Phonon-Induced Zero-bias Currents in Solids

Abstract

Zero-bias current induced by injected phonons in metals and one-dimensional charge density wave (CDW) systems attached on the surface of the piezoelectric substrate is investigated microscopically based on the second order response theory. In contrast to the shift currents discovered by von Baltz and Kraut in which the zero-bias current is induced by AC electric field in systems without inversion symmetry, propagating phonons break the inversion symmetry in the presesnt case. The effects of both deformation potential and piezoelectric potential are taken into account. In the CDW system, zero-bias current appears below the transition temperature and its magnitude strongly depends on the position of the chemical potential. Possible experimental consequences are discussed.

Figures (4)

• Figure 1: (Color online) Schemetic representation of $I$(current)-$V$(voltage) curves in the presence of zero-bias currents together with ordinary Ohmic currents. Zero-bias current can be either plus (solid circle) for holes or minus (cross) for electrons at $V=0$. $V$ represents the voltage applied to the sample.
• Figure 2: Feynman diagram for the second order response theory. Solid lines represent thermal Green's functions and the wavy lines represent the perturbation $H'(t)$. The relation $\bm q = \bm q_1 + \bm q_2$ has been noted. Note that the vertices associated with the perturbation have Matsubara frequencies $i\omega_{\lambda 1}$ and $i\omega_{\lambda 2}$ with $\omega_{\lambda 1}>0$ and $\omega_{\lambda 2}>0$.
• Figure 3: $\langle j_x \rangle / j_{0}$ as a function of $\mu/t$ at $T=0$, where $j_{0} = |e| Q \Omega v_{\rm F} \hbar |A_{\bm Q}|^2 L/(t\Gamma^2)$ with a unit of energy $t$. $\Gamma$ is fixed at $\Gamma/t = 0.05$ and $\Delta$ are chosen as $\Delta/t=0.1, 0.5$ and $1.0$.
• Figure 4: $\langle j_x \rangle/j_0$ as a function of temperature for several values of the chemical potential $\mu$. [$\mu/\Delta_0=0.05, 0.25, 0.50, 0.75$, and $0.95$ from top to bottom.] The unit of energy is taken as $\Delta_0$ that is the magnitude of the gap at $T = 0$. $\Gamma$ is fixed at $\Gamma/\Delta_0 = 0.10$. The inset shows the positions of the chemical potentials.