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Register a new userTemperature dependent equilibration of spin orthogonal quantum Hall edge modes
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Added by
Biswajit Karmakar Dr.
Publication date
2021
fields
Physics
and research's language is
English
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Conductance of the edge modes as well as conductance across the co-propagating edge modes around the u = 4/3, 5/3 and 2 quantum Hall states are measured by individually exciting the modes. Temperature dependent equilibration rates of the outer unity conductance edge mode are presented for different filling fractions. We find that the equilibration rate of the outer unity conductance mode at u = 2 is higher and more temperature sensitive compared to the mode at fractional filling 5/3 and 4/3. At lowest temperature, equilibration length of the outer unity conductance mode tends to saturate with lowering filling fraction u by increasing magnetic field B. We speculate this saturating nature of equilibration length is arising from an interplay of Coulomb correlation and spin orthogonality.
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Fractional conductance is measured by partitioning $ u = 1$ edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the $ u = 1$ plateau respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance $e^2/3h$ arising from edge reconstruction. The results reveal remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing field.
We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter -- playing the role of an effective interaction strength within an idealized model of thermal reservoirs -- is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.
We propose and analyse a scheme for performing a long-range entangling gate for qubits encoded in electron spins trapped in semiconductor quantum dots. Our coupling makes use of an electrostatic interaction between the state-dependent charge configurations of a singlet-triplet qubit and the edge modes of a quantum Hall droplet. We show that distant singlet-triplet qubits can be selectively coupled, with gate times that can be much shorter than qubit dephasing times and faster than decoherence due to coupling to the edge modes. Based on parameters from recent experiments, we argue that fidelities above 99% could in principle be achieved for a two-qubit entangling gate taking as little as 20 ns.
A monolayer of WTe$_2$ has been shown to display quantum spin Hall (QSH) edge modes persisting up to 100~K in transport experiments. Based on density-functional theory calculations and symmetry-based model building including the role of correlations and substrate support, we develop an effective electronic model for WTe$_2$ which fundamentally differs from other prototypical QSH settings: we find that the extraordinary robustness of quantum spin Hall edge modes in WTe$_2$ roots in a glide symmetry due to which the topological gap opens away from high-symmetry points in momentum space. While the indirect bulk gap is much smaller, the glide symmetry implies a large direct gap of up to 1~eV in the Brillouin zone region of the dispersing edge modes, and hence enables sharply boundary-localized QSH edge states depending on the specific boundary orientation.
We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial non-equilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: its properties depend on the full functional form of the initial electron distribution, and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an over-estimate or an under-estimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor u=1 we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor u=2 we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at u=2 from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.
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