The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

Abstract

We generalize the continuum model for Moiré structures made from twisted graphene layers, in order to include lattice relaxation and the formation of channels at very small (marginal) twist angles. We show that a precise description of the electronic structure at such small angles can be achieved by i) calculating first the relaxed atomic structure, ii) projecting the interlayer electronic hopping parameters using a suitable basis of Bloch states, and iii) increasing the number of harmonics in the continuum approximation to interlayer hopping. The results show a complex structure of quasi one dimensional states when a finite bias is applied. * Niels.Walet@manchester.ac.uk; http://bit.ly/nielswalet † Francisco.Guinea@imdea.org

Perfect one-dimensional chiral states in biased twisted bilayer graphene

“…This is natural because the AB and BA regions (where the energy band is gapped out) significantly expand under the lattice relaxation, and the wave amplitude must be confined to the narrow boundary region. 19,20 The similar, zigzag-shaped wave func-tion was also reported in a recent work 19 . Interestingly, we see that the relaxed TBG's wave function in Fig.…”

“…The real TBG is not a simple stack of rigid graphene layers as assumed in the previous section, but it has a spontaneous lattice relaxation and resulting AB/BA domain formation [31][32][33]35,[45][46][47][48][49][50][51][52][53] . Such a structural deformation modifies the electronic band structure 19,20,35,44,50,[52][53][54] . Here we calculate the energy band structures in the presence of the lattice strain using the tight-binding method 50 .…”

“…In this paper, we theoretically study the electronic structure of small-angle TBG with a large interlayer bias (i.e., potential asymmetry between the top and bottom layers), and demonstrate the formation of perfect onedimensional (1D) states within well-defined energy windows on either side of zero energy. The effect of the interlayer bias on TBG was investigated in the previous theoretical works [14][15][16][17][18][19][20][21] , and it was found that a large enough bias gives rise to a network of topological channels on the domain boundaries between AB and BA stacking regions 15,[17][18][19][20][21] . There the electronic states at AB and BA regions are locally gapped out by the interlayer bias 22 , and two topological modes per spin and per valley necessarily appear on each AB-BA boundary [23][24][25][26][27][28][29] , reflecting that the two regions have different quantized values of single-valley Hall conductivity, ±e 2 /h.…”

Charge density wave and finite-temperature transport in minimally twisted bilayer graphene

“…In addition to the flatband electronic structure at magic angle, the minimally twisted bilayer graphene (mTBLG) with a tiny twist angle ( 1 • ) can realize a network of one-dimensional (1D) conducting states in the presence of a perpendicular electric field [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. [See Fig.…”

Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene

“…The mTBLG hosts a triangular network of onedimensional (1D) conducting channels when a large electric field is externally applied in theẑ direction (out of plane) [12][13][14][15][16][17][18][19][20][21][22][23]. Low-energy electronic states in AB and BA regions are gapped out by the electric field, but domain walls separating the two regions support gapless 1D channels, which are valley Hall kink states with valley-dependent chiralities [24][25][26][27].…”