Reading and manipulating valley quantum states in Graphene Arindam Ghosh Department of Physics Indian Institute of Science Atindra Nath Pal Vidya Kochat Atin Pal et al. ACS Nano 5, 2075 (2011) Atin Pal and Arindam Ghosh PRL 102, 126805 (2009) Atin Pal, Vidya Kochat & Arindam Ghosh PRL 109, 196601 (2012)

Layout A brief introduction to Graphene – The valleys Uniqueness in the structure of graphene – Valleys and new effects in quantum transport Graphene as an electronic component Valley manipulation with disorder and gate Valley reading: Mesoscopic conductance fluctuations in Graphene Graphene on crystalline substrates: Manipulating valleys at atomic scales Conclusions

Graphene

Graphene excitement Electronics of Graphene Backbone of post-Silicon nanoelectronics, Flexible Higher mobility, speed, robustness, miniaturization > 100 GHz transistors (Can be upto 1.4 THz) Electrical sensor for toxic gas Novel Physics – Astrophysics, Spintronics… more? Strongest material known – Electromechanical sensing Bio-compatibility: Bio sensing, DNA sequencing Transparent – Application in solar cells

What is different in Graphene? Existence of valleys

Single layer graphene: Sublattice symmetry Pseudospin

Single layer graphene: Valleys K’ K k Valleys

Implications to Random Matrix Theory and universality class Suzuura & Ando, PRL (2002) Removed Effective spin rotation symmetry broken Wigner-Dyson orthogonal symmetry class Valley symmetry Preserved Effective spin rotation symmetry preserved Wigner-Dyson symplectic symmetry class

Valley-phenomenology in graphene Valleytronics Valley-based electronics, equivalent to SPIN (generation and detection of valley state) Valley Hall Effect Analogous to Spin Hall effect (Berry phase supported topological transport) Valley-based quantum computation Example: Zero and One states are valley singlet and triplets in double quantum dot structures

Phenomenology Half-integer integer Quantum Hall effect Berry phase Observed Absence of backscattering Antilocalization Klein Tunneling Valley Hall Effect Valley Physics Nontrivial universality class Universality of mesoscopic fluctuations? Magnetism Time reversal symmetry Edges , magnetic impurities, adatoms, ripples…

Graphene: An active electrical component

The Graphene field-effect transistor Au contact pads 300 nm Silicon dioxide (dielectric) Heavily doped Silicon (Gate) VBG

Exfoliation of Graphene Typical HOPG (highly oriented pyrolitic graphite ) surface prior to exfoliation

The Graphene field-effect transistor Au contact pads 300 nm Silicon dioxide (dielectric) Heavily doped Silicon (Gate) VBG

Effect of valleys on quantum transport in graphene

Disorder in graphene Atomic scale defects: Grain boundaries, topological defects, edges, vacancies… Charged impurity Source of short range scattering Removes valley degeneracy Long range scattering Substrate traps, ion drift, free charges Does not affect valley degeneracy Linear variation of conductivity Graphene Silicon oxide Doped silicon

Valley symmetry: Quantum transport Isospin singlet Broken valley symmetry Isospin singlet Isospin triplet Presence of Valley symmetry Quantum correction to conductivity

Weak localization correction in Graphene Short range scattering Negative MR: Localization Long range scattering Positive MR: Anti-Localization PRL (2009): Savchenko Group

Effect of valleys on mesoscopic fluctuations in graphene?

Universal Conductance Fluctuations In a regular disordered metal Bi film (Birge group, 1990) Aperiodic yet reproducible fluctuation of conductance with magnetic field, Fermi Energy and disorder configuration For L < L: dG  e2/h Quantum interference effect, same physics as weak localization Independent of material properties, device geometry: UNIVERSAL

Conductance fluctuations at low temperatures DG  e2/h  Universal conductance fluctuations

Density dependence of conductance fluctuations 10 mK B = 0 Need to find Conductance variance in single phase coherent box

Evaluating phase coherent conductance fluctuations in Graphene Lf W L Classical superposition

DEVICE 1 T = 10mK B = 0

DEVICE 2

Valley symmetry: UCF Universal Conductance fluctuations Number of gapless diffuson and Cooperon modes Low density: Valley symmetry preserved High density: Valley symmetry destroyed

Implications to Random Matrix Theory and universality class Suzuura & Ando, PRL (2002) Removed Effective spin rotation symmetry broken Wigner-Dyson orthogonal symmetry class Short range scattering Intervalley scattering by atomically sharp defects Valley symmetry Preserved Effective spin rotation symmetry preserved Wigner-Dyson symplectic symmetry class Long range scattering Long range Coulomb potential from trapped charges

Temperature dependence 1 Factor of FOUR enhancement in UCF near the Dirac Point Possible evidence of density dependent crossover in universality class

GRAPHENE ON BN (INSULATOR) BINARY HYBRIDS GRAPHENE ON BN (INSULATOR) GRAPHENE BORON NITRIDE

GRAPHENE/BN GRAPHENE/BN BINARY HYBRIDS VERTICALLY ALIGNED OVERLAY EL9 Paritosh Karnatak Dr. Srijit Goswami GRAPHENE/BN BINARY HYBRIDS VERTICALLY ALIGNED OVERLAY 15 µm GRAPHENE EL9 Tape Glass 15 µm h-BN (exfoliated) GRAPHENE on h-BN Aligner Si/SiO2 GRAPHENE/BN

GRAPHENE/BN GRAPHENE-hBN HYBRIDS ULTRA-HIGH MOBILITY SiO2 DOPED SILICON SiO2 GRAPHENE/BN

GRAPHENE/BN GRAPHENE-hBN HYBRIDS QUANTUM HALL EFFECT 1/Rxy = gsgv(n+1/2)e2/h = 2x2 (n+1/2)e2/h GRAPHENE-hBN HYBRIDS QUANTUM HALL EFFECT n = 0, 1, 2,… LIFTING OF 4-FOLD DEGENERACY GRAPHENE/BN

Summary A new effect of valley quantum state on the quantum transport in graphene revealed The valley states are extremely sensitive to nature of scattering of charge in graphene The degeneracy of the valley and singlet states can be tuned with external electric field Universal conductance fluctuations can act as a readout of the valley states Single layer graphene shows a density dependent crossover in it universality class , along with a exact factor of four change in its conductance fluctuation magnitude Valley degeneracy can be tuned with other means as well, such as external periodic potential from the substrate THANK YOU