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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, (2009) Atin Pal, Vidya Kochat & Arindam Ghosh PRL 109, (2012)
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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
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Graphene
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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
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What is different in Graphene?
Existence of valleys
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Single layer graphene: Sublattice symmetry
Pseudospin
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Single layer graphene: Valleys
K’ K k Valleys
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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
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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
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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…
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Graphene: An active electrical component
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The Graphene field-effect transistor
Au contact pads 300 nm Silicon dioxide (dielectric) Heavily doped Silicon (Gate) VBG
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Exfoliation of Graphene
Typical HOPG (highly oriented pyrolitic graphite ) surface prior to exfoliation
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The Graphene field-effect transistor
Au contact pads 300 nm Silicon dioxide (dielectric) Heavily doped Silicon (Gate) VBG
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Effect of valleys on quantum transport in graphene
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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
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Valley symmetry: Quantum transport
Isospin singlet Broken valley symmetry Isospin singlet Isospin triplet Presence of Valley symmetry Quantum correction to conductivity
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Weak localization correction in Graphene
Short range scattering Negative MR: Localization Long range scattering Positive MR: Anti-Localization PRL (2009): Savchenko Group
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Effect of valleys on mesoscopic fluctuations in graphene?
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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
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Conductance fluctuations at low temperatures
DG e2/h Universal conductance fluctuations
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Density dependence of conductance fluctuations
10 mK B = 0 Need to find Conductance variance in single phase coherent box
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Evaluating phase coherent conductance fluctuations in Graphene
Lf W L Classical superposition
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DEVICE 1 T = 10mK B = 0
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DEVICE 2
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Valley symmetry: UCF Universal Conductance fluctuations
Number of gapless diffuson and Cooperon modes Low density: Valley symmetry preserved High density: Valley symmetry destroyed
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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
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Temperature dependence
1 Factor of FOUR enhancement in UCF near the Dirac Point Possible evidence of density dependent crossover in universality class
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GRAPHENE ON BN (INSULATOR)
BINARY HYBRIDS GRAPHENE ON BN (INSULATOR) GRAPHENE BORON NITRIDE
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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
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GRAPHENE/BN GRAPHENE-hBN HYBRIDS ULTRA-HIGH MOBILITY SiO2
DOPED SILICON SiO2 GRAPHENE/BN
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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
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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
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