Quantum dot attached to topological wires has become an interesting setup to study Majorana bound... more Quantum dot attached to topological wires has become an interesting setup to study Majorana bound state in condensed matter[1]. One of the major advantage of using a quantum dot for this purpose is that it provides a suitable manner to study the interplay between Majorana bound states and the Kondo effect. Recently we have shown that a non-interacting quantum dot side-connected to a 1D topological superconductor and to metallic normal leads can sustain a Majorana mode even when the dot is empty. This is due to the Majorana bound state of the wire leaking into the quantum dot. Now we investigate the system for the case in which the quantum dot is interacting[3]. We explore the signatures of a Majorana zero--mode leaking into the quantum dot, using a recursive Green's function approach. We then study the Kondo regime using numerical renormalization group calculations. In this regime, we show that a "0.5" contribution to the conductance appears in system due to the presence of the Majorana mode, and that it persists for a wide range of the dot parameters. In the particle-hole symmetric point, in which the Kondo effect is more robust, the total conductance reaches $3e^2/2h$, clearly indicating the coexistence of a Majorana mode and the Kondo resonance in the dot. However, the Kondo effect is suppressed by a gate voltage that detunes the dot from its particle-hole symmetric point as well as by a Zeeman field. The Majorana mode, on the other hand, is almost insensitive to both of them. We show that the zero--bias conductance as a function of the magnetic field follows a well--known universal curve. This can be observed experimentally, and we propose that this universality followed by a persistent conductance of $0.5,e^2/h$ are evidence for the presence of Majorana--Kondo physics. This work is supported by the Brazilians agencies FAPESP, CNPq and FAPEMIG. [1] A. Y. Kitaev, Ann.Phys. {bf 303}, 2 (2003). [2] E. Vernek, P.H. Penteado, A. C. Seridonio, J. C. Egues, Phys. Rev. B {bf 89}, 165314 (2014). [3] David A. Ruiz-Tijerina, E. Vernek, Luis G. G. V. Dias da Silva, J. C. Egues, Phys. Rev B {bf 91}, 115435 (2015).
ABSTRACT We have recently shown [Phys. Rev. B 89, 165314 (2014)] that a noninteracting quantum do... more ABSTRACT We have recently shown [Phys. Rev. B 89, 165314 (2014)] that a noninteracting quantum dot coupled to a one-dimensional topological superconductor and to normal leads can sustain a Majorana mode even when the dot is expected to be empty, i.e., when the dot energy level is far above the Fermi level of the leads. This is due to the Majorana bound state of the wire leaking into the quantum dot. Here we extend this previous work by investigating the low-temperature quantum transport through an interacting quantum dot connected to source and drain leads and side coupled to a topological wire. We explore the signatures of a Majorana zero mode leaking into the quantum dot for a wide range of dot parameters, using a recursive Green’s function approach. We then study the Kondo regime using numerical renormalization group calculations. We observe the interplay between the Majorana mode and the Kondo effect for different dot-wire coupling strengths, gate voltages, and Zeeman fields. Our results show that a “0.5” conductance signature appears in the dot despite the interplay between the leaked Majorana mode and the Kondo effect. This robust feature persists for a wide range of dot parameters, even when the Kondo correlations are suppressed by Zeeman fields and/or gate voltages. The Kondo effect, on the other hand, is suppressed by both Zeeman fields and gate voltages. We show that the zero-bias conductance as a function of the magnetic field follows a well-known universality curve. This can be measured experimentally, and we propose that the universal conductance drop followed by a persistent conductance of 0.5e2/h is evidence of the presence of Majorana-Kondo physics. These results confirm that this “0.5” Majorana signature in the dot remains even in the presence of the Kondo effect.
The role of symmetries on nanoscale structures is essential for the different physical behavior e... more The role of symmetries on nanoscale structures is essential for the different physical behavior exhibited in these systems while its understanding offers deeper insights into the observed properties. The ability to fabricate structures such as quantum dot arrays with tailored symmetries provides further motivation to understand the interplay of geometrical and orbital symmetries in interacting systems at low temperatures, where
ABSTRACT A double quantum dot device, connected to two channels that only see each other through ... more ABSTRACT A double quantum dot device, connected to two channels that only see each other through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. By using a two-impurity Anderson model, and parameter values obtained from experiment [S. Amasha {\it et al.}, Phys. Rev. Lett. {\bf 110}, 046604 (2013)], it is shown that, by applying a moderate magnetic field, and adjusting the gate potential of each quantum dot, opposing spin polarizations are created in each channel. Furthermore, through a well defined change in the gate potentials, the polarizations can be reversed. This polarization effect is clearly associated to a spin-orbital Kondo state having a Kondo peak that originates from spatially separated parts of the device. This fact opens the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.
We present studies of the Coulomb blockade and Kondo regimes of transport of a quantum dot connec... more We present studies of the Coulomb blockade and Kondo regimes of transport of a quantum dot connected to current leads through spin-polarizing quantum point contacts (QPCs) [1]. This configuration, arising from the effect of lateral spin-orbit fields, results in spin-polarized currents even in the absence of external magnetic fields and greatly affects the correlations in the dot. Using an equation-of-motion
Single electron transistors can be manufactured by coupling a Carbon Nanotubes (CNT) to metal lea... more Single electron transistors can be manufactured by coupling a Carbon Nanotubes (CNT) to metal leads. In this case the Kondo effect may arise. The difference between the Kondo effect in CNT and the same effect in quantum dots (QD) comes from the degeneracy of the chiral states of the CNT. While in QDs the Kondo effect is related to the
We present studies of the Coulomb blockade and Kondo regimes of transport through a quantum dot c... more We present studies of the Coulomb blockade and Kondo regimes of transport through a quantum dot connected to current leads through spin-polarizing quantum point contacts (QPCs). This structure, arising from the effect of lateral spin-orbit fields defining the QPCs, results in spin-polarized currents even in the absence of external magnetic fields and greatly affects the correlations in the dot. Using equation-of-motion and numerical renormalization group calculations we obtain the conductance and spin polarization for this system under different parameter regimes. We find that the system exhibits spin-polarized conductance in both the Coulomb blockade and Kondo regimes, all in the absence of applied magnetic fields. We analyze the role that the spin-dependent tunneling amplitudes of the QPC play in determining the charge and net magnetic moment in the dot. These effects, controllable by lateral gate voltages, may provide an alternative approach for exploring Kondo correlations, as w...
Quantum dot attached to topological wires has become an interesting setup to study Majorana bound... more Quantum dot attached to topological wires has become an interesting setup to study Majorana bound state in condensed matter[1]. One of the major advantage of using a quantum dot for this purpose is that it provides a suitable manner to study the interplay between Majorana bound states and the Kondo effect. Recently we have shown that a non-interacting quantum dot side-connected to a 1D topological superconductor and to metallic normal leads can sustain a Majorana mode even when the dot is empty. This is due to the Majorana bound state of the wire leaking into the quantum dot. Now we investigate the system for the case in which the quantum dot is interacting[3]. We explore the signatures of a Majorana zero--mode leaking into the quantum dot, using a recursive Green's function approach. We then study the Kondo regime using numerical renormalization group calculations. In this regime, we show that a "0.5" contribution to the conductance appears in system due to the presence of the Majorana mode, and that it persists for a wide range of the dot parameters. In the particle-hole symmetric point, in which the Kondo effect is more robust, the total conductance reaches $3e^2/2h$, clearly indicating the coexistence of a Majorana mode and the Kondo resonance in the dot. However, the Kondo effect is suppressed by a gate voltage that detunes the dot from its particle-hole symmetric point as well as by a Zeeman field. The Majorana mode, on the other hand, is almost insensitive to both of them. We show that the zero--bias conductance as a function of the magnetic field follows a well--known universal curve. This can be observed experimentally, and we propose that this universality followed by a persistent conductance of $0.5,e^2/h$ are evidence for the presence of Majorana--Kondo physics. This work is supported by the Brazilians agencies FAPESP, CNPq and FAPEMIG. [1] A. Y. Kitaev, Ann.Phys. {bf 303}, 2 (2003). [2] E. Vernek, P.H. Penteado, A. C. Seridonio, J. C. Egues, Phys. Rev. B {bf 89}, 165314 (2014). [3] David A. Ruiz-Tijerina, E. Vernek, Luis G. G. V. Dias da Silva, J. C. Egues, Phys. Rev B {bf 91}, 115435 (2015).
ABSTRACT We have recently shown [Phys. Rev. B 89, 165314 (2014)] that a noninteracting quantum do... more ABSTRACT We have recently shown [Phys. Rev. B 89, 165314 (2014)] that a noninteracting quantum dot coupled to a one-dimensional topological superconductor and to normal leads can sustain a Majorana mode even when the dot is expected to be empty, i.e., when the dot energy level is far above the Fermi level of the leads. This is due to the Majorana bound state of the wire leaking into the quantum dot. Here we extend this previous work by investigating the low-temperature quantum transport through an interacting quantum dot connected to source and drain leads and side coupled to a topological wire. We explore the signatures of a Majorana zero mode leaking into the quantum dot for a wide range of dot parameters, using a recursive Green’s function approach. We then study the Kondo regime using numerical renormalization group calculations. We observe the interplay between the Majorana mode and the Kondo effect for different dot-wire coupling strengths, gate voltages, and Zeeman fields. Our results show that a “0.5” conductance signature appears in the dot despite the interplay between the leaked Majorana mode and the Kondo effect. This robust feature persists for a wide range of dot parameters, even when the Kondo correlations are suppressed by Zeeman fields and/or gate voltages. The Kondo effect, on the other hand, is suppressed by both Zeeman fields and gate voltages. We show that the zero-bias conductance as a function of the magnetic field follows a well-known universality curve. This can be measured experimentally, and we propose that the universal conductance drop followed by a persistent conductance of 0.5e2/h is evidence of the presence of Majorana-Kondo physics. These results confirm that this “0.5” Majorana signature in the dot remains even in the presence of the Kondo effect.
The role of symmetries on nanoscale structures is essential for the different physical behavior e... more The role of symmetries on nanoscale structures is essential for the different physical behavior exhibited in these systems while its understanding offers deeper insights into the observed properties. The ability to fabricate structures such as quantum dot arrays with tailored symmetries provides further motivation to understand the interplay of geometrical and orbital symmetries in interacting systems at low temperatures, where
ABSTRACT A double quantum dot device, connected to two channels that only see each other through ... more ABSTRACT A double quantum dot device, connected to two channels that only see each other through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. By using a two-impurity Anderson model, and parameter values obtained from experiment [S. Amasha {\it et al.}, Phys. Rev. Lett. {\bf 110}, 046604 (2013)], it is shown that, by applying a moderate magnetic field, and adjusting the gate potential of each quantum dot, opposing spin polarizations are created in each channel. Furthermore, through a well defined change in the gate potentials, the polarizations can be reversed. This polarization effect is clearly associated to a spin-orbital Kondo state having a Kondo peak that originates from spatially separated parts of the device. This fact opens the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.
We present studies of the Coulomb blockade and Kondo regimes of transport of a quantum dot connec... more We present studies of the Coulomb blockade and Kondo regimes of transport of a quantum dot connected to current leads through spin-polarizing quantum point contacts (QPCs) [1]. This configuration, arising from the effect of lateral spin-orbit fields, results in spin-polarized currents even in the absence of external magnetic fields and greatly affects the correlations in the dot. Using an equation-of-motion
Single electron transistors can be manufactured by coupling a Carbon Nanotubes (CNT) to metal lea... more Single electron transistors can be manufactured by coupling a Carbon Nanotubes (CNT) to metal leads. In this case the Kondo effect may arise. The difference between the Kondo effect in CNT and the same effect in quantum dots (QD) comes from the degeneracy of the chiral states of the CNT. While in QDs the Kondo effect is related to the
We present studies of the Coulomb blockade and Kondo regimes of transport through a quantum dot c... more We present studies of the Coulomb blockade and Kondo regimes of transport through a quantum dot connected to current leads through spin-polarizing quantum point contacts (QPCs). This structure, arising from the effect of lateral spin-orbit fields defining the QPCs, results in spin-polarized currents even in the absence of external magnetic fields and greatly affects the correlations in the dot. Using equation-of-motion and numerical renormalization group calculations we obtain the conductance and spin polarization for this system under different parameter regimes. We find that the system exhibits spin-polarized conductance in both the Coulomb blockade and Kondo regimes, all in the absence of applied magnetic fields. We analyze the role that the spin-dependent tunneling amplitudes of the QPC play in determining the charge and net magnetic moment in the dot. These effects, controllable by lateral gate voltages, may provide an alternative approach for exploring Kondo correlations, as w...
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