Nonreciprocal Current-Induced Zero-Resistance State in Valley-Polarized Superconductors

Abstract

The recently observed nonreciprocal current-induced zero-resistance state (CIZRS) in twisted trilayer graphene/WSe$_2$ heterostructure has posed a significant theoretical challenge. In the experiment, the system shows a zero-resistance state only when a sufficiently large current is applied in a particular direction, while stays in an incipient superconducting state with small resistance when the current is small or flows in the opposite direction. In this Letter, we provide a theory of CIZRS. We show that the threefold degenerate Fulde-Ferrell (FF) states are stabilized by the valley polarization and trigonal warping effects of twisted trilayer graphene/WSe$_2$ heterostructures. Moreover, a current flowing in a particular direction breaks the threefold degeneracy and favors a particular FF pairing domain. We therefore propose that the incipient superconducting state is naturally understood as a multidomain state where the interdomain supercurrent is difficult to flow due to the tiny Josephson coupling caused by the mismatch of Cooper-pair momenta between different FF domains. Nevertheless, a sufficiently large current in a particular direction can selectively populate a certain FF state and create monodomain pathways with zero resistance. Crucially, due to the threefold symmetry of the system, a current flowing in the opposite direction can fail to generate the zero-resistance pathways, thus giving rise to the observed nonreciprocity. Finally, we suggest that the long-sought-after triangular finite-momentum state can also be realized in valley-polarized superconductors.

Figures (6)

• Figure 1: (a),(b) Fermi surfaces of the SLS model for (a) $\delta\mu=0$ and (b) $\delta\mu=0.35$. Here and hereafter, we adopt $t=1$, $\mu=-0.65$, and $\phi=-0.2\pi$. The red and blue lines indicate Fermi surfaces of the valley $\eta=+$ and $-$, i.e., $\varepsilon_{+,\bm{k}}=0$ and $\varepsilon_{-,\bm{k}}=0$, respectively. (c),(d) Nestings of the Fermi surfaces for $\delta\mu=0.35$. Red and blue curves indicate $\varepsilon_{+,\bm{k}}=0$ and $\varepsilon_{-,-\bm{k}+\bm{q}}=0$, respectively, with (c) $\bm{q}=(0.33,0)$ and (d) $\bm{q}=(-0.19,0)$.
• Figure 2: (a) The $T-\delta\mu$ phase diagram of the SLS model for $t=1$, $\mu=-0.65$, and $\phi=-0.2\pi$. We adopt $u=0.596$, which gives the transtion temperature $T_{\rm c0}\simeq 0.15$ for $\delta\mu=0$. The black, red, and blue solid lines indicate the second-order phase transition from the normal state to Bardeen-Cooper-Schrieffer (BCS), Fulde-Ferrell (FF), and triangular (Tri) states, respectively. The red dotted lines are the guide for the eye. (b) Equilibrium Cooper-pair momentum along the transition line shown in panel (a). (c) Pairing susceptibility $\chi(\bm{q})$ near $\bm{q}=0$ for $\delta\mu=0.35$ and $T=0.08\simeq T_{\rm c}(\delta\mu)$.
• Figure 3: The quartic Ginzburg-Landau coefficients $\beta,$ (black) $\beta',$ (red) and $\beta"$ (blue) calculated along the transition line shown in Fig. \ref{['fig:phase_diagram']}(a).
• Figure 4: Thermodynamic phase diagrams of the spatially uniform FF states in the current density $\bm{j}=(j_x,j_y)$ (a) without and (b),(c) with nematicity. The panels (b) and (c) correspond to the cases of $\bm{j}_{\rm nem}$ parallel and antiparallel to $\hat{x}$. The red, blue, and yellow regions indicate the FF states with Cooper-pair momentum $\bm{q}_0$, $\bm{q}_1$, and $\bm{q}_2$, respectively.
• Figure 5: (a)-(c) Schematic $(I_x,I_y)$ phase diagrams and (d),(e) current-resistivity relation of the trigonal FF superconductors. Panels (a)-(c) correspond to Figs. \ref{['fig:pd_j']} (a)-(c), and show the phase diagrams (a) with and (b),(c) without nematicity, with a phenomenologically introduced randomness $\delta I$. The white region indicates a multidomain state, and thus is resistive. Panels (d) and (e) indicate the expected resistance in $(I_x,0)$ and $(0,I_y)$ for panel (a), where $R_{\rm N}$ indicates the normal-state resistance.