Thermoelectric Properties of Fe0.2Co3.8Sb12-xTex ... - Physics

Universal Conductance Fluctuations as a direct probe to valley coherence and
universality class of disordered graphene
Vidya Kochat, Atindra Nath Pal and Arindam Ghosh
Department of Physics, Indian Institute of Science, Bangalore – 560012.
Quantum interference of carriers produces reproducible fluctuations of the order of e 2 /h in the
electrical conductance of mesoscopic semiconductors and metal films as the Fermi energy, magnetic field or
disorder configuration is varied. Both universal conductance fluctuations (UCF) and weak localization (WL)
effects are inevitable components of quantum transport in disordered metals at low temperatures as they
encode crucial information on phase coherence, nature of scattering and symmetry properties of the
Hamiltonian that govern the level statistics of the underlying disordered system. Unlike in conventional metal
films and doped semiconductors where UCF and WL are mainly due to inelastic scattering mechanisms, the
scenario in graphene is more complex due to the existence of two degenerate valleys (K and K’) in its
hexagonal Brillouin zone. The quantum correction to conductivity in graphene is determined by the elastic
scattering mechanisms involving the valleys, namely the inter-valley and intra-valley scattering, in addition to
the phase breaking inelastic scattering events and these competing mechanisms are reflected in the WL and
weak anti-localization of carriers.
Here we present the first unambiguous observation of the effect of valley symmetry on UCF in
monolayer disordered graphene. The UCF magnitude within a single phase coherent box in graphene is
suppressed by an exact factor of four as the carrier density is increased from close to the Dirac point, where
long range Coulomb potential fluctuations dominate, to the high electron or hole density regime, where
potential fluctuations are primarily short range in nature. This also implies a density dependent crossover of
the universality class of graphene from symplectic near the Dirac point to orthogonal at high densities. We also
find that in the presence of a magnetic field, the UCF magnitude decreases by an exact factor of two and this
corresponds to a transition from the symplectic / orthogonal ensemble to the unitary ensemble characterized
by the absence of time reversal symmetry. This work also examines the robustness of time reversal symmetry
in mesoscopic graphene which has been controversial owing to pseudo-magnetic fields arising from ripples,
local moments at edges etc.
The valleys which resemble a spin-like entity can be exploited to form the platform for a new
emerging field termed as valleytronics, having applications ranging from valley-based quantum computation,
to valley filters or polarizers. Our experiments underline a new method using UCF that can probe the valley
coherent states in graphene at low temperatures.
Reference:
Atindra Nath Pal, Vidya Kochat and Arindam Ghosh, Phys. Rev. Lett. 109, 196601 (2012).