Reading and manipulating valley quantum states in Graphene

Reading and manipulating valley quantum states in Graphene Atindra Nath Pal Arindam Ghosh Department of Physics Indian Institute of Science 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) Vidya Kochat

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 Ø 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? Ø Strongest material known – Electromechanical sensing Ø Bio-compatibility: Bio sensing, DNA sequencing Ø Transparent – Application in solar cells

What is different in Graphene? Existence of valleys

Single layer graphene: Sublattice symmetry A B Pseudospin

Single layer graphene: Valleys E Valleys K’ K k

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

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 Berry phase Observed Half-integer Quantum Hall effect Absence of backscattering Antilocalization Klein Tunneling Valley Physics Valley Hall Effect 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 q Atomic scale defects: Grain boundaries, topological defects, edges, vacancies… 1. 2. Source of short range scattering Removes valley degeneracy q Charged impurity 1. 2. 3. 4. 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 L Bi film (Birge group, 1990) q Aperiodic yet reproducible fluctuation of conductance with magnetic field, Fermi Energy and disorder configuration q For L < L : d. G e 2/h q Quantum interference effect, same physics as weak localization q Independent of material properties, device geometry: UNIVERSAL

Conductance fluctuations at low temperatures DG e 2/h Universal conductance fluctuations

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

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

DEVICE 1 T = 10 m. K 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 Short range scattering Effective spin rotation symmetry broken Wigner-Dyson orthogonal symmetry class Intervalley scattering by atomically sharp defects Valley symmetry Preserved Long range scattering Effective spin rotation symmetry preserved Long range Coulomb potential from trapped charges Wigner-Dyson symplectic symmetry class

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

BINARY HYBRIDS GRAPHENE ON BN (INSULATOR) GRAPHENE BORON NITRIDE

GRAPHENE/BN BINARY HYBRIDS VERTICALLY ALIGNED OVERLAY 15 µm Dr. Srijit Goswami Paritosh Karnatak GRAPHENE EL 9 Tape Glass h-BN (exfoliated) GRAPHENE on h-BN m µ 15 Aligner Si/Si. O 2 GRAPHENE/BN

GRAPHENE-h. BN HYBRIDS ULTRA-HIGH MOBILITY Graphene h-BN Si. O 2 DOPED SILICON GRAPHENE/BN

GRAPHENE-h. BN HYBRIDS QUANTUM HALL EFFECT 1/Rxy = gsgv(n+1/2)e 2/h = 2 x 2 (n+1/2)e 2/h 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