Gate-Tunable Transport and 1D Channel in a Graphene Nanoslide

TL;DR

The graphene nanoslide realizes a single strain-induced pseudogauge barrier whose transport and 1D channel properties can be tuned by a bottom gate. By solving the closed-form scattering problem, analyzing bound states, and characterizing the local density of states, the work reveals a hybrid pseudogauge-electrostatic cavity in the bipolar regime and a gate-tunable 1D channel that can be valley-chiral or counterpropagating. The authors further develop a transfer-matrix framework and validate the theory with tight-binding simulations, obtaining gate-tunable resonances when bound states merge with the Dirac continuum and a sublattice- and electron-hole–dependent LDOS. Collectively, this provides a noninteracting theoretical foundation for strain-engineered graphene devices and a platform for exploring tunable 1D transport and Luttinger-liquid physics in graphene-based nanoelectronics.

Abstract

We present a theory of the graphene nanoslide, a fundamental device for graphene straintronics that realizes a single pseudogauge barrier. We solve the scattering problem in closed form and demonstrate that the nanoslide gives rise to a hybrid pseudogauge and electrostatic cavity in the bipolar regime, and hosts one-dimensional transverse channels. The latter can be tuned using a bottom gate between valley chiral or counterpropagating modes, as well as one-dimensional flatbands. Hence, the local density of states near the barrier depends strongly on the gate voltage with a tunable sublattice and electron-hole asymmetry. In the presence of electron-electron interactions, the nanoslide allows for in-situ tuning between a chiral and ordinary Tomonaga-Luttinger liquid.

Figures (5)

• Figure 1: Graphene nanoslide. (a) Illustration of the graphene nanoslide device for the transport axis $x$ along the armchair lattice direction. (b) Height profile, pseudogauge barrier, and pseudomagnetic dipole of the nanoslide. (c) Two-terminal conductance as a function of carrier density in the leads for $V_b = 0$. Calculated with the transfer-matrix method for a linear density profile (see inset) with $\alpha = 0.8$, $l = 100$ nm, and $n_i = -V_i |V_i| / ( \pi v_F^2 )$ ($i=1,2$) the density in the leads. The dashed lines follow from Eq. \ref{['eq:interference']} for $\delta = 0.16$ and match the resonances in the bipolar regime ($n_1/n_2 < 0$). (d) Two-terminal conductance for $n_1 = n_2$ in units of the ballistic conductance as a function of the pseudogauge [$\alpha \sim \Delta^2 / (da_0)$] and electrostatic [$\gamma \sim V_b l / v_F$] barrier.
• Figure 2: Tight-binding simulations. Two-terminal conductance calculated with tight binding for $x \parallel$ armchair, using the height profile \ref{['eq:h']} for $\Delta = 1$ nm and $d = 10$ nm. We use the hopping function $t(r) = -t_0\exp \left[ \beta(1 - r/a_0) \right]$ with $t_0 = 3$ eV and $\beta = 3.37$pereira_tight-binding_2009. (a) Only the strain barrier as a function of density $n$ and $\alpha_\text{tb} \equiv \beta \Delta |\Delta| / (3a_0d)$. (b) Line cuts marked in (a). Deviations from Eq. \ref{['eq:g2']} (dashed line) for $n > 10^{12}$ cm$^{-2}$ appear when $\lambda_F$ becomes comparable to the barrier width $d$. (c) With a potential $V(x) = V_b \mathop{\mathrm{sech}}\nolimits^4(4x/l)$ due to a bottom gate for $l = 50$ nm where $\gamma = V_bl / (3v_F)$ and $n = 10^9$ cm$^{-2}$.
• Figure 3: Gate-tunable 1D channel. (a) Velocity $v_+(\alpha,\gamma)$ of bound states with dispersion $E_b = v_\pm k_y$ with $v_-(\alpha,\gamma) = -v_+(\alpha,-\gamma)$. Solid and dashed curves give $v_+ = 0$ and $|v_+| = v_F$, respectively. (b) Phase diagram: orange (cyan) regions host valley chiral (counterpropagating) modes. A typical bound-state dispersion is sketched for valley $K$ (blue) and $K'$ (red), where the gray cone gives the bulk continuum.
• Figure 4: Local density of states. (a)--(b) Analytical result of the low-energy theory for $\alpha = 0.8$ and $\gamma = 0$. (a) Fluctuations of the LDOS (solid) showing contributions from scattering (dashed) and bound (dotted) states. (b) Sublattice-resolved LDOS fluctuations. (c)--(e) Tight-binding results for $\Delta = 1 \mathord{\rm nm}$, $d = 10 \mathord{\rm nm}$, $n = 10^{12} \mathord{\rm cm^{-2}}$, and potential $V(x) = V_b \mathop{\mathrm{sech}}\nolimits^4(4x/l)$ with $l = 100 \mathord{\rm nm}$. (c) LDOS fluctuations for sublattice A versus $x$ and $V_b$. Triangles at $V_b = 0, \pm 0.3 \mathord{\rm eV}$ indicate the ranges of line cuts in (d) and (e).
• Figure S1: Two-terminal conductance $G(n_1,n_2)$ (top row) and resistance (bottom row) for a graphene nanoslide with $\alpha = 0.8$ as a function of the density in the leads $n_1$ and $n_2$ using a linear density profile. Here the distance between leads $l$ is indicated at the top, and we use the transfer-matrix method with $N = 201$ for the simulation. Dashed lines in the top row correspond to the quantization rule of the main text with $\delta = 0.16$, and where black ($+$) and gray ($-$) correspond to time-reversed phases.