Ab Initio Theory of Gate Induced Gaps in Graphene Bilayers

Size: px

Start display at page:

Download "Ab Initio Theory of Gate Induced Gaps in Graphene Bilayers"

Edwin Griffith
5 years ago
Views:

1 Title APS Marh Meeting Ab Initio Theory of Gate Indued Gaps in Graphene Bilayers The University of Texas at Austin Hongki Min, B.R.Sahu, Sanjay K.Banerjee and A.H.MaDonald Phys. Rev.B 75, 555 (007)

2 Outline We study the gate voltage indued gap in graphene bilayers using ab initio density funtional theory. Our alulations onfirm the qualitative piture suggested by phenomenologial tight-binding models. We disuss sreening of the external potential and quantify the role of rystalline inhomogeneity using a tight-binding self-onsistent Hartree alulation.. Introdution. Ab initio Calulations 3. Self-onsistent Hartree Calulations

3 . Introdution ) Graphene Graphene is a two-dimensional honeyomb lattie of arbon atoms. a.46a K M K σ, σ* Energy bands at low energies are desribed by a D Diralike equation with linear dispersion near K/K'. Energy (ev) π, π* K M K

4 . Introdution ) Graphene bilayer Graphene bilayer is omposed of a pair of oupled graphene monolayers. A band gap opens if on-site energy differene U between two layers is non-zero. U an be ontrolled by doping or an external eletri field. U=U top -U bottom a.46a B ~ B A top A ~ d bottom 3.35 A

5 . Introdution 3) Band struture ontrol by doping Angle-resolved photoemission spetrosopy (ARPES) ARPES tight-binding Ohta et al. Siene 33, 95 (006)

6 . Introdution 4) Band struture ontrol by an external eletri field Shemati illustration of a iruit with a bilayer graphene gate Soure SiO Bilayer graphene SiO Drain E gap (ev) gate (ev) Possible appliation to a swith devie

7 . Ab Initio Calulations ) Ab initio density funtional theory (DFT) alulations All-eletron linearized augmented plane wave Generalized-gradient approximation Superell alulation, z 0 ~6A A periodi zig-zag potential was applied. d z 0 a periodi zig-zag potential

8 . Ab Initio Calulations ) Bilayer graphene band struture A energy gap opens by an external eletri field. The low energy bands develop a Mexian hat struture. =eed Energy (ev) K M K =0.0 ev =0.5 ev =.0 ev K M A tunable energy gap semiondutor K

9 . Ab Initio Calulations 3) Evolution of tight-binding parameters Tight-binding parameters were extrated from DFT energy bands near K. They show the external eletri field dependene. U=U top -U bottom top B A ~ U (ev) γ (ev) 0 3 B ~ A bottom 0.6eV, 3 0.3eV (ev) (ev)

10 . Ab Initio Calulations 4) Evolution of energy gap For γ 3 =0, E U r r U r as U inreases. gap Energy gap saturates ~0.3 ev. top bottom 3 0 B ~ B A A ~ Energy (ev) U E gap E gap (ev) ab initio DFT tight-binding, γ 3 =0.0 ev tight-binding, γ 3 =0.3 ev K U (ev)

11 3. Self-onsistent Hartree Calulations ) Continuum Hartree Potential Method A two-body interation in a plane wave basis Vˆ k, k, q,, V, ( q) k q, k q, k, k, A mean-field Hartree approximation Vˆ k, k, k, k q for A, B for top, bottom Brillouin zone whole plane k, V, ' (0) k, ' ' k, ' '

12 3. Self-onsistent Hartree Calulations ) Lattie Hartree Potential Method Choose Bloh states as a basis ikr ( x ) e ( xrτ ) N k, R k τ for A, B for top, bottom Brillouin zone displaement low k ~ B, ~ V A, ' ', high (0) ~ A k, ' ' k, ' ' B (H) high (H) low B ~ B A top A ~ bottom

13 3. Self-onsistent Hartree Calulations 3) Sreening effets Enhaned sreening at small U ab initio DFT Hartree Hartree+lattie In DFT, the sreening /U is more pronouned. Underestimation of gap? σ-orbital ontribution? Fitting inauray in tight-binding parameters? U (ev)

14 Summary Using ab initio density funtional theory, we showed that band struture an be ontrolled by applying an external eletri field. The eletri field dependene of tight-binding parameters were obtained from the DFT results. Energy (ev) =0.0 ev =0.5 ev =.0 ev K The sreening effet seen in the DFT results were ompared with a tight-binding self-onsistent Hartree method inluding rystalline inhomogeneity orretions. /U ab initio DFT Hartree Hartree+lattie Phys. Rev.B 75, 555 (007) U (ev)

A model for measurement of the states in a coupled-dot qubit

A model for measurement of the states in a oupled-dot qubit H B Sun and H M Wiseman Centre for Quantum Computer Tehnology Centre for Quantum Dynamis Griffith University Brisbane 4 QLD Australia E-mail: