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Papers by Aabir Mukhopadhyay

Research paper thumbnail of Anomalous topology and synthetic flat band in multi-terminal Josephson Junctions

arXiv (Cornell University), Sep 25, 2023

Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthe... more Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthetic band topology owing to their periodic dependence on the Josephson phase bias. We demonstrate that the BdG symmetry adds a twist to this topological character, i.e, gap closing points may or may not correspond to change of Chern number, hence extending the standard paradigm for topological bands. We further show that the topology of Andreev bands depends only on the scattering matrix of the junction and is independent of the topological nature of superconductors forming the JJ hence indicating a universal behaviour of multi-terminal JJ. We also show that the chiral junction, supported by quantum Hall state at the junction region, leads to flat Andreev bands (implying absence of DC Josephson effects) that are devoid of Berry curvature ( implying absence of AC Josephson effects). Such electrically inert JJ may be useful for storage of quantum information in future quantum devices.

Research paper thumbnail of Identification of odd-frequency superconducting pairing in Josephson junctions

arXiv (Cornell University), Nov 23, 2023

Research paper thumbnail of Spontaneous fractional Josephson current in parafermion junctions

Physical review, Mar 30, 2023

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge mode... more We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, ν = 1/m, m ∈ 2Z + 1, this leads to an electrical control of either Majorana (m = 1) or parafermion (m = 1) zero modes.

Research paper thumbnail of Spontaneous fractional Josephson current from parafermions

arXiv (Cornell University), Aug 10, 2022

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge mode... more We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, ν = 1/m, m ∈ 2Z + 1, this leads to an electrical control of either Majorana (m = 1) or parafermion (m = 1) zero modes.

Research paper thumbnail of Thermal bias induced charge current in a Josephson junction: From ballistic to disordered

Physical Review B

It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scatter... more It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scattering amplitudes, which breaks the ω → −ω symmetry (where ω is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a nonzero thermal-bias induced charge current above the gap, when the junction length is of the order of coherence length of the superconductor and the corresponding response confirms to the universal sinusoidal dependence on φ 12 , where φ 12 is the superconducting phase bias. In presence of multiple scatterers in the junction region, we have numerically shown that the sign of the even-in-φ 12 part of the this response fluctuates violently from one disorder configuration to another hence averaging to vanishingly small values while the odd part tends towards the universal sinusoidal dependence on φ 12 as we approach the large disorder limit under disorder averaging.

Research paper thumbnail of Thermal signature of Majorana fermions in Josephson junction

Existence of distinctive correlation between the thermal conductance and the Josephson current ac... more Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies.

Research paper thumbnail of Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator a... more A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.

Research paper thumbnail of Thermoelectric response of Josephson junction: from ballistic to disordered

It is known that Josephson junction (JJ) hosting scattering centers with energy dependent scatter... more It is known that Josephson junction (JJ) hosting scattering centers with energy dependent scattering amplitudes which breaks the ω → −ω symmetry (where ω is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a non-zero thermoelectric response when the junction length is of the order of coherence length of the superconductor and the corresponding thermoelectric coefficient confirms to the universal sinusoidal dependence on φ12, where φ12 is the superconducting phase bias. In presence of multiple scatterers in the junction region, we have numerically shown that the sign of the even-in-φ12 part of the thermoelectric coefficient fluctuates violently from one disorder configuration to another hence averaging to vanishingly small values while the odd part tends towards the universal sinusoidal dependence on φ12 as we approach the large disorder limit...

Research paper thumbnail of Thermal signature of Majorana fermions in Josephson junction

arXiv: Mesoscale and Nanoscale Physics, 2019

Existence of distinctive correlation between the thermal conductance and the Josephson current ac... more Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies.

Research paper thumbnail of Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator a... more A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.

Research paper thumbnail of Thermal signature of the Majorana fermion in a Josephson junction

Physical Review B

Possible signatures of "Majorana end states" are discussed by combining information extracted fro... more Possible signatures of "Majorana end states" are discussed by combining information extracted from subgap Cooper pair transport and transport of heat by excited quasiparticles above the gap across a thermally biased Josephson junction setup formed out of a one-dimensional (1D) topological superconductor hosting Majorana end states. We show that the presence of Majorana end states results in two sets of testable relations: (i) the ratios between the various multiterminal thermal conductances is independent of the Josephson phase bias, and (ii) the phase independence of the ratios of "ratios of the phase derivative of multiterminal thermal conductance and the corresponding Josephson current", in a three-terminal setup. We contrast out findings with a Josephson junction setup composed of a 1D topological superconductor hosting "Andreev type end states" and show that they violate the above-mentioned relations. We also discuss how the presence of nonequilibrium noise in thermal current influences our predictions.

Research paper thumbnail of Anomalous topology and synthetic flat band in multi-terminal Josephson Junctions

arXiv (Cornell University), Sep 25, 2023

Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthe... more Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthetic band topology owing to their periodic dependence on the Josephson phase bias. We demonstrate that the BdG symmetry adds a twist to this topological character, i.e, gap closing points may or may not correspond to change of Chern number, hence extending the standard paradigm for topological bands. We further show that the topology of Andreev bands depends only on the scattering matrix of the junction and is independent of the topological nature of superconductors forming the JJ hence indicating a universal behaviour of multi-terminal JJ. We also show that the chiral junction, supported by quantum Hall state at the junction region, leads to flat Andreev bands (implying absence of DC Josephson effects) that are devoid of Berry curvature ( implying absence of AC Josephson effects). Such electrically inert JJ may be useful for storage of quantum information in future quantum devices.

Research paper thumbnail of Identification of odd-frequency superconducting pairing in Josephson junctions

arXiv (Cornell University), Nov 23, 2023

Research paper thumbnail of Spontaneous fractional Josephson current in parafermion junctions

Physical review, Mar 30, 2023

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge mode... more We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, ν = 1/m, m ∈ 2Z + 1, this leads to an electrical control of either Majorana (m = 1) or parafermion (m = 1) zero modes.

Research paper thumbnail of Spontaneous fractional Josephson current from parafermions

arXiv (Cornell University), Aug 10, 2022

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge mode... more We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, ν = 1/m, m ∈ 2Z + 1, this leads to an electrical control of either Majorana (m = 1) or parafermion (m = 1) zero modes.

Research paper thumbnail of Thermal bias induced charge current in a Josephson junction: From ballistic to disordered

Physical Review B

It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scatter... more It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scattering amplitudes, which breaks the ω → −ω symmetry (where ω is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a nonzero thermal-bias induced charge current above the gap, when the junction length is of the order of coherence length of the superconductor and the corresponding response confirms to the universal sinusoidal dependence on φ 12 , where φ 12 is the superconducting phase bias. In presence of multiple scatterers in the junction region, we have numerically shown that the sign of the even-in-φ 12 part of the this response fluctuates violently from one disorder configuration to another hence averaging to vanishingly small values while the odd part tends towards the universal sinusoidal dependence on φ 12 as we approach the large disorder limit under disorder averaging.

Research paper thumbnail of Thermal signature of Majorana fermions in Josephson junction

Existence of distinctive correlation between the thermal conductance and the Josephson current ac... more Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies.

Research paper thumbnail of Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator a... more A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.

Research paper thumbnail of Thermoelectric response of Josephson junction: from ballistic to disordered

It is known that Josephson junction (JJ) hosting scattering centers with energy dependent scatter... more It is known that Josephson junction (JJ) hosting scattering centers with energy dependent scattering amplitudes which breaks the ω → −ω symmetry (where ω is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a non-zero thermoelectric response when the junction length is of the order of coherence length of the superconductor and the corresponding thermoelectric coefficient confirms to the universal sinusoidal dependence on φ12, where φ12 is the superconducting phase bias. In presence of multiple scatterers in the junction region, we have numerically shown that the sign of the even-in-φ12 part of the thermoelectric coefficient fluctuates violently from one disorder configuration to another hence averaging to vanishingly small values while the odd part tends towards the universal sinusoidal dependence on φ12 as we approach the large disorder limit...

Research paper thumbnail of Thermal signature of Majorana fermions in Josephson junction

arXiv: Mesoscale and Nanoscale Physics, 2019

Existence of distinctive correlation between the thermal conductance and the Josephson current ac... more Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies.

Research paper thumbnail of Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator a... more A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.

Research paper thumbnail of Thermal signature of the Majorana fermion in a Josephson junction

Physical Review B

Possible signatures of "Majorana end states" are discussed by combining information extracted fro... more Possible signatures of "Majorana end states" are discussed by combining information extracted from subgap Cooper pair transport and transport of heat by excited quasiparticles above the gap across a thermally biased Josephson junction setup formed out of a one-dimensional (1D) topological superconductor hosting Majorana end states. We show that the presence of Majorana end states results in two sets of testable relations: (i) the ratios between the various multiterminal thermal conductances is independent of the Josephson phase bias, and (ii) the phase independence of the ratios of "ratios of the phase derivative of multiterminal thermal conductance and the corresponding Josephson current", in a three-terminal setup. We contrast out findings with a Josephson junction setup composed of a 1D topological superconductor hosting "Andreev type end states" and show that they violate the above-mentioned relations. We also discuss how the presence of nonequilibrium noise in thermal current influences our predictions.