Quantum interference noise near the Dirac point in graphene

Effects of disorder on the electronic transport properties of graphene are strongly affected by the Dirac nature of the charge carriers in graphene. This is particularly pronounced near the Dirac point, where relativistic charge carriers cannot efficiently screen the impurity potential. We have studied time-dependent quantum conductance fluctuations in graphene in the close vicinity of the Dirac point at low temperatures. We show that the low-frequency noise arises from the quantum interference effects due to scattering on slowly fluctuating impurities. An unusually large reduction of the noise power in magnetic field suggests that an additional symmetry plays an important role in this regime.

Figure 1

(a) False-color scanning electron microscope image of a typical single-layer device (SL1). The graphene flake is highlighted in green, and the top gates are shown in blue. The distance between the voltage leads is typically around 1 $\mu$m. The scale bar is 3 $\mu$m long. (b) Raman spectra of one of the samples. The observed peak structure is characteristic for single-layer graphene. (c) Schematic of the four-probe measurement setup with external voltage probes. (d) Resistance as a function of top-gate voltage for zero back-gate voltage for sample SL1. The Dirac point, or the charge neutrality point, is located at $V_{Tg}=-0.3$ V.

Figure 2

(a) Noise power as a function of frequency (plotted on a log-log scale) for two different values of the top-gate voltage. The straight line shows the $1/f$ dependence of the noise spectra. (b) Noise power (left) and resistance (right) as a function of top-gate voltage in the vicinity of the Dirac point. (c) Normalized noise power as a function of magnetic field for a single-layer graphene device. It is evident that the relative noise is reduced by a factor of 4 from its zero-magnetic-field value above a certain field. The straight line indicates the reduction of the zero-field value by a factor of 4.

Figure 3

(a) Schematic of pairs of electron trajectories that form closed loops. The conductance fluctuations are caused by interference between paths from A to B and those from C to D that intersect somewhere in the interior of the sample. The diffuson contribution is shown in the upper panel: all the paths in the loop are traversed in the same sense, and the magnetic field does not introduce a relative phase factor. In the cooperon channel, shown in the bottom panel, the magnetic field introduces a relative phase when the loop is traversed in the opposite sense. In this case, contributions from various loops no longer add in a coherent way, and the quantum corrections to conductivity disappear. (b) Magnetoresistance as a function of magnetic field for various top-gate voltages with zero back-gate voltage (sample SL1). A negative magnetoresistance is observed in the vicinity of the Dirac point, with the maximum of magnetoresistance observed close to zero top gate. As the gate voltage is increased in both directions, the magnetoresistance decreases. (c) Relative noise power for different top-gate voltages as a function of a magnetic field (sample SL1). The reduction of the relative noise power by about a factor of 4 is observed at zero top-gate voltage, but this factor decreases for larger values of top-gate voltage.

Figure 4

(a) Normalized noise power is shown as a function of inverse temperature on a log-linear scale. The line represents a linear fit, and the normalized noise power shows an $exp(1/T)$ dependence on temperature. (b) Relative noise power is plotted as a function of magnetic field for different temperatures. The reduction of the relative noise power by a factor of 4 is observed at 250 mK, but the reduction is smaller at higher temperatures. (c) Resistance as a function of temperature is shown for $V_{Tg},V_{Bg}=0$, in the regime highlighted in Fig. 2. The slight increase of the resistance with decreasing temperature indicates insulating behavior. (d) Magnetoresistance as a function of magnetic field is shown for two different temperatures. It is evident that a much smaller magnetoresistance is observed at higher temperatures.