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Quantized Heat Transport in Integer Quantum Hall in Graphene
Quantized Heat Transport in Integer Quantum Hall in Graphene
Schematic of the device structure and measurement set-up
Top: The increased temperatures T_M of the floating reservoir are plotted (solid circles) as a function of dissipated power J_Q for different filling factor. Bottom: Difference between J_Q among different filling factor is plotted with square of T_M
The integer and fractional quantum Hall phases are exotic topological electronic phases of clean two dimensional electron gas. These electronic phases emerged, when clean two dimensional electron gas is subjected to high magnetic field at very low temperature. In high quality system like graphene or GaAs based quantum wells, integer quantum Hall effect (IQHE) is realized, in which Hall conductivity exhibits quantized plateaus at integer multiple of e^2/h (where e is the electronic charge, h is the Planck’s constant), when chemical potential lies in between two landau levels and transport occurs via electronic edge states.
In our recent works, we measured the quantized thermal conductance of electronic edge channel using Jhonson-Noise thermometry. Jhonson thermal noise is a fluctuation in electric current, that is directly related to the temperature of system. This is a non-invasive technique to measure the electron temperature without any thermal coupling.
Quantized Heat Transport in Fractional Quantum Hall in Graphene
Quantized Heat Transport in Fractional Quantum Hall in Graphene
Electrical conductance and the thermal noise as a function of gate voltage. Along with integer plateaus , fractional plateaus also appears at 4/3 e^2/h. Red curve is measured thermal noise, which also shows the plateaus exactly at the same gate voltages as found in conductance data.
Dissipated power in floating contact is plotted as function of square of electron temperature of floating contact. Solid circles represent the experimental data and solid lines is the fit of these data. slopes of lines gives the value of thermal conductance.
When the landau levels are partially filled, electron-electron interaction is only the relevant term in Hamiltonian. This drive the electronic system a new phase, called fractional quantum Hall state (FQH). In this phase, Hall conductivity exhibits quantized plateaus at fractional multiple of e^2/h. In this phase, quasi particle excitation is neither fermion nor boson. They are called anyons and exhibit a different particle statistics. We measured the thermal conductance of 1/3 like state and found that the quantized thermal conductance is same as it was for the integer quantum Hall states. Our result reestablish the fact that the quatized thermal conductance is independent of statistics of carriers.
Quantized Heat Transport in hole like anyons in Graphene
Quantized Heat Transport in hole like anyons in Graphene
Schematic of the edge structure of 5/3 states
Although the measured thermal conductance of IQH as well as particle like FQH states are consistent with theoretical prediction and earlier observations in GaAs based system. However thermal conductance of hole like FQH is always debatable due to equilibration of counter propagating bare edge modes. Depending on the equlibration extent, measured value might change from a one universal topological value to a completely new topological value , as equlibration changes from full equlibration to no equilibration. In our current ongoing work, we are exploring the properties of these kind of FQH states in bilayer graphene.
Along with the hole like abelian anyons properties, we are also interested to explore even denominator fractional quantum Hall states, which are believed to follow non abelian braiding statistics. The many particle states of these non Abelian anyons, which have the topological degeneracy are used to store the quantum information. It is believed that this topological state of matter (non Abelian phase) is a potential candidate which can be used for the fault-tolerant topological quantum compuatation. The unitary gate operations which are essential for the quantum computation are carried out by braiding the quasiparticles, which actually reshuffle the system among different topologically degenerate wavefunction. The non Abelian braiding statistics of these anyons can be used to manipulate the quantum information in a manner that is inherently protected from errors caused by local perturbation in hamiltonian.
Equilibration of quantum Hall edges in graphene
Equilibration of quantum Hall edges in graphene
Top: Device schematic of bilayer graphene p-n-p junction device. With Help of back gate, overall density is controlled and local top gate change the electron density beneath it. Bottom: 2D plot of conductance as a function of νBG and νTG at 10 T magnetic field. The horizontal and vertical strips in the unipolar regime corresponds to back gate and top gate filling factor, respectively. Quantized conductance of 2e2/h is observed for νBG =−2 from νTG = −2 to νTG = −5. Similarly for νBG = −4, quantized conductance of 4e2/h is observed from νTG = −4 to νTG = −5. The checkerboard pattern in the bipolar regime is represented by a red dashed line.
Top: 2D color plot of transconductance dG/dVBG as a function of VBG and perpendicular magnetic field B. Clear Landau levels can be seen emitting from VBG = -1.3 V at B = 0 T. Bottom: Two probe resistance as a function of back gate voltage at zero top gate voltage measured at 40 mK and 10 T magnetic field. All the degeneracy of the zero energy Landau level is lifted, leading to the observation of QH plateaus at an integer multiple of e^2/h.
Top: schematic of edge states in p-n-p regime. Bottom: Cut line (conductance trace) from 2D color plot (first figure bottom panel).
Since The discovery of quantum Hall, the equilibration of quantum Hall edges has always been an important quest in this field. Since then, many attempts has been made including in graphene quantum Hall also. In fact, equilibration physics has been studied in graphene and bilayer graphene earlier but those studies were limited to intrinsic landau levels. In our measurement, we have studied the equilibration of quantum Hall edges in a high quality dual gated bilayer graphene device in both unipolar and bipolar regimes when all the degeneracies of the zero energy Landau level are completely lifted. We find that in the unipolar regime when the filling factor under the top gate region is higher than the back gate filling factor, the equilibration is partial based on their spin polarization. However, the mixing of the edge states in the bipolar regime is insensitive to the spin configurations of the Landau levels and the values are very close to the full equilibration prediction. This has been explained by Landau level collapsing at the sharp p-n junction in our thin hBN (∼15 nm) encapsulated device, in consistent with the existing theory.
Localization physics in graphene moiré superlattices
Localization physics in graphene moiré superlattices
Moire device schematic with measurement setup
Left : Typical gate response of a graphene/hBN moire super lattice. Along with the resistance peak near 0 gate voltage, two other peaks also appears symmetrically around primary peak. These two symmetric peak appears due to reconstruction of band structure due to moire super lattice potential. Middle: The magneto conductance data near clone Dirac center (CDC) at different carrier concentrations. Positive magneto conductance is signature of weak antilocalization. Right: Phase diagram of magneto conductance with different scattering time.
Conductance is plotted as a function of gate voltage and magnetic field
Left: line data taken from 2D color plot is plotted with filling factor. Trace taken beyond the clone Dirac point is in out of phase with respect to data taken near primary Dirac point. Right: Landau level index plotted with 1/B. Intercept gives the value of Berry phase pf π near PDC and 2π near CDC.
Since the discovery of graphene, the localization physics has been studied extensively, and both weak antilocalization (WAL) and weak localization (WL) have been observed. A graphene superlattice (GSL) with multiple Dirac cones has emerged as a focus point in condensed-matter physics in recent years. However, the localization physics at multiple Dirac cones has not been studied to date. Here, we study the magnetoconductance in hexagonal boron nitride-graphene moiré-superlattice devices. Our magneto conductance results show a clear signature of WL at the cloned Dirac cone (CDC) over one decade of variation of both carrier concentration and temperature in the two devices. In contrast, the WAL becomes stronger at the primary Dirac cone (PDC) with increasing temperature and lower carrier concentration in one device, in agreement with previous studies, whereas the other device shows stronger WAL for both lower temperature and carrier concentration. Since the observation of WAL at PDC is expected in a cleaner device due to the π Berry phase, it is natural to ask whether the observation of WL at CDC in our GSL devices has any connection to Berry phase change or not. In order to address this issue we measure the Shubnikov–de Haas (SdH) resistance oscillations, which show a shift of the Berry phase by π from PDC to CDC, indicating the role of the Berry phase for observing WL at CDC.
Quantum Spin Hall effect in bilayer graphene/WSe2 Heterostructures
Quantum Spin Hall effect in bilayer graphene/WSe2 Heterostructures
Top: Quantization of the 4-probe resistance to h/2e2 at several values of Vtg (keeping Vbg fixed),. The inset is a schematic of the 4-probe measurement configuration - the red and green lines represent the spin-filterededge-modes.Bottom: Plot of 4-probe R versus n and |D|. The projection on the R − n plane shows that the quantization is around n = 0, while theprojection on the R −D shows the quantization over a range of values of the displacement field.
Top: Quantization of the 2-probe resistance to 3h/2e2. The data were acquired simultaneously with the data presented in (A).Bottom: Plot of 4-probe R versus n and |D|. The projection on the R − n plane shows that the quantization is around n = 0, while theprojection on the R −D shows the quantization over a range of values of the displacement field.
Topological insulators are phases of matter possessing a distinct set of properties which are invariant under local perturbations.The bulk of these novel phases often have a bandgap in bulk and is topologically distinct from the vacuum. In two-spatial dimensions, this leads to the appearance of dissipationless, one-dimensional edge-modes. Using a Bilayer graphene (BLG) and WSe2 hetero structure, we present the experimental realization of one such phase - the quantum Spin Hall insulator. Due to proximity of WSe2, strong spin orbit interaction induces in BLG. This results into appearance of quantum spin Hall phase. Our experiment shows the presence of perfectly quantized helical edge modes in the absence of a magnetic field in conformity with theoretical predictions. Our work exemplifies how band structure engineering induced by an innovative combination of materials can lead to the emergence of exciting phases of matter.
Ref: ACS Nano 2020
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