Quantum dots with a large Thouless number $g$ embody a regime where both disorder and interactions can be treated nonperturbatively using large- $N$ techniques (with $N=g$ ) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large- $N$ approach, as we illustrate with two experimentally relevant examples.Quantum dots with a large Thouless number $g$ embody a regime where both disorder and interactions can be treated nonperturbatively using large-$N$ techniques (with $N=g$) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large-$N$ approach, as we illustrate with two experimentally relevant examples.

arXiv:cond-mat/0406029Physical Review BOct 15, 200410 citations

Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point

Gu Zhang, E. Novais, Harold U. Baranger

We 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.We 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.

arXiv:2108.00064Physical review. B./Physical review. BOct 25, 20213 citations

Towards Autonomous Tuning of Double Quantum Dots

Jana Darulová, Sebastian Pauka, Alice Mahoney +6 more

Bulletin of the American Physical SocietyMar 8, 20190 citations

Universal interacting crossover regime in two-dimensional quantum dots

Ganpathy N. Murthy

Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.Interacting electrons in quantum dots with large Thouless number $g$ in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.

arXiv:0706.3406Physical Review BFeb 21, 20087 citations

Quantum dots with a large Thouless number

g

embody a regime where both disorder and interactions can be treated nonperturbatively using large-

N

techniques (with

N=g

) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at this energy scale. The nonperturbative physics of this regime can only be described by the large-

N

approach, as we illustrate with two experimentally relevant examples.

Interacting electrons in quantum dots with large Thouless number

g

in the three classical random matrix symmetry classes are well understood. When a specific type of spin-orbit coupling known to be dominant in two-dimensional semiconductor quantum dots is introduced, we show that an interacting quantum critical crossover energy scale emerges and low-energy quasiparticles generically have a decay width proportional to their energy. The low-energy physics of this system is an example of a universal interacting crossover regime.