and electron-electron interactions in a parameters range that is compatible with actual implementation in few-monolayer transition-metal-oxide (TMO) heterostructures.

Figure 1

Illustration of the charge generation and collection along quantum coherent pathways in a few-monolayer oxide heterostructure (top). The process is modelled out of equilibrium via an effective one-dimensional open quantum system for a single excitation (middle) in Sec. 2 and in equilibrium via an effective many-particle Hubbard-model (bottom) in Sec. 3.

Figure 2

Numerics for (a) maximal current, $I_{\mathrm{se}}$, obtainable in the single-particle approximation from maximization of Eq. (6) in a chain of length $N=10$, as a function of both the coupling to the sink ${\gamma }_{\text{out}}$ and dephasing ${\gamma }_{\varphi }$. The vertical dashed line indicates the optimal coupling out which agrees with the superradiant transition ${\gamma }_{\text{out}}={\gamma }^{\mathrm{st}}$ shown in (b). (b) Decay widths as a function of the coupling to the sink ${\gamma }_{\text{out}}$ in absence of dephasing. Blue circles mark the largest width, green triangles indicate the average of all other widths. The dashed vertical line indicates the superradiant transition, namely, where the average widths have a maximum.

Figure 3

Analytical formula (black solid line) and numerics (markers) for (a) average transfer time, Eq. (9), [(b) and (d)] NESS current, Eq. (12), and (c) maximal current in the single-particle approximation, Eq. (17). (a) The average transfer time is minimal at the superradiant transition ${\gamma }^{\mathrm{st}}$ (vertical dashed line) and increases with increasing values of ${\gamma }_{\varphi }$. At large ${\gamma }_{\varphi }$, the minimum peak turns into a plateau. Far from the superradiant transition, $\tau$ is almost independent of ${\gamma }_{\varphi }$. (b,d) Below $1/\tau$ (vertical dashed lines) the current is linearly proportional to ${\gamma }_{\text{in}}$. Above $1/\tau$ the current saturates because all the calculations are here done in the single-excitation subspace (cf. Appendix pp2). For (b), ${\gamma }_{\varphi }=0.1t/\hslash$ and for (d) ${\gamma }_{\text{out}}={\gamma }^{\mathrm{st}}$. (c) Below the value of the dephasing ${\tilde{\gamma }}_{\varphi }$, Eq. (15), (vertical dashed lines) the current $I$ is independent of ${\gamma }_{\varphi }$. Above ${\tilde{\gamma }}_{\varphi }$ the current decreases $\propto {\gamma }_{\varphi }^{-1}$ (dash-dotted line).

Figure 4

(a) Sketch of the one-dimensional model solved within DMFT. (b) Conductance $g$ (in units of the conductance quantum $e^2/h$) as a function of the coupling to the sinks $\gamma$ for different values of the local Hubbard interaction $U_{\mathrm{eff}}$. The maximum of $g$, marker of the superradiant transition, is found at approximatively ${\gamma }^{\mathrm{st}}=2t$ (dashed black line) and it is nearly independent on $U_{\mathrm{eff}}$. (Inset) Suppression of the conductance at the superradiant transition $g^{\mathrm{st}}$ as a function of $U_{\mathrm{eff}}$. (c) Evolution with $\gamma$ of the site-resolved local spectral function $A\left(\hslash \omega \right)$, for the sites labeled as in panel (a). The states localized at the edge of the chain become superradiant both at $U_{\mathrm{eff}}=0$ and at finite $U_{\mathrm{eff}}$. The effect is symmetric on the other half of the chain. The results are obtained for $N=10$ with a regularization $\eta /t=0.03$ for the analytic continuation of the retarded Green's function.

Figure 5

(a) Perovskite structures of ${\mathrm{LaVO}}_3$ and ${\mathrm{SrVO}}_3$. The few-monolayer (${\mathrm{SrVO}}_3{)}_n$/(${\mathrm{LaVO}}_3{)}_m$/(${\mathrm{SrVO}}_3{)}_n$ heterostructure constitutes a promising platform to realize coherence-enhancement transport schemes. (b) Cartoon of the real-space electronic configuration (left and right panels) and energy-levels scheme (central panels) of the $d_{yz}\text{−}{d}_{yz}$ optical transition, which results in the photoinjection of an electron-hole excitation. The black arrows indicate the electronic spin configuration in the orbital- and spin-ordered state at $T<T_c$. The red arrows indicate the spin configuration of the photoexcitation. The energy cost for the $d_{yz}\text{−}{d}_{yz}$ optical transition is $U\text{−}{J}_H\simeq 1.8$ eV, $J_H$ being the Hund's coupling. (c) Real part of the $c$-axis optical conductivity of bulk ${\mathrm{LaVO}}_3$, as measured by optical spectroscopy. The data are taken from Ref. [57]. At $T<T_c$, the optical conductivity evidences the appearance of a well defined absorption feature at $\simeq 1.8$ eV for light polarization parallel to the $c$ axis. The dashed line represents the Lorentz oscillator, which accounts for the 1.8 eV optical transition. The estimated transition width is $\mathrm{\Gamma }/2\simeq 300$ meV.

Figure 6

Value of the current (6) as a function of the pumping ${\gamma }_{\text{in}}$ for zero dephasing (blue curve) and large dephasing ${\gamma }_{\varphi }$ (red curve) in the single-excitation approximation (se) computed from Eq. (12). Symbols indicate the same current (6), but in the full excitation manifold (me): Blue circles for zero dephasing, and red squares for ${\gamma }_{\varphi }=10$. As one can see, both the single-particle approximation and the full excitation calculation give rise to the same current for ${\gamma }_{\text{in}}\le 1/\tau$, the latter being shown as vertical dashed lines.

Figure 7

Effect of disorder and losses on the maximal current. (a) Ensemble averaged maximal NESS current $\langle I_{\mathrm{se}}\rangle$ as a function of the disorder strength $W$ and the dephasing ${\gamma }_{\varphi }$ at the superradiant transition ${\gamma }^{\mathrm{st}}$ obtained from averaging over 100 realizations of the disorder. For $W<\tilde{W}=t$ (left of the vertical full line), the current is independent of $W$, and maximal and independent of the dephasing for ${\gamma }_{\varphi }\le {\tilde{\gamma }}_{\varphi }$ (below the horizontal dashed line). For $W>\tilde{W}=t$, we see the dephasing-assisted transport regime: The current is suppressed by localization and is maximal at ${\gamma }_{\varphi }\approx W/\left(\sqrt{6}\hslash \right)$ (diagonal dashed-dotted line). (b) Current as a function of the losses at ${\gamma }_{\varphi }=0$ and ${\gamma }_{\text{out}}={\gamma }^{\mathrm{st}}$. For ${\gamma }_{\mathrm{loss}}\ge {\tilde{\gamma }}_{\text{loss}}={\tau }^{-1}{|}_{{\gamma }_{\mathrm{loss}}=0}$ (vertical dashed line) the current is strongly suppressed.

Figure 8

In conventional photovoltaic devices, the high-energy excitation created by photoabsorption first thermalizes and then migrates to the electrodes (continuum) with an effective drift velocity $v_d$ and can be trapped in low-energy states created by defects in the structure (blue arrows). In the few-atomic layers devices, we consider here the excitation migrates to the electrodes before thermalization occurs in a time $\tau$ that is minimal at the superradiant transition (red arrows).