Tuning equilibration of quantum Hall edge states in graphene – Role of crossed electric and magnetic fields

Abstract

We probe quantum Hall effect in a tunable 1-D lateral superlattice (SL) in graphene created using electrostatic gates. Lack of equilibration is observed along edge states formed by electrostatic gates inside the superlattice. We create strong local electric field at the interface of regions of different charge densities. Crossed electric and magnetic fields modify the wavefunction of the Landau Levels (LLs) -a phenomenon unique to graphene. In the region of copropagating electrons and holes at the interface, the electric field is high enough to modify the Landau levels resulting in increased scattering that tunes equilibration of edge states and this results in large longitudinal resistance.Magnetotransport across one-dimensional superlattice (SL) had been studied in two-dimensional electron gas in semiconductor heterostructures (2DEGS) [1][2][3][4][5][6], reporting dissipationless transport across high potential barriers [1] and magnetic commensurability oscillations in longitudinal resistance [3]. The motivation was to study various competing length scales and energy scales between tunable SL potential and quantum Hall system. Graphene offers the advantage of large cyclotron gap allowing quantum Hall effect to be observed at room temperature [7][8][9]. Substrate induced SL in graphene in the presence of magnetic field led to the experimental observation of Hofstadter butterfly physics [10][11][12]. The ability to create abrupt (∼ 10 nm) tunable barriers in graphene allows new aspects to be explored. In addition, new physics, due to the role of crossed electric and magnetic field, that cannot be seen in conventional 2DEGS can be studied in SL structures based on graphene.In this letter, we study magneto transport in an electrostatically defined 1D lateral SL in graphene [13]. In our device we apply a perpendicular magnetic field and periodically modulate the charge carrier density in adjacent "ribbons" of graphene, tuning from an array of p-p' (or n-n' ) to an array of p-n' junctions. Changing the magnetic field allows us to vary l B relative to λ; and changing the gate voltage allows us to tune the SL potential strength relative to LL spacing. The relative abruptness, bipolarity of charge carriers, large modulation and unequally spaced LLs distinguishes the present work from the previous work on 1D SL using 2DEGS systems [1][2][3][4]14].Apart from the length scales, we also study the energy scales involved. The competition between SL amplitude (V 0 ) and LL spacing (hω c , whereh = h/2π, h being the Planck's constant, and ω c is the cyclotron frequency) gives rise to three regimes. When V 0 >>hω c , SL effect dominates giving rise to extra Dirac points [15]. In the other extreme when V 0 <<hω c , quantum Hall effect in * sudipta.tifr@gmail.com † deshmukh@tifr.res.in graphene is restored [15]. However, the situation is more complex and little explored when V 0 andhω c have comparable contribution, and we have experimentally probed this regime in graphene.The goal of our work is to extend quantum Hall studies be...

Conductance oscillations in Chern insulator junctions: Valley-isospin dependence and Aharonov-Bohm effects

“…The observation of non-integer conductance plateaus in bipolar graphene quantum Hall systems has been interpreted by the equilibration of interface states at the p-n junction, with theoretical efforts supporting experimental findings by considering edge and interface disorders [19][20][21][22] . Junction conductance via interface equilibration has also been reported for pn-p junctions in quantum Hall graphene systems [23][24][25] , with the consideration that there can be reflections at the bipolar junction. These studies were carried out in macroscopic systems where mesoscopic fluctuations were ignored 4 .…”

Equilibration of quantum hall edge states and its conductance fluctuations in graphene p-n junctions

“…In the unipolar regime (with ν BG > ν T G ) the QH edge states in the top gate region is fully transmitted as shown in Figure 1 (c) and the resistance is given as [18] …”

“…For the bipolar regime, the average value of the resistance depends on the equilibration of the interface states ( Fig. 1a and 1b) and in the case of full mixing the resistance can be written as [18] …”

“…The CFs are shown to decrease with bias voltages as well as with temperature beyond a critical value. The CFs vanish completely at high temperature (7 K) and the exact value of the QH plateau was recovered (Ref [18]). However, there is a discrepancy between the amplitude of CFs of our experiment with the theoretical values (Abanin et al [6]) at low filling factors.…”

Interplay of filling fraction and coherence in symmetry broken graphene p-n junction

“…The understanding of edge dynamics make an electron interferometer suitable for exploring exotic phenomena like fractional statistics, quantum entanglement, and non-abelian excitations [1][2][3][4][5] . A graphene p-n junction (PNJ) naturally harboring co-propagating electron and hole-like edge states offers an ideal platform [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to study the edge or equilibration dynamics. The equilibration of such edge states is predicted to be facilitated by inter-channel tunneling via either incoherent or coherent scattering mechanism [23][24][25][26][27][28][29][30][31] depending on the microscopic details of the interface.…”