Modeling unit and model architecture are two key factors of Recurrent Neural Network Transducer (RNN-T) in end-to-end speech recognition. To improve the performance of RNN-T for Mandarin speech recognition task, a novel transformer transducer with the combination architecture of self-attention transformer and RNN is proposed. And then the choice of different modeling units for transformer transducer is explored. In addition, we present a new mix-bandwidth training method to obtain a general model that is able to accurately recognize Mandarin speech with different sampling rates simultaneously. All of our experiments are conducted on about 12,000 hours of Mandarin speech with sampling rate in 8kHz and 16kHz. Experimental results show that Mandarin transformer transducer using syllable with tone achieves the best performance. It yields an average of 14.4% and 44.1% relative Word Error Rate (WER) reduction when compared with the models using syllable initial/final with tone and Chinese character, respectively. Also, it outperforms the model based on syllable initial/final with tone with an average of 13.5% relative Character Error Rate (CER) reduction.