# Browsing by Author "Zhang, Gu"

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Item Open Access Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point(Physical Review B, 2021-10-25) Zhang, Gu; Novais, E; Baranger, Harold UWe find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature—we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.Item Open Access Rescuing a Quantum Phase Transition with Quantum Noise.(Physical review letters, 2017-02) Zhang, Gu; Novais, E; Baranger, Harold UWe show that placing a quantum system in contact with an environment can enhance non-Fermi-liquid correlations, rather than destroy quantum effects, as is typical. The system consists of two quantum dots in series with two leads; the highly resistive leads couple charge flow through the dots to the electromagnetic environment, the source of quantum noise. While the charge transport inhibits a quantum phase transition, the quantum noise reduces charge transport and restores the transition. We find a non-Fermi-liquid intermediate fixed point for all strengths of the noise. For strong noise, it is similar to the intermediate fixed point of the two-impurity Kondo model.Item Open Access Stabilization of a Majorana Zero Mode through Quantum Frustration.(Physical Review B, 2020-07-01) Zhang, Gu; Baranger, Harold UWe analyze a system in which a topological Majorana zero mode (MZM) combines with a MZM produced by quantum frustration. At the boundary between the topological and non-topological states, a MZM does not appear. The system that we study combines two parts, a grounded topological superconducting wire that hosts two MZM at its ends, and an on-resonant quantum dot connected to two dissipative leads. The quantum dot with dissipative leads creates an effective two-channel Kondo (2CK) state in which quantum frustration yields an isolated MZM at the dot. We find that coupling the dot to one of the wire Majoranas stabilizes the MZM at the other end of the wire. In addition to providing a route to achieving an unpaired Majorana zero mode, this scheme provides a clear signature of the presence of the 2CK Majorana.Item Open Access Studies on the effect of noise in boundary quantum phase transitions(2018) Zhang, GuBoundary quantum phase transitions are abrupt ground state transitions triggered by the change of the boundary conditions at single or multiple (but finite) points.

When boundary effects dominate, understanding boundary quantum phase transitions requires a deeper knowledge of strongly correlated electron systems that is beyond the widely applied mean field treatment.

Meanwhile, with strong boundary effect, most systems with boundary quantum phase transition can generally be considered as effectively zero-dimensional, with reservoir details ignored. Consequently, the critical features of boundary quantum phase transitions only involve long-time correlations instead of long-range ones.

On the other hand, different from the geometrical confinement of boundaries, dissipation or quantum noise widely exists along the entire system.

In bulk quantum phase transitions, dissipation decreases system coherence by reducing the long-range correlations.

This fact makes it plausible that dissipation destroys the critical behavior of the quantum critical points.

The effect of dissipation, however, remains unclear in boundary quantum phase transition systems due to their lack of long-range correlations.

In this thesis I thus focus on the effect of dissipation in boundary quantum phase transitions.

These studies are motivated and encouraged by recent experimental triumphs where dissipation is realized and precisely measured in mesoscopic systems, which provide experimental evidences to check theoretical researches.

This thesis involves multiple dissipative mesoscopic systems, including the dissipative two impurity Kondo, two channel Kondo, resonant level, and Anderson models.

To begin with, the effect of dissipation in two impurity Kondo model has been explored and we find that the presence of dissipation restores the quantum phase transition by reducing the unwanted charge tunneling process. We further provide the phase diagram for the system that has an exotic double-quantum-critical-point feature.

After that, the non-equilibrium $I$-$V$ feature of a dissipative resonant level model is studied.

This model has been experimentally proven to host a boundary quantum phase transition.

With different tuning parameters, we calculate the $I$-$V$ feature at both the quantum critical point and in the crossover regime analytically. The theoretical calculation agrees remarkably with the experimental data.

As the spinful version of the resonant level model, the dissipative Anderson model has multiple unique features, including the experimentally observed peak position shifting and dissipation dependent saturated peak conductance. Through renormalization group studies and mapping the model to the quantum Brownian motion model, we understand these features qualitatively.

As an example of the application of above research achievements, we study the stabilization of a Majorana zero mode with the quantum frustration in a dissipative resonant level model. The Majorana zero mode is known to be unstable against the coupling to its partner at the other end of the Majorana hosted nanowire.

We prove that the Majorana zero mode can be stabilized by coupling its partner to the quantum dot of a frustrated dissipative resonant level model, where an isolated impurity Majorana fermion is produced.

Finally, we study the relation between boundary quantum phase transitions and geometric phases. The calculation is carried out at the Toulouse point of a dissipative resonant level model.

Although it satisfies the criteria of bulk quantum phase transitions to host a non-trivial geometric phase, the dissipative resonant level model has zero geometric phase due to the identical zero geometric curvature. This phenomenon is generally explained by studying the geometric tensor of boundary quantum phase transition-hosted systems.