This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, and studies the Zeeman effects on the d-wave superconducting gap and th...This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, and studies the Zeeman effects on the d-wave superconducting gap and thermodynamic potential. The Josephson currents in the d-wave superconductor（S）/insulating layer（I）/d-wave S junctions are calculated as a function of the temperature, exchange field, and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss. It is found that the Josephson critical currents in d-wave S/d-wave S junction to a great extent depend on the relative orientation of the effective exchange field of the two S electrodes, and the crystal orientation of the d-wave S. The exchange field under certain conditions can enhance the Josephson critical current in a d-wave S/I/d-wave S junction.展开更多
We consider a highly unconventional superconducting state with chiral d-wave symmetry in doped graphene under strain with the Gutzwiller–RVB method in the momentum space. It is shown that flat bands emerge in the nor...We consider a highly unconventional superconducting state with chiral d-wave symmetry in doped graphene under strain with the Gutzwiller–RVB method in the momentum space. It is shown that flat bands emerge in the normal state for reasonable strain. As a result, the superconducting critical temperature is found to be linearly proportional to the strength of the electron–electron interaction. Furthermore, the chiral d-wave superconducting state is shown with coexistence of the charge density wave and the pair density wave. There are different coexisting states with those orders under different doping levels.展开更多
This paper applies the Bogoliubov-de Gennes equation and the Blonder-Tinkham-Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor jun...This paper applies the Bogoliubov-de Gennes equation and the Blonder-Tinkham-Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent Is. We find that （i） a three-humped structure appears at a nearly critical supercurrent Is and z ≈ 0.5 for the normal metal/insulator/metal/dx^2＋y^2-wave superconductor junction; （ii） the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/dxy-wave superconductor junction; （iii） the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent Is.展开更多
We have studied the quasiparticle transport in quantum-wire /ferromagnetic-insulator/d wave super- conductor Junction （q/FI/d） in the framework of the Blonder-Tinkham-Klapwijk model. We calculate the tunneling condu...We have studied the quasiparticle transport in quantum-wire /ferromagnetic-insulator/d wave super- conductor Junction （q/FI/d） in the framework of the Blonder-Tinkham-Klapwijk model. We calculate the tunneling conductance in q/FI/d as a function of the bias voltage at zero temperature and finite temperature based on Bogoliubov- de Gennes equations. Different from the case in normal-metal/insulator/d wave superconductor Junctions, the zero-bias conductance peaks vanish for the single-mode case. The tunneling conductance spectra depend on the magnitude of the exchange interaction at the ferromagnetic-insulator.展开更多
Motivated by recent advances in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model...Motivated by recent advances in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to have three interesting superfluid phases: atomic, molecular, and atomic–molecular. In great contrast to what was previously known about the p-wave case, the atomic superfluid is found to be momentum-independent for the d-wave case discussed here. The Bogoliubov spectra above each superfluid phase are obtained both analytically and numerically.展开更多
Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional...Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting.We show that due to the interplay of Rashba spin-orbit coupling and Zeeman splitting and d-wave pairing,the current-phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned.In particular,anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken,which can be realized by tuning some relevant parameters of the system,including the relative orientations and the strengths of the Zeeman field and the spin-orbit field in the bridge region,the relative orientations of the a axes in two superconductor leads,or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads.We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.展开更多
Solving the Bogoliubov-de Gennes equation, the energy levels of bound statesare obtained in the ferromagnetic superconductor. The Josephson currents in a ferromagneticsuperconductor/Insulator/d-wave superconductor jun...Solving the Bogoliubov-de Gennes equation, the energy levels of bound statesare obtained in the ferromagnetic superconductor. The Josephson currents in a ferromagneticsuperconductor/Insulator/d-wave superconductor junction are calculated as a function of the exchangefield, temperature, and insulating barrier strength. It is found that the Josephson criticalcurrent is always suppressed by the presence of exchange Geld h and depends on crystalline axisorientation of d-wave superconductor.展开更多
The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari...The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 151-154, 2012, has been removed from this site.展开更多
Track finding is a complex optimization problem,originally introduced in particle physics for the reconstruction of the trajectories of particles.A track is typically composed of several consecutive segments,which tog...Track finding is a complex optimization problem,originally introduced in particle physics for the reconstruction of the trajectories of particles.A track is typically composed of several consecutive segments,which together form a smooth curve without any bifurcations.In this paper,we investigate various modeling approaches to assess their effectiveness and impact when applied to track finding,using both quantum and classical methods.We present implementations of three classical models using CPLEX,two quantum models on actual D-Wave quantum computers,and one quantummodel on a D-Wave simulator.The results show that,while CPLEX provides better results than D-Wave on small instances,D-Wave is able to propose solutions in shorter computation times for large instances,although the gap with the optimal solution tends to increase.To the best of our knowledge,this is the first numerical study comparing a non-quantum approach based on classical algorithms(Simplex and Branch and Bound)used in commercial software with a quantum approach offered by D-Wave.The results do not show the quantum supremacy typically expected,but they do demonstrate that quantum solutions can be competitive with classical approaches,and even more efficient than some classical modeling and solving methods.展开更多
Quantum computing is generally considered non-threatening to symmetric ciphers.Quantum attacks on symmetric ciphers require a thorough analysis of their internal structures,posing considerable difficulties and challen...Quantum computing is generally considered non-threatening to symmetric ciphers.Quantum attacks on symmetric ciphers require a thorough analysis of their internal structures,posing considerable difficulties and challenges.As of 2023,Google’s quantum supremacy chip,Sycamore,is still incapable of cryptanalysis.Leveraging D-Wave’s quantum annealing exploits the unique quantum tunneling effect,providing an edge in solving combinatorial optimization problems.It can be regarded as a class of artificial intelligence algorithm that can achieve global optimization.We propose a quantum heuristic symmetric cipher attack algorithm for substitution-permutation network(SPN)symmetric ciphers,which transforms the plaintext-ciphertext propagation rules within SPN structure into the problem of solving a constrained quadratic model(CQM).A novel reduction algorithm is employed to eliminate redundant constraint conditions.The D-Wave Advantage quantum computer is used to recover the encryption sub-keys.Using the quantum approximate optimization algorithm,IBM Q Experience can only recover two rounds of the Heys Cipher sub-key,whereas D-Wave Advantage achieves complete key recovery,validating its potential in quantum symmetric cipher attacks.展开更多
Integer factorization,the core of the Rivest−Shamir−Adleman(RSA)attack,is an exciting but formidable challenge.As of this year,a group of researchers’latest quantum supremacy chip remains unavailable for cryptanalysi...Integer factorization,the core of the Rivest−Shamir−Adleman(RSA)attack,is an exciting but formidable challenge.As of this year,a group of researchers’latest quantum supremacy chip remains unavailable for cryptanalysis.Quantum annealing(QA)has a unique quantum tunneling advantage,which can escape local extremum in the exponential solution space,finding the global optimal solution with a higher probability.Consequently,we consider it an effective method for attacking cryptography.According to Origin Quantum Computing,QA computers are able to factor numbers several orders of magnitude larger than universal quantum computers.We try to transform the integer factorization problem in RSA attacks into a combinatorial optimization problem by using the QA algorithm of D-Wave quantum computer,and attack RSA-2048 which is composed of a class of special integers.The experiment factored this class of integers of size 22048,N=p×q.As an example,the article gives the results of 10 RSA-2048 attacks in the appendix.This marks the first successful factorization of RSA-2048 by D-Wave quantum computer,regardless of employing mathematical or quantum techniques,despite dealing with special integers,exceeding 21061−1 of California State University.This experiment verifies that the QA algorithm based on D-Wave is an effective method to attack RSA.展开更多
Integer factorization (IFP), also called prime factorization, is an important problem in number theory, cryptography, and quantum computation. Factoring large integers to attack the RSA cryptosystem is intractable for...Integer factorization (IFP), also called prime factorization, is an important problem in number theory, cryptography, and quantum computation. Factoring large integers to attack the RSA cryptosystem is intractable for powerful supercomputers, let alone classical computers. In 1994, Shor [1]presented an algorithm that potentially enabled a quantum computer to find prime factors in polynomial time.展开更多
In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Un...In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.展开更多
This work is the first to determine that a real quantum computer(including generalized and specialized)can decipher million-scale RSA relying solely on quantum algorithms,showing the real attack potential of D-Wave ma...This work is the first to determine that a real quantum computer(including generalized and specialized)can decipher million-scale RSA relying solely on quantum algorithms,showing the real attack potential of D-Wave machines.The influence of different column widths on RSA factorization results is studied on the basis of a multiplication table,and the optimal column method is determined by traversal experiments.The traversal experiment of integer factorization within 10000 shows that the local field and coupling coefficients are 75%–93%lower than the research of Shanghai University in 2020 and more than 85%lower than that of Purdue University in 2018.Extremely low Ising model parameters are crucial to reducing the hardware requirements,prompting factoring 1245407 on the D-Wave 2000Q real machine.D-Wave advantage already has more than 5000 qubits and will be expanded to 7000 qubits during 2023–2024,with remarkable improvements in decoherence and topology.This machine is expected to promote the solution of large-scale combinatorial optimization problems.One of the contributions of this paper is the discussion of the long-term impact of D-Wave on the development of post-quantum cryptography standards.展开更多
We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnet...We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.展开更多
基金supported by the Natural Science Foundation of Education Bureau of Jiangsu Province of China (Grant No 05KJB140008)the '333' Project Funds of Jiangsu Province of China
文摘This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, and studies the Zeeman effects on the d-wave superconducting gap and thermodynamic potential. The Josephson currents in the d-wave superconductor（S）/insulating layer（I）/d-wave S junctions are calculated as a function of the temperature, exchange field, and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss. It is found that the Josephson critical currents in d-wave S/d-wave S junction to a great extent depend on the relative orientation of the effective exchange field of the two S electrodes, and the crystal orientation of the d-wave S. The exchange field under certain conditions can enhance the Josephson critical current in a d-wave S/I/d-wave S junction.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11804213 and 11605109)
文摘We consider a highly unconventional superconducting state with chiral d-wave symmetry in doped graphene under strain with the Gutzwiller–RVB method in the momentum space. It is shown that flat bands emerge in the normal state for reasonable strain. As a result, the superconducting critical temperature is found to be linearly proportional to the strength of the electron–electron interaction. Furthermore, the chiral d-wave superconducting state is shown with coexistence of the charge density wave and the pair density wave. There are different coexisting states with those orders under different doping levels.
基金Project supported by the Natural Science Foundation of Jiangsu Provincial Education Commission of China (Grant No06KJB140009)
文摘This paper applies the Bogoliubov-de Gennes equation and the Blonder-Tinkham-Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent Is. We find that （i） a three-humped structure appears at a nearly critical supercurrent Is and z ≈ 0.5 for the normal metal/insulator/metal/dx^2＋y^2-wave superconductor junction; （ii） the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/dxy-wave superconductor junction; （iii） the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent Is.
基金The project supported by the Natural Science Foundation of the Education Committee of Jiangsu Province of China under Grant No.06KJB140009
文摘We have studied the quasiparticle transport in quantum-wire /ferromagnetic-insulator/d wave super- conductor Junction （q/FI/d） in the framework of the Blonder-Tinkham-Klapwijk model. We calculate the tunneling conductance in q/FI/d as a function of the bias voltage at zero temperature and finite temperature based on Bogoliubov- de Gennes equations. Different from the case in normal-metal/insulator/d wave superconductor Junctions, the zero-bias conductance peaks vanish for the single-mode case. The tunneling conductance spectra depend on the magnitude of the exchange interaction at the ferromagnetic-insulator.
基金supported by the AFOSR (Grant No. FA9550-16-1-0006)the MURI-ARO (Grant No. W911NF17-1-0323)+2 种基金the National Natural Science Foundation of China (Grant Nos. 11904228, 11804221, and 11655002)the National Postdoctoral Program for Innovative Talents of China (Grant No. BX201700156)the Science and Technology Commission of Shanghai Municipality,China (Grant No. 16DZ2260200)。
文摘Motivated by recent advances in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to have three interesting superfluid phases: atomic, molecular, and atomic–molecular. In great contrast to what was previously known about the p-wave case, the atomic superfluid is found to be momentum-independent for the d-wave case discussed here. The Bogoliubov spectra above each superfluid phase are obtained both analytically and numerically.
文摘Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting.We show that due to the interplay of Rashba spin-orbit coupling and Zeeman splitting and d-wave pairing,the current-phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned.In particular,anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken,which can be realized by tuning some relevant parameters of the system,including the relative orientations and the strengths of the Zeeman field and the spin-orbit field in the bridge region,the relative orientations of the a axes in two superconductor leads,or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads.We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.
文摘Solving the Bogoliubov-de Gennes equation, the energy levels of bound statesare obtained in the ferromagnetic superconductor. The Josephson currents in a ferromagneticsuperconductor/Insulator/d-wave superconductor junction are calculated as a function of the exchangefield, temperature, and insulating barrier strength. It is found that the Josephson criticalcurrent is always suppressed by the presence of exchange Geld h and depends on crystalline axisorientation of d-wave superconductor.
文摘The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 151-154, 2012, has been removed from this site.
文摘Track finding is a complex optimization problem,originally introduced in particle physics for the reconstruction of the trajectories of particles.A track is typically composed of several consecutive segments,which together form a smooth curve without any bifurcations.In this paper,we investigate various modeling approaches to assess their effectiveness and impact when applied to track finding,using both quantum and classical methods.We present implementations of three classical models using CPLEX,two quantum models on actual D-Wave quantum computers,and one quantummodel on a D-Wave simulator.The results show that,while CPLEX provides better results than D-Wave on small instances,D-Wave is able to propose solutions in shorter computation times for large instances,although the gap with the optimal solution tends to increase.To the best of our knowledge,this is the first numerical study comparing a non-quantum approach based on classical algorithms(Simplex and Branch and Bound)used in commercial software with a quantum approach offered by D-Wave.The results do not show the quantum supremacy typically expected,but they do demonstrate that quantum solutions can be competitive with classical approaches,and even more efficient than some classical modeling and solving methods.
文摘Quantum computing is generally considered non-threatening to symmetric ciphers.Quantum attacks on symmetric ciphers require a thorough analysis of their internal structures,posing considerable difficulties and challenges.As of 2023,Google’s quantum supremacy chip,Sycamore,is still incapable of cryptanalysis.Leveraging D-Wave’s quantum annealing exploits the unique quantum tunneling effect,providing an edge in solving combinatorial optimization problems.It can be regarded as a class of artificial intelligence algorithm that can achieve global optimization.We propose a quantum heuristic symmetric cipher attack algorithm for substitution-permutation network(SPN)symmetric ciphers,which transforms the plaintext-ciphertext propagation rules within SPN structure into the problem of solving a constrained quadratic model(CQM).A novel reduction algorithm is employed to eliminate redundant constraint conditions.The D-Wave Advantage quantum computer is used to recover the encryption sub-keys.Using the quantum approximate optimization algorithm,IBM Q Experience can only recover two rounds of the Heys Cipher sub-key,whereas D-Wave Advantage achieves complete key recovery,validating its potential in quantum symmetric cipher attacks.
文摘Integer factorization,the core of the Rivest−Shamir−Adleman(RSA)attack,is an exciting but formidable challenge.As of this year,a group of researchers’latest quantum supremacy chip remains unavailable for cryptanalysis.Quantum annealing(QA)has a unique quantum tunneling advantage,which can escape local extremum in the exponential solution space,finding the global optimal solution with a higher probability.Consequently,we consider it an effective method for attacking cryptography.According to Origin Quantum Computing,QA computers are able to factor numbers several orders of magnitude larger than universal quantum computers.We try to transform the integer factorization problem in RSA attacks into a combinatorial optimization problem by using the QA algorithm of D-Wave quantum computer,and attack RSA-2048 which is composed of a class of special integers.The experiment factored this class of integers of size 22048,N=p×q.As an example,the article gives the results of 10 RSA-2048 attacks in the appendix.This marks the first successful factorization of RSA-2048 by D-Wave quantum computer,regardless of employing mathematical or quantum techniques,despite dealing with special integers,exceeding 21061−1 of California State University.This experiment verifies that the QA algorithm based on D-Wave is an effective method to attack RSA.
文摘Integer factorization (IFP), also called prime factorization, is an important problem in number theory, cryptography, and quantum computation. Factoring large integers to attack the RSA cryptosystem is intractable for powerful supercomputers, let alone classical computers. In 1994, Shor [1]presented an algorithm that potentially enabled a quantum computer to find prime factors in polynomial time.
基金partially supported by the NSF grant DMS-0710831
文摘In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.
基金supported by the Special Zone Project of National Defense Innovation.
文摘This work is the first to determine that a real quantum computer(including generalized and specialized)can decipher million-scale RSA relying solely on quantum algorithms,showing the real attack potential of D-Wave machines.The influence of different column widths on RSA factorization results is studied on the basis of a multiplication table,and the optimal column method is determined by traversal experiments.The traversal experiment of integer factorization within 10000 shows that the local field and coupling coefficients are 75%–93%lower than the research of Shanghai University in 2020 and more than 85%lower than that of Purdue University in 2018.Extremely low Ising model parameters are crucial to reducing the hardware requirements,prompting factoring 1245407 on the D-Wave 2000Q real machine.D-Wave advantage already has more than 5000 qubits and will be expanded to 7000 qubits during 2023–2024,with remarkable improvements in decoherence and topology.This machine is expected to promote the solution of large-scale combinatorial optimization problems.One of the contributions of this paper is the discussion of the long-term impact of D-Wave on the development of post-quantum cryptography standards.
基金The author thanks Professor D.Y. Xing for useful discussion. This work is supported by the Jiangsu Planned Projects for Postdoctoral Research Funds, the Natural Science Foundation of Education Bureau of Jiangsu Province of China (Grant No. 05KJB 14008).
文摘We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.
