Remote Mesoscopic Signatures of Induced Magnetic Texture in Graphene

Mesoscopic conductance fluctuations are a ubiquitous signature of phase-coherent transport in small conductors, exhibiting universal character independent of system details. In this Letter, however, we demonstrate a pronounced breakdown of this universality, due to the interplay of local and remote phenomena in transport. Our experiments are performed in a graphene-based interaction-detection geometry, in which an artificial magnetic texture is induced in the graphene layer by covering a portion of it with a micromagnet. When probing conduction at some distance from this region, the strong influence of remote factors is manifested through the appearance of giant conductance fluctuations, with amplitude much larger than $e^2/h$. This violation of one of the fundamental tenets of mesoscopic physics dramatically demonstrates how local considerations can be overwhelmed by remote signatures in phase-coherent conductors.

Figure 1

(a) Optical micrograph showing the interaction-detection geometry of device ID:1. Electrodes 1–8 are Ohmic (Cr/Au: $5/75$-nm) contacts, used to make the differential-conductance measurements. The (20-nm thick) Co ferromagnet that defines the interaction region is denoted as $\mathcal{I}$, and the shape of the graphene sheet is enclosed by the white dotted line. (b) Computed charge density difference at the graphene-Co(111) interface. Electron loss (enrichment) is displayed in red (blue). The graphene layer (at top) is indicated by brown spheres and the yellow spheres represent Co atoms. (c) Calculated band structure of graphene near the $K$ and $K^{\prime }$ points. Red (blue) bands correspond to spin-down (spin-up) states. (d) Differential conductance measured in the interaction-detection geometry, comparing the effect of including (red or blue data) or excluding (black data) the interaction region ($\mathcal{I}$) in the measurement path. (e),(f) Illustration of the manner in which the structure around zero bias changes as the gate voltage is varied. All data in (d)–(f) are from ID:1, with red (blue) data obtained while sweeping the bias voltage up (down). (d) $V_g-V_D=-114$, (e) $V_g-V_D=-113$, (f) $V_g-V_D=-100\mathrm{V}$.

Figure 2

Gate-voltage-dependent evolution of differential conductance for ID:1, measured with $\mathcal{I}$ excluded from the current path (external voltages, probes 5 and 8; $V_{\mathrm{eff}}$, probes 6 and 7). (Lower) (i)–(v) Representative examples of the differential conductance at different gate voltages. $\mathrm{\Delta }{g}_d$ is defined as the variation of differential conductance, relative to its minimum value ($g_{d_{\min }}$, in units of $e^2/h$) over the indicated bias range. (i) $g_{d_{\min }}=49.7$, (ii) $g_{d_{\min }}=50.4$, (iii) $g_{d_{\min }}=54.6$, (iv) $g_{d_{\min }}=62.3$, (v) $g_{d_{\min }}=61.5$.

Figure 3

Gate-voltage-dependent evolution of differential conductance for ID:1, measured with $\mathcal{I}$ included in the current path (external voltages, probes 1 and 8; $V_{\mathrm{eff}}$, probes 6 and 7). (Lower) (i)–(v) Representative examples of the differential conductance at different gate voltages. $\mathrm{\Delta }{g}_d$ is defined as the variation of differential conductance, relative to its minimum value ($g_{d_{\min }}$, in units of $e^2/h$) over the indicated bias range. (i) $g_{d_{\min }}=52.0$, (ii) $g_{d_{\min }}=44.8$, (iii) $g_{d_{\min }}=60.0$, (iv) $g_{d_{\min }}=66.0$, (v) $g_{d_{\min }}=40.0$.

Figure 4

(a) Variation of the zero-bias conductance [$g_d(V_d)=0$] of ID:1 as a function of hole concentration. Filled symbols (crosses) correspond to measurements performed with the magnetic element included in (excluded from) the current path. Red (black) data points correspond to measurements performed while sweeping the bias voltage up; down-sweep data are indicated in blue (gray). (Inset) Plots the difference in the zero-bias conductance [$\delta g_d(V_d=0)$] from measurements performed with and without the magnet present. Red (blue) data were obtained by subtracting the sweep-up (sweep-down) measurements of the main figure. (b) (upper) Color contour showing the variation of $g_d$ as a function of the effective bias and temperature. Line plots (i)–(iv) correspond to the temperatures (15, 25, 35, and 45 K, respectively) denoted by red dashed lines in the contour. Vertical scale is the same in all cases. Panel (v) shows, for comparison, a typical differential-conductance trace obtained (at 3 K) with the magnet excluded from the current path.